Event-triggered wireless resource optimization method and system for cyber-physical systems

Abstract

The embodiment of the application relates to the technical field of information physical system, in particular to an event-triggered information physical system wireless resource optimization method and system, the method comprises the following steps: obtaining the corresponding relationship between a packet loss rate and a transmission power of a sending end and a selection probability of a cellular network based on a bit error rate; introducing an event triggering mechanism at a controller end, optimizing the data transmission times between the controller and an actuator; analyzing the stability of a closed loop system after the event triggering mechanism is introduced, and obtaining a constraint condition for stabilizing the closed loop system; taking the constraint condition as a constraint, constructing a multi-objective optimization function; solving the multi-objective optimization function by using a genetic algorithm, and obtaining an optimal triggering coefficient, an optimal transmission power and an optimal cellular network selection probability under the premise of guaranteeing system performance. The optimization method provided by the application can balance the communication energy saving, system performance and data transmission cost of a unit-level CPS in a heterogeneous wireless network.

Description

TECHNICAL FIELD

[0001] Embodiments of the present application relate to the technical field of information physical system, and particularly relate to an event-triggered information physical system wireless resource optimization method and system. BACKGROUND

[0002] Cyber-Physical Systems (CPS) as an integrated computing, network and physical process engineering system emerges, which enables seamless interaction between network services and physical components. CPS is based on computing, sensing, communication and embedded system technology, and is a natural product of the rapid development of Information and Communications Technology (ICT) in recent decades, which will change the way people interact with the physical world. CPS is composed of a large number of sensors, shared communication networks, control decision units and actuator units, and the above basic components are connected by a communication network to form a feedback control loop mechanism.

[0003] In the traditional control system, the controlled device is controlled and monitored through a network with sufficient communication resources, so that the expected control and state estimation actions are implemented in a Time-Triggered (TT) manner. TT is considered more suitable for hard real-time systems and safety-critical systems due to its predictability and ease of implementation. However, the TT-based control and estimation method often leads to overuse of available computing and communication resources, and considering that embedded system components are usually powered by batteries, data communication is usually energy-consuming. At present, CPS mostly transmits information through a shared wireless communication network, which has limited network bandwidth, so the design of controllers and estimators should fully consider the resource constraints caused by limited bandwidth and limited computing and processing capabilities of battery-powered system components.

[0004] CPS transmits information through a shared communication network. Compared with wired networks, wireless communication networks usually have problems such as packet loss, network congestion, and delay, so the real-time and reliability of CPS are no longer guaranteed, and the system performance is greatly affected. As is known to all, the more control instructions sent by the controller, the better the system performance, but a large number of control instructions will occupy too many computing resources and communication resources, and accelerate the energy consumption of the communication node. This shows that in the CPS based on wireless network communication, the improvement of system performance and the effective use of resources are contradictory, which poses a severe challenge to the design of sensors and controllers. Therefore, it is of great theoretical and practical significance to study the balance between the efficient use of computing and communication resources and the system performance in CPS. SUMMARY

[0005] The embodiment of the present application provides a kind of event trigger-based information physical system wireless resource optimization method and system, realize the balance between system performance, communication energy saving and data transmission cost.

[0006] To solve the above technical problems, the embodiment of the present application provides an event trigger-based information physical system wireless resource optimization method, comprising the following steps: based on the bit error rate, the corresponding relationship between the packet loss rate of the information physical system and the transmission power of the sending end, and the selection probability of the cellular network is obtained;Introduce an event triggering mechanism at the controller end, optimize the number of data transmissions between the controller and the actuator;The stability of the closed-loop system after introducing the event triggering mechanism is analyzed, and the constraint condition for stabilizing the closed-loop system is obtained;The constraint condition is taken as a constraint, and the system decay rate, the transmission power of the sending end, the event triggering coefficient and the total cost of data transmission are taken as the objective function to construct a multi-objective optimization function;Solve the multi-objective optimization function by using genetic algorithm, and obtain the optimal triggering coefficient, the optimal transmission power and the optimal cellular network selection probability under the premise of ensuring system performance.

[0007] In some example embodiments, based on the bit error rate, the corresponding relationship between the packet loss rate of the information physical system and the transmission power of the sending end, and the selection probability of the cellular network is obtained, comprising: based on the data error of the wireless channel, the bit error rate is obtained;The data error is obtained by inter-symbol interference and multipath interference in the wireless channel;Based on the bit error rate and the packet loss rate when the cellular network sends data and the packet loss rate when the WiFi network sends data, the packet loss rate of the information physical system is obtained;Based on the probability of successful information transmission under the heterogeneous wireless communication mode and the packet loss rate when the cellular network sends data and the packet loss rate when the WiFi network sends data, the corresponding relationship between the packet loss rate of the information physical system and the transmission power of the sending end and the selection probability of the cellular network is obtained.

[0008] In some example embodiments, the bit error rate is shown in formula (1):

[0009] SER≈e -νσ (1)

[0010] Wherein, SER represents the bit error rate;ν is a coefficient related to the wireless network parameters of the noise, attenuation, inter-symbol interference and multiple access interference of the transmission channel;σ is the transmission power of the sending end;The bit error rates of the cellular network and the WiFi network are obtained respectively by formula (1), and the bit error rates of the cellular network and the WiFi network are represented as Wherein, ν1 and ν2 represent the coefficients related to the parameters of the cellular network and the WiFi network respectively, and σ1 and σ2 represent the transmission power of the cellular network and the WiFi network respectively;The packet loss rate of the information physical system is shown in formula (2):

[0011]

[0012] Where q is the packet loss rate of the cyber-physical system; p1 is the probability of the information transmission result occurring when data packets are sent via cellular base stations; p2 is the probability of the information transmission result occurring when data packets are sent via WiFi; and α is the selection probability of the cellular network.

[0013] In some exemplary embodiments, an event triggering mechanism is introduced at the controller end to optimize the number of data transmissions between the controller and the actuator. This includes: designing an event-triggered intelligent controller in the closed-loop system and optimizing the number of data transmissions between the controller and the actuator based on triggering rules.

[0014] In some exemplary embodiments, the triggering rules are as shown in formula (3):

[0015]

[0016] Where k is the current time; k s It is the system number The moment of the second closed loop; The trigger coefficient is a positive real number; δV(x(k) s )) is the trigger threshold; It is the number of steps the actuator performs for zero-order hold; It is the number of steps that the event triggers take to predict the future state of the system.

[0017] In some exemplary embodiments, the stability of the closed-loop system after the introduction of the event triggering mechanism is analyzed, including: verifying that the Lyapunov function of the cyber-physical system decreases between two adjacent closed-loop times, and analyzing the expected operation of the system between two adjacent closed-loop times.

[0018] In some exemplary embodiments, a multi-objective optimization function is constructed, including: transforming the balance problem among communication energy saving, system performance, and data transmission cost into a multi-objective optimization problem as shown in formula (4):

[0019]

[0020]

[0021]

[0022] 0 < δ < ξ

[0023] 0<ξ≤ξ0

[0024] 0≤σ1≤σ 10

[0025] 0≤σ2≤σ 20

[0026] 0≤α≤1

[0027] q1<q2 (4)

[0028] where ξ = pδ / (1-qγ) is the attenuation rate of the closed-loop system; ξ0<1 is the pre-given upper bound of the system attenuation rate; is the communication packet loss rate; γ>1 is related to the divergence rate of the open-loop system; σ1is the transmission power of the cellular network; σ 10 is the pre-given upper bound of σ1; σ2is the transmission power of the WiFi network; σ 20 is the pre-given upper bound of σ2; δ is the event-triggering coefficient; α is the probability of using the cellular network to transmit data under the heterogeneous wireless communication mode; f is the total cost of using the heterogeneous wireless communication network to transmit data.

[0029] In some example embodiments, after constructing the multi-objective optimization function, and before solving the multi-objective optimization function by using the genetic algorithm, further comprising: converting the multiple objective functions in formula (4) into a single objective function by using the weighting method in the optimization algorithm, as shown in formula (5):

[0030]

[0031] where C = [c1c2c3c4c5] T is a non-negative weight vector, The size of the weight coefficient determines the importance of each objective function; formula (4) is rewritten as formula (6):

[0032]

[0033]

[0034]

[0035] 0<δ<ξ

[0036] 0<ξ≤ξ0

[0037] 0≤σ1≤σ 10

[0038] 0≤σ2≤σ 20

[0039] 0≤α≤1

[0040] q1<q2 (6)

[0041] where the system attenuation rate is ξ = pδ / (1-qγ), and the system packet loss rate is

[0042] In some example embodiments, the genetic algorithm is used to solve the multi-objective optimization function, including: using the genetic algorithm to solve a nonlinear programming problem of the multi-objective optimization function to obtain optimal σ1, σ2, δ, α solutions under weight coefficients c1, c2, c3, c4, and c5; maximizing the triggering coefficient δ to reduce the number of sending of the control signal at the controller end, minimizing the transmission power σ1, σ2 to reduce the working energy consumption of the communication node, and minimizing the cellular network selection probability α to reduce the cost of data transmission of the system, and compromising between the communication energy saving, the system performance, and the data transmission cost to achieve a balance among the communication energy saving, the system performance, and the data transmission cost.

[0043] In a second aspect, the embodiments of the present application also provide an event-triggered information physical system wireless resource optimization system, including an optimization processing module, a multi-objective optimization function construction module, and a calculation module connected in sequence; the optimization processing module is configured to obtain a corresponding relationship between a packet loss rate of the information physical system and a transmission power of a sending end and a selection probability of a cellular network based on a bit error rate, and introduce an event triggering mechanism at a controller end to optimize a data transmission number between the controller and an actuator; the multi-objective optimization function construction module is configured to analyze stability of a closed loop system after the event triggering mechanism is introduced, and obtain a constraint condition for stabilizing the closed loop system; and the constraint condition is taken as a constraint, and a system decay rate, the transmission power of the sending end, an event triggering coefficient, and a total data transmission cost are taken as objective functions to construct a multi-objective optimization function; and the calculation module is configured to use a genetic algorithm to solve the multi-objective optimization function to obtain optimal triggering coefficients, optimal transmission powers, and optimal cellular network selection probabilities under a premise of ensuring system performance.

[0044] The technical scheme provided by the embodiments of the present application has at least the following advantages:

[0045] The embodiments of the present application provide an event-triggered information physical system wireless resource optimization method and system, the method including the following steps: obtaining a corresponding relationship between a packet loss rate of an information physical system and a transmission power of a sending end and a selection probability of a cellular network based on a bit error rate; introducing an event triggering mechanism at a controller end to optimize a data transmission number between the controller and an actuator; analyzing stability of a closed loop system after the event triggering mechanism is introduced, and obtaining a constraint condition for stabilizing the closed loop system; taking the constraint condition as a constraint, and taking a system decay rate, the transmission power of the sending end, an event triggering coefficient, and a total data transmission cost as objective functions to construct a multi-objective optimization function; using a genetic algorithm to solve the multi-objective optimization function to obtain optimal triggering coefficients, optimal transmission powers, and optimal cellular network selection probabilities under a premise of ensuring system performance.

[0046] The application studies the balance between communication energy saving, system performance and data transmission cost of unit-level CPS in heterogeneous wireless networks and proposes an event-triggered information physical system wireless resource optimization method. First, according to the bit error rate, the packet loss rate is related to the transmission power of the sending end and the selection probability of the cellular network. It is known that the packet loss rate is inversely proportional to the transmission power of the sending end and the selection probability of the cellular network, that is, the system performance and the communication energy saving are contradictory to each other, and the data transmission cost is also contradictory to each other. Then, the event trigger is introduced at the controller end to reduce the data transmission times between the controller and the actuator, saving battery energy, network resources and computing resources. Next, it is proved that the closed-loop system still maintains overall stability after introducing the event trigger mechanism, and the constraint condition for making the closed-loop system stable is obtained. These constraint conditions are used as constraints, and the system decay rate, the transmission power of the sending end, the event trigger coefficient and the total data transmission cost are used as objective functions to construct a multi-objective optimization function. The genetic algorithm is used to solve the multi-objective optimization function to obtain the optimal trigger coefficient, the optimal transmission power and the optimal cellular network selection probability under the premise of ensuring system performance. Finally, the numerical simulation verifies that the event-triggered information physical system wireless resource optimization method provided by the application can balance the system performance, communication energy saving and data transmission cost. BRIEF DESCRIPTION OF DRAWINGS

[0047] One or more embodiments are illustrated by way of example in the figures that are part of this disclosure and which are illustrative, but not restrictive, of the embodiments, unless otherwise specified, the drawings in the figures do not constitute a proportional limit.

[0048] Figure 1 A flowchart of an event-triggered information physical system wireless resource optimization method provided by an embodiment of the application is shown in the figure.

[0049] Figure 2 A CPS core concept diagram provided by an embodiment of the application is shown in the figure.

[0050] Figure 3 A feedback loop mechanism diagram provided by an embodiment of the application is shown in the figure.

[0051] Figure 4 A unit-level CPS diagram in a heterogeneous wireless network provided by an embodiment of the application is shown in the figure.

[0052] Figure 5 A smart controller design diagram provided by an embodiment of the application is shown in the figure.

[0053] Figure 6 A timing diagram between two adjacent closed loops of CPS provided by an embodiment of the application is shown in the figure.

[0054] Figure 7The mobile device provided by an embodiment of the present application is located at The iterative process and the optimal solution of GA;

[0055] Figure 8 The mobile device provided by an embodiment of the present application is located at The iterative process and the optimal solution of GA;

[0056] Figure 9 The CPS simulation model based on intelligent sensors provided by an embodiment of the present application is shown in the figure;

[0057] Figure 10 The controller simulation model provided by an embodiment of the present application is shown in the figure;

[0058] Figure 11 The mobile device simulation model based on intelligent sensors provided by an embodiment of the present application is shown in the figure;

[0059] Figure 12 The parameter configuration of the discrete state space provided by an embodiment of the present application is shown in the figure;

[0060] Figure 13 The TT simulation model provided by an embodiment of the present application is shown in the figure;

[0061] Figure 14 The parameter configuration of the Bernoulli binary sequence generator provided by an embodiment of the present application is shown in the figure;

[0062] Figure 15 The ET simulation model provided by an embodiment of the present application is shown in the figure;

[0063] Figure 16 The mobile device provided by an embodiment of the present application is located at The system state trajectory comparison under two kinds of controller designs when the mobile device is located at

[0064] Figure 17 The mobile device provided by an embodiment of the present application is located at The communication node working condition comparison under two kinds of controller designs when the mobile device is located at

[0065] Figure 18 The mobile device provided by an embodiment of the present application is located at The system state trajectory comparison under two kinds of controller designs when the mobile device is located at

[0066] Figure 19 The mobile device provided by an embodiment of the present application is located at The communication node working condition comparison under two kinds of controller designs when the mobile device is located at

[0067] Figure 20A structure schematic diagram of an event-triggered information physical system wireless resource optimization system provided by an embodiment of the present application. DETAILED DESCRIPTION

[0068] As known from the background, in a CPS based on wireless network communication, the improvement of system performance and the effective use of resources are contradictory to each other, which poses a severe challenge to the design of sensors and controllers, and therefore, it is of important theoretical and practical significance to study the balance between the efficient use of computing and communication resources and the system performance in a CPS.

[0069] For a wireless sensing and control system, transmission energy usually accounts for a dominant part of the total energy cost, and therefore, it is necessary to carefully allocate transmission power to alleviate the battery limit. Power allocation (also referred to as power control) is a hot research topic in recent years. For example, a related technology studies the transmission power control problem in a resource-limited wireless sensor network, uses a resource-efficient algorithm based on a minimum-maximum model control predictor to optimally allocate power to all channels, and the design can easily implement a robust control law on a commercial sensor platform with extremely limited computing and storage resources. A related technology proposes a closed-loop power control design based on an adaptive quantization / reconstruction step rule, which shows better performance than a traditional fixed power control algorithm. A related technology proposes a power control algorithm for a wireless sensor network, specifically, one is based on a Markov chain described multiplication increase and decrease power control, and the other is based on average packet error rate power control. A related technology proposes a new and practical distributed active power control technology based on quantitative feedback theory for IEEE 802.15.4 wireless sensor networks. A related technology considers a state estimation sensor power allocation problem with energy constraints. Due to the limited available communication energy, the sensor must decide whether to send its data to a remote estimator. A related technology constructs an effective sensor data scheduling scheme to minimize the estimation error and meet the energy constraints. Another related technology considers the periodic sensor transmission power allocation problem with average energy constraints, and studies the optimal sensor power scheduling to minimize the average error covariance.

[0070] In addition, other researches not only consider the energy consumption constraint, but also take into account other communication constraints, such as delay, bandwidth, interference, etc. One related art researches the optimal power control, rate adaptation and scheduling problem of sensor nodes in a wireless networked control system to provide maximum adaptability while meeting the requirements of packet generation period, transmission delay, reliability and energy. One related art first proposes a design framework of a heuristic scheduling algorithm, and further proposes an optimal polynomial time algorithm for the power control and rate adaptation problem, which minimizes the time required for concurrent transmission of sensor nodes while meeting the requirements of each sensor node, and the performance of the algorithm is close to the optimal solution. One related art researches the control task scheduling problem based on a shared wireless communication medium, and in order to avoid interference, a centralized scheduler decides which control task to access the channel at each time according to the random wireless channel conditions experienced by the system. One related art proposes the problem of designing a channel-aware scheduling and transmit power allocation mechanism, in which the channel-aware scheduling mechanism schedules control tasks in favorable channel conditions to prevent control tasks from being scheduled in unfavorable conditions. The above mechanisms guarantee that all control tasks have a Lyapunov-like performance under channel conditions, while minimizing the total power consumption. One related art researches network control of a set of battery-powered systems with severely limited communication capacity and power resources, and proposes a collaborative design framework for communication scheduling, transmit power allocation and stable control. By effectively allocating communication channels and appropriately allocating transmit power, the system is stabilized, the energy consumption is within the energy budget, and the channel allocation ensures that all devices can access the network when needed, and the power allocation ensures the expected rate of successful packet transmission for each channel. One related art considers the power allocation and stabilization of linear devices under a wireless fading channel, and derives a transmit power allocation method that can achieve linear quadratic regulator (LQR) control at the minimum energy cost. One related art proposes a simple method for handling power control in wireless ad hoc networks, which has good performance in terms of throughput, delay and energy consumption. The above researches propose various solutions to ensure the performance of the control system under the premise of energy saving, but few solutions combine ET and power control, so the results obtained have a certain conservatism.

[0071] In a related art, how to reduce the communication requirement of networked control systems is studied, the schedulability of periodic tasks is considered from a new perspective of real-time control system performance optimization, and the maximum allowable time is obtained to ensure the stability of system performance. However, the method used therein results in inherent periodic transmission. In recent years, event-triggered technology in control design has received more and more attention, which advocates that only when some functions of the system state exceed the threshold can the event trigger be driven. Event triggering provides an effective method to determine when to execute the sampling action, and it ensures that only the state signals that are really "necessary" are sent to the controller, so the number of state signals transmitted is relatively small.

[0072] Compared with the traditional periodic sampling method, the event-triggered sampling method has the following advantages: 1) it is more essential to the behavior of human beings as a controller; 2) it reduces the release time of the sensor and lightens the network communication burden; 3) it reduces the computing cost of the controller. Therefore, many researchers introduce the event-triggered mechanism to reduce data transmission in the control system to cope with the limitation of communication resources such as limited network bandwidth, while efficiently utilizing network resources and saving energy consumption. For example, a related art proposes a new event-triggered scheme to reduce the communication load in the network, and the event generator is located between the sensor and the controller to determine whether the new sampled state should be sent to the controller. A related art studies the event-triggered communication scheme and H ∞ control co-design method, which takes into account the communication delay and packet loss in network signal transmission while ensuring the H ∞ performance of the system, and better utilizes network resources.

[0073] In addition, other studies have also designed different ETMs to adapt to different control systems. One related art studies the passive event-triggered problem of networked control systems with actuator faults, gives a sufficient condition for the asymptotic stability of networked control systems (NCSs) with actuator faults and event-triggered mechanism based on Lyapunov-Krasovskii functional method, establishes a controller design method using Wirtinger inequality and linear matrix inequality, and the proposed strategy can reduce the transmission times, thereby saving communication resources. One related art considers network time delay on the basis of using Wirtinger inequality and linear matrix inequality to establish the research of controller. One related art proposes a distributed control strategy for networked control systems composed of multiple control loops, reduces the energy consumption of the network from the transmission times and idle listening period on the premise of ensuring the global consistent ultimate boundedness of each control loop based on self-triggered sampler. However, since any self-triggered control can cause the controlled system to run in an open-loop state for an arbitrarily long time, the control strategy proposed by one related art has the defect of relying on the robustness of the closed-loop system. One related art solves the timing problem of networked control systems by using a distributed event-triggered feedback scheme in networked control systems that allow packet loss and transmission delay, and only when the local state error of the subsystem exceeds the threshold, the subsystem broadcasts its state information to its neighbors. This scheme is decentralized in a certain sense, that is, the broadcasting decision of each subsystem is made using its local sampling data, so each subsystem does not need to exchange redundant information with other systems. One related art studies the scheduling problem of event-triggered controllers in multi-loop networked control systems, and compares different multiple access control (MAC) protocols in simulation. One related art proposes a distributed primal-dual algorithm based on distributed event-triggered network utility maximization problem and proves the convergence of the algorithm. One related art proposes a decentralized event-triggered feedback scheme suitable for linear time-invariant networks, studies the asymptotic stability of networked control systems without considering packet loss and transmission delay. One related art studies the event-triggered broadcast of state information in nonlinear distributed networked control systems. The above studies design various event-triggering mechanisms to reduce data transmission in control systems in response to the limitation of limited communication resources such as network bandwidth for different control systems, but few solutions research combines event-triggering ET and power control.

[0074] To solve the above technical problems, the embodiment of the present application provides an event-triggered information physical system wireless resource optimization method and system, which comprises the following steps: obtaining the corresponding relationship between the packet loss rate of the information physical system and the transmission power of the sending end and the selection probability of the cellular network based on the bit error rate; introducing an event triggering mechanism at the controller end to optimize the data transmission times between the controller and the actuator; analyzing the stability of the closed loop system after introducing the event triggering mechanism and obtaining the constraint condition for stabilizing the closed loop system; taking the constraint condition as a constraint and taking the system decay rate, the transmission power of the sending end, the event triggering coefficient and the total data transmission cost as the objective function to construct a multi-objective optimization function; solving the multi-objective optimization function by using a genetic algorithm to obtain the optimal triggering coefficient, the optimal transmission power and the optimal cellular network selection probability under the premise of ensuring the system performance. The present application realizes the balance among the system performance, communication energy saving and data transmission cost by providing an event-triggered information physical system wireless resource optimization method and system.

[0075] The embodiments of the present application will be described in detail below with reference to the accompanying drawings. However, those skilled in the art can understand that in the embodiments of the present application, many technical details are proposed in order to enable the reader to better understand the present application. However, the technical solutions claimed by the present application can be realized even without these technical details and various changes and modifications based on the following embodiments.

[0076] Referring to Figure 1 The embodiment of the present application provides an event-triggered information physical system wireless resource optimization method, which comprises the following steps:

[0077] Step S1, obtaining the corresponding relationship between the packet loss rate of the information physical system and the transmission power of the sending end and the selection probability of the cellular network based on the bit error rate.

[0078] Step S2, introducing an event triggering mechanism at the controller end to optimize the data transmission times between the controller and the actuator.

[0079] Step S3, analyzing the stability of the closed loop system after introducing the event triggering mechanism and obtaining the constraint condition for stabilizing the closed loop system.

[0080] Step S4, taking the constraint condition as a constraint and taking the system decay rate, the transmission power of the sending end, the event triggering coefficient and the total data transmission cost as the objective function to construct a multi-objective optimization function;

[0081] Step S5, solving the multi-objective optimization function by using a genetic algorithm to obtain the optimal triggering coefficient, the optimal transmission power and the optimal cellular network selection probability under the premise of ensuring the system performance.

[0082] The application aims at the balance among system performance, communication energy saving and data transmission cost, and provides an event-triggered wireless resource optimization method for information physical systems. Firstly, the packet loss rate is related to the transmission power of the sending end and the selection probability of the cellular network according to the bit error rate. It is known that the packet loss rate is inversely proportional to the transmission power of the sending end and the selection probability of the cellular network, that is, the system performance and the communication energy saving are contradictory to each other, and the data transmission cost is also contradictory to each other. Then, the event trigger is introduced at the controller end to reduce the data transmission times between the controller and the actuator, and save the battery energy, network resources and computing resources. Next, it is proved that the closed-loop system still maintains overall stability after the introduction of the event trigger mechanism, and the constraint condition for making the closed-loop system stable is obtained. These constraint conditions are used as constraints, and the system decay rate, the transmission power of the sending end, the event trigger coefficient and the total data transmission cost are used as objective functions to construct a multi-objective optimization function. The genetic algorithm is used to solve the multi-objective optimization function to obtain the optimal trigger coefficient, the optimal transmission power and the optimal cellular network selection probability under the premise of ensuring the system performance. Finally, it is verified through numerical simulation that the event-triggered wireless resource optimization method for information physical systems provided by the application can balance the system performance, communication energy saving and data transmission cost.

[0083] In some embodiments, step S1 obtains the corresponding relationship between the packet loss rate of the information physical system and the transmission power of the sending end and the selection probability of the cellular network based on the bit error rate, including the following steps:

[0084] Step S101 obtains the bit error rate based on the data error of the wireless channel. The data error is obtained by the inter-symbol interference and the multi-path interference in the wireless channel.

[0085] Step S102 obtains the packet loss rate of the information physical system based on the bit error rate and the packet loss rate when the cellular network transmits data and the packet loss rate when the WiFi network transmits data.

[0086] Step S103 obtains the corresponding relationship between the packet loss rate of the information physical system and the transmission power of the sending end and the selection probability of the cellular network based on the probability of successful information transmission under the heterogeneous wireless communication mode and the packet loss rate when the cellular network transmits data and the packet loss rate when the WiFi network transmits data.

[0087] In some embodiments, the event trigger mechanism is introduced at the controller end in step S2 to optimize the data transmission times between the controller and the actuator, including: designing an event-triggered intelligent controller for the closed-loop system, and optimizing the data transmission times between the controller and the actuator based on the trigger rule.

[0088] In some embodiments, the analysis of the stability of the closed-loop system after the introduction of the event-triggered mechanism in step S3 includes: verifying that the Lyapunov function of the information-physical system at adjacent two closed-loop time points is in a decreasing relationship, and analyzing the expected running condition of the system between the adjacent two closed-loop time points.

[0089] In some embodiments, the construction of the multi-objective optimization function in step S4 includes: converting the balance problem among the communication energy saving, system performance, and data transmission cost into a multi-objective optimization problem.

[0090] It should be noted that, after the construction of the multi-objective optimization function in step S4, and before the solution of the multi-objective optimization function by using the genetic algorithm in step S5, there is further including: converting the multiple objective functions in the multi-objective optimization problem into a single objective function by using the weighting method in the optimization algorithm, and solving the multi-objective optimization function.

[0091] In some embodiments, the solution of the multi-objective optimization function by using the genetic algorithm in step S5 includes: solving the nonlinear programming problem of the multi-objective optimization function by using the genetic algorithm to obtain the optimal σ1, σ2, δ, α solution under the weight coefficients c1, c2, c3, c4, c5; maximizing the triggering coefficient δ to reduce the number of sending of the control signal at the controller end, minimizing the transmission power σ1, σ2 to reduce the working energy consumption of the communication node, minimizing the cellular network selection probability α to reduce the cost of system data transmission, and balancing among the communication energy saving, system performance, and data transmission cost to achieve the balance among the communication energy saving, system performance, and data transmission cost while satisfying ξ≤ξ0.

[0092] The event-triggered information-physical system wireless resource optimization method provided in the present application will be described in detail below through specific embodiments.

[0093] The information-physical system (Cyper-Physical Systems, CPS) appears as an engineering system integrating computing, network, and physical process, which enables seamless interaction between network services and physical components. The CPS is composed of three main parts: 1) communication; 2) control; 3) computing, and the conceptual structure is as follows: Figure 2CPS is built on computing, sensing, communication and embedded system technologies, and is a natural product of the rapid development of Information and Communications Technology (ICT) in recent decades, which will change the way people interact with the physical world. The potential of CPS to change all aspects of life is enormous. Concepts such as self-driving cars, robotic surgery, smart buildings, smart grids, smart manufacturing and implantable medical devices are just a few examples of what is already available. The emergence and development of CPS covers many fields and realizes various applications in different fields.

[0094] CPS is composed of a large number of sensors, shared communication networks, control decision units and actuator units. The basic components are connected by a communication network to form a feedback control loop mechanism, as shown in Figure 3 In traditional control systems, the controlled device is controlled and monitored through a network with sufficient communication resources, so the expected control and state estimation actions are implemented in a Time-Triggered (TT) manner. TT is considered more suitable for hard real-time systems and safety-critical systems due to its predictability and ease of implementation. However, the TT-based control and estimation method often leads to overuse of available computing and communication resources, and considering that embedded system components are usually powered by batteries, data communication is usually energy-consuming. Currently, CPS mostly transmits information through shared wireless communication networks, which have limited network bandwidth, so the design of controllers and estimators should fully consider the problem of resource constraints caused by limited bandwidth and limited computing and processing capabilities of battery-powered system components. Some scholars first proposed the idea of Event-Triggered (ET), which proposes that "the most appropriate sampling method is to transmit only important data, i.e. new values obtained when data changes by a given increment". Compared with time triggering, event triggering follows the principle of on-demand reaction, with better utilization of computing, communication, battery device resources and flexibility.

[0095] CPS (Communication-Based System) transmits information through a shared communication network. Compared to wired networks, wireless communication networks often suffer from packet loss, network congestion, and latency issues, compromising the real-time performance and reliability of CPS and significantly impacting system performance. It is well known that the more control commands sent by the controller, the better the system performance. However, a large number of control commands consume excessive computing and communication resources and accelerate energy consumption at communication nodes. This illustrates that in CPS based on wireless network communication, improving system performance and efficiently utilizing resources are contradictory. This poses a significant challenge to the design of sensors and controllers. Therefore, researching the balance between efficient utilization of computing and communication resources and system performance in CPS has important theoretical and practical significance.

[0096] Figure 4 A schematic diagram of cell-level CPS in a heterogeneous wireless network is shown. Consider, for example... Figure 4 The framework shown comprises a feedback control loop consisting of a device moving within a limited location, a remote controller performing control calculations and decisions, and heterogeneous WiFi and cellular networks. Communication links from the sensor to the controller and from the controller to the actuator can be closed via either a WiFi network or a cellular network. This embodiment assumes that the mobile device has both WiFi and cellular network interfaces, and it determines whether to transmit sampling signals via a cellular base station (BS) or WiFi, considering its mobility, network heterogeneity, and system stability. This embodiment assumes that the state of the controlled object is described by the following linear time-invariant discrete system model.

[0097] x(k+1)=Ax(k)+Bu(k) (1)

[0098] in, For the system's state variables, the matrix and For a system constant matrix of appropriate dimension, This is the control input for the system.

[0099] This application's embodiments assume that in a heterogeneous wireless communication network, mobile devices can connect via cellular networks from any location, while whether they can connect via WiFi depends on the specific location. Let... and Let these be the sets of locations with and without WiFi. Then there are... in It is the set of all locations. Figure 4 For example, there are Because WiFi is deployed in these three locations.

[0100] On the one hand, from the perspective of CPS, using wireless network to transmit sensor-end feedback quantity x(k) and controller-end control quantity u(k) means that the accuracy and real-time performance of signal transmission cannot be guaranteed. Unlike CPS using wired network for transmission, the scale of CPS using wireless communication is usually small, so the influence of time delay on the performance of CPS is not dominant. Meanwhile, considering the high real-time requirement of control system, when the receiving end receives a data packet with time-out delay, the data packet will be discarded actively, and no time-out retransmission operation will be performed. Therefore, the embodiments of the present application mainly consider the influence of data packet loss on the performance of the system under wireless communication mode.

[0101] The embodiments of the present application let ρ(k) represent the information transmission result at time k, ρ(k)=1 represents successful information transmission, otherwise represents failed information transmission, and:

[0102] ρ(k)=ρ sc (k)ρ ca (k) (2)

[0103] Wherein, ρ sc (k) represents the transmission result of the sampling signal generated by the sensor end through the feedback channel, and ρ ca (k) represents the transmission result of the control signal generated by the controller end through the forward channel. The embodiments of the present application assume that the information transmission of the feedback channel and the forward channel is independent of each other, that is, ρ sc (k) and ρ ca (k) are independent of each other. Let p(k) be the probability of ρ(k) occurring, the embodiments of the present application assume that the probability has no explicit dependence on time, that is, p(k)=p, then:

[0104]

[0105] Wherein, p=p sc p ca , p sc and p ca are the probabilities of ρ sc (k) and ρ ca (k) occurring, respectively.

[0106] Let ρ1(k) and ρ2(k) represent the information transmission results when the mobile device transmits data packets through the cellular BS and the WiFi at time k, respectively, and let p1(k) and p2(k) represent the probabilities of ρ1(k) and ρ2(k), respectively. The embodiments of the present application assume that the probabilities have no explicit dependence on time, so p1(k) = p1 and p2(k) = p2. In addition, the embodiments of the present application assume that the cellular BS is more reliable than the WiFi connection, i.e., p1 > p2. This assumption is based on the fact that the operation schemes of the cellular network and the WiFi are different. The connection of the former is usually guaranteed by a reliable Internet Service Provider (ISP) and the user pays for the subscription package, while the connection of the latter is usually free but has low reliability due to competition.

[0107] The embodiments of the present application assume that, in the heterogeneous wireless communication mode, the mobile device connects through the cellular BS at each location with a probability of α, and connects through the WiFi with a probability of 1-α. Then, we have:

[0108] ρ(k) = α ρ1(k) + (1-α) ρ2(k) (4)

[0109]

[0110] According to equation (5), the probability of successful information transmission in the heterogeneous wireless communication mode is p = α p1 + (1-α) p2. In addition, based on the fact that the operation schemes of the cellular network and the WiFi are different, the embodiments of the present application assume that the costs of transmitting data through the cellular BS and the WiFi are f1 and f2, respectively, and f1 > f2. Therefore, the total cost of transmitting data in the heterogeneous wireless communication mode is:

[0111] f = α f1 + (1-α) f2 = f2 + α (f1-f2) (6)

[0112] According to equations (3) and (4), due to the packet loss caused by the heterogeneous wireless network, the actual control amount received by the actuator is:

[0113] u(k) = ρ(k) u0(k) (7)

[0114] where u0(k) is the control amount actually generated by the controller.

[0115] On the other hand, there are inter-symbol interference and multi-path interference in the wireless channel, and the data error caused by these interferences is the main reason for the data packet loss. This is because when the receiver detects that the data packet has an error through checksum, parity check, cyclic redundancy check (CRC) and other methods, it will directly discard this data packet. In the scenario where the reliability requirement is high but the real-time requirement is not so high, if the sending end does not receive the acknowledgement signal sent by the receiving end within a certain time, it will retransmit the data packet until the corresponding acknowledgement signal is received. But in the scenario where the real-time requirement is high, retransmission will consume a certain amount of time, so the sending end does not perform other operations after the data packet is discarded. CPS belongs to the second case, thus causing data packet loss. The noise, attenuation, wireless multi-path fading, interference and other wireless channel factors of the transmission channel and the transmission power of the sending end will all affect the occurrence of data error, so the symbol error rate (SER) can be expressed as:

[0116] SER≈e -νσ (8)

[0117] wherein v is a coefficient related to the wireless network parameters such as the noise, attenuation, inter-symbol interference, multi-access interference and the like of the transmission channel, and σ is the transmission power of the sending end. Therefore, the symbol error rates of the cellular network and the WiFi network can be expressed as wherein v1 and v2 represent the coefficients related to the parameters of the cellular network and the WiFi network respectively, and σ1 and σ2 represent the transmission powers of the cellular network and the WiFi network respectively.

[0118] According to the above analysis, in the CPS system shown in Figure 2 , the packet loss rate q is approximately equal to the symbol error rate SER, and according to formula (5) and formula (8), we can get:

[0119]

[0120]

[0121] wherein q1 and q2 represent the packet loss rates when data is transmitted through the cellular network and the WiFi network respectively, and formula (9) and formula (10) are substituted into formula (5) to get:

[0122]

[0123] At this point, the packet loss rate q can be expressed as a function of the probability α and the transmission power σ1, σ2 of the sending end.

[0124] As is well known, the lower the packet loss rate, the fewer control signals are lost in the forward channel, and the more control signals reach the actuator. The more control signals the actuator receives, the faster the system stabilizes. In other words, system performance is linked to the packet loss rate. Furthermore, according to equation (11), the packet loss rate q is not only related to the transmission power σ1 and σ2, but also to the selection probability α of using a cellular network for data transmission. Under the premise that parameters such as α, ν1, and ν2 are determined, the packet loss rate q is inversely proportional to the transmission power σ1 and σ2 of the transmitting end. Since the transmission power represents the energy consumption of the transmitting node, the relationship between system performance and energy consumption can be obtained: the higher the energy consumption, the better the system performance, and the lower the energy consumption, the worse the system performance. Therefore, how to maintain a balance between system performance and energy consumption is a thorny issue.

[0125] Given that parameters such as σ1, σ2, ν1, and ν2 are fixed, the packet loss rate q is inversely proportional to the selection probability α of the cellular network. According to equation (6), the selection probability represents the data transmission cost of the transmitting node. Thus, the relationship between system performance and data transmission cost can be obtained: the higher the data transmission cost, the better the system performance; the lower the data transmission cost, the worse the system performance. Maintaining a balance between system performance and data transmission cost is also a challenging problem.

[0126] The design of the intelligent controller will be described in detail below.

[0127] To achieve a balance between system performance, energy consumption, and data transmission costs, the embodiments of this application target... Figure 4 The closed-loop system design is as follows Figure 5 The diagram illustrates an event-triggered (ET) based intelligent controller. The sensor end only needs to periodically sample the system state and transmit the sampled feedback via a heterogeneous wireless network. Upon receiving the state feedback, the controller uses the ET to determine whether to initiate control calculations, generate control signals, and send them. Furthermore, it employs multi-objective optimization to determine the optimal transmission power and the network used for data transmission; hence, it is called an intelligent controller. The control calculation function generates control quantities based on the received state feedback.

[0128] u0(k)=Kx(k) (12)

[0129] Where u0(k) is the actual control quantity generated by the controller. Let be the system's feedback gain matrix.

[0130] This application uses Lyapunov's second method to analyze the stability of the system, and constructs the following function:

[0131]

[0132] Where P is a symmetric positive definite matrix. And the following symbols are defined:

[0133]

[0134]

[0135]

[0136] Among them, V c (x(k+m)) is the Lyapunov function of the system after m steps in closed-loop state at time k; V o (x(k+m)) is the Lyapunov function of the system after m steps of open-loop operation at time k; V h (x(k+m)) is the Lyapunov function of the system after running m steps in the zero-order hold-state at time k.

[0137] Existing optimal control systems achieve good system performance using the TT (Time Trigger) method, but this wastes computing, communication resources, and battery power. This application's embodiment replaces TT with ET (Electronic Time Trigger) to save system energy. This significantly increases the time interval between two adjacent triggers, but at the cost of some system performance. The triggering rule is designed as follows:

[0138]

[0139] Where k is the current time; k s It is the system number The moment of the second closed loop; The trigger coefficient is a positive real number; δV(x(k) s )) is the trigger threshold; This is the number of steps the actuator performs for zero-order hold. To prevent the open-loop system from diverging due to data packet loss and ET, this embodiment sets that after each trigger, the actuator will set the control quantity u(k) at the time of triggering. s Keep h0 steps, when k∈(k s ,k s When +h0] is active, system performance is guaranteed, and the event trigger does not work in order to avoid control conflicts; This refers to the number of steps the event trigger predicts for the future state of the system. To prevent the system from diverging due to prolonged open-loop operation, this embodiment compares the system state after running in an open-loop state for m0 steps at time k with the trigger threshold. If the condition is met, the trigger is triggered in advance, shortening the time interval between two adjacent triggers, and the system tends to be stable at a faster speed. The value of constant m0 needs to be determined before the system starts and is set at the event trigger end, and its specific value can be adjusted according to the actual situation; The value of constant h0 also needs to be determined before the system starts and is set at the actuator end, but its specific value is obtained by linear matrix inequality in the following.

[0140] Under the trigger rule of formula (17), the sensor at time k sends the feedback to the controller through the wireless communication link after sampling the system state. Since the wireless channel transmission may cause packet loss, the controller only transmits data to the event trigger when receiving the sampling data sent by the sensor. After the event trigger receives the system state x(k), it first judges the working state of the actuator. If the actuator is in the zero-order hold stage, that is, when k s <k≤k s +h0, the event trigger ends immediately; otherwise, the event trigger compares the system state V(x(k+m0)|x(k)) of the system after m0 steps of open-loop state at time k with the trigger threshold δV(x(k s )), and judges whether the trigger threshold is met. If the trigger condition is not met, the event trigger ends; otherwise, the controller will perform control calculation and send the generated control signal to the actuator. The algorithm flow is shown in Table 1, and only when the actuator is not in the zero-order hold state and the trigger condition (17) is met, the event trigger constitutes a trigger.

[0141] Table 1 Algorithm flow of event trigger mechanism

[0142]

[0143]

[0144] The present application adopts an intelligent controller closed-loop system, so according to the above design, when k s ,k s+1 ), the control law of the controller can be rewritten as:

[0145]

[0146] According to formula (2), the above formula can be rewritten as:

[0147]

[0148] Where k s s represents the time of the s-th closed loop of the system, and the value of function θ(k) represents the triggering condition of the event trigger, as follows:

[0149]

[0150] Define event ε(k), which means CPS is in closed-loop state at time k. In the original closed-loop system, the sensor samples the system state periodically, and transmits the feedback signal to the controller through the wireless channel. The controller calculates the control signal according to the received feedback signal, and transmits the generated control signal to the actuator through the wireless channel. The actuator updates the system state according to the specified model after receiving the control signal, thus forming a closed loop. At this time, the system closed-loop condition is ε(k) = {ρ sc (k) = 1} v {ρ ca (k) = 1}, which can be rewritten as ε(k) = {ρ(k) = 1}, that is, as long as the data of the feedback channel and the forward channel are transmitted successfully at the same time, the system will be closed-loop.

[0151] After introducing ET, the sensor still samples the system state periodically and transmits the feedback signal through the wireless channel. However, at the controller end, only after successfully receiving the feedback signal and the event trigger being activated, the subsequent operations will be performed. At this time, the system closed-loop condition is ε(k) = {ρ sc (k) = 1}∩{θ(k) = 1}∩{ρ ca (k) = 1}, that is, at time k, the sensor successfully feeds back the sampled data to the controller through the wireless channel, then the system state satisfies formula (17) and the event trigger is triggered, the controller generates the control signal according to formula (12) and sends it, and finally the actuator successfully receives the control signal and updates the system state according to the specified model.

[0152] According to formula (2), the above closed-loop condition can be rewritten as: ε(k) = {ρ(k) = 1}∩{θ(k) = 1}, otherwise, the CPS does not satisfy the closed-loop condition.

[0153] In summary, the ET is set at the controller end in the embodiments of the present application, and the sensor end only needs to retain its original computing device and does not need to be changed. However, due to the introduction of ET, the controller end needs to store the system state x(k s ) at the last closed-loop time, and needs to calculate the system state and the trigger threshold after m0 steps of open-loop operation, so it needs to add some storage and computing devices to realize the ET. In this way, the communication times between the controller and the actuator will be greatly reduced, achieving the purpose of energy saving. Further energy saving effect can be realized by the power optimization function designed later.

[0154] The stability of the closed-loop system after introducing the event trigger mechanism is analyzed below, and the constraint condition for making the closed-loop system stable is obtained.

[0155] Lemma 1: Let A be an n-order real symmetric matrix, and let λmax ,λ min are the maximum and minimum of all eigenvalues of A, respectively, then λ min X T X≤X T AX≤λ max X T X。

[0156] Theorem 1: For given constants 0 < β < 1, γ > 1, If the packet loss rate 0 < q < 1 / γ of the closed-loop system with intelligent controller and the event-triggered parameter 0 < δ < 1 satisfy pδ / (1-qγ) < 1, and there exist a symmetric positive definite matrix and a matrix satisfying the following inequalities:

[0157] (A+BK) T P(A+BK)≤βP

[0158] A T PA≤γP

[0159]

[0160] then for any k ∈ (k s ,k s+1 ], the formula (22) is established:

[0161]

[0162] where k s represents the s-th closed-loop time of the system, s = 0, 1, 2,...; the system decay rate ξ = pδ / (1-qγ); the packet loss rate λ min (P), λ max (P) are the minimum and maximum eigenvalues of the matrix P, respectively, and the matrix P is a symmetric positive definite matrix in the Lyapunov function.

[0163] Proof: The Lyapunov function constructed in the present application is positive definite and has a first-order continuous partial derivative for all x(k). It is only necessary to prove that is semi-negative definite to obtain a system that is stable in the sense of Lyapunov. That is, in order to prove that the closed-loop system still maintains overall stability after the introduction of event triggering, it is only necessary to prove that and V(x(k))→0 as k→∞.

[0164] According to the design of the event trigger in the foregoing, the CPS behavior between any two closed loops can be divided into a closed-loop stage, a zero-order holding stage, and an open-loop stage, and the timing diagram is as shown in Figure 6is shown. Assume that the CPS is in closed-loop at time k s , i.e., event ε(k s ) occurs, then we have:

[0165] x(k s +1) = Ax(k s ) + Bu(k s )

[0166] = Ax(k s ) + Bu0(k s )

[0167] = Ax(k s ) + BKx(k s )

[0168] = (A + BK)x(k s ) (23)

[0169] From equation (23), we can get that when k = k s +1, the system satisfies:

[0170] V(x(k)) = V c (x(k s +1) | x(k s ))

[0171] = V((A + BK)x(k s ))

[0172] = x T (k s )(A + BK) T P(A + BK)x(k s )

[0173] ≤ βx T (k s )Px(k s )

[0174] = βV(x(k s )) (24)

[0175] After that, the system enters the zero-order hold phase k ∈ (k s , k s + ho], the actuator maintains the control amount u(k s ), so we have:

[0176]

[0177] Similarly, according to equation (23), when k ∈ (k s +1, k s + ho], the system satisfies:

[0178]

[0179] At this point, the system has experienced the closed-loop phase and the zero-order hold phase. Thereafter, the actuator sets the input to 0 and the event trigger starts to work normally according to the formula V(x(k s +h0))≤δV(x(k s )) that is, the event trigger has not reached the triggering threshold at the time k s +h0, and V(x(k s +h0)) can still have a large gap with the triggering threshold δV(x(k s )), so the CPS will run in an open-loop mode for a period of time. It is assumed that at the time k s +h0, the Lyapunov function of the system satisfies the following equation:

[0180] V h (x(k s +h0)|x(k s ))=δ s V(x(k s )) (27)

[0181] where δ s is a constant and satisfies δ s ≤δ. In addition, the embodiments of the present application assume that the event trigger will be activated at the time k s +h0+n s +1, so there is:

[0182] V o (x(k s +h0+n s )|x(k s +h0))

[0183] ≤δV(x(k s ))

[0184] <V o (x(k s +h0+n s +1)|x(k s +h0)) (28)

[0185] Since long-time open-loop operation can have an adverse effect on system performance, we need to shorten the number of steps n s of open-loop operation of the system as much as possible, so the embodiments of the present application compare the Lyapunov function of the system after running in an open-loop mode for m0 steps with the event triggering threshold, which can activate the event trigger in advance without affecting the stability of the system. Compared with the case without adding prediction, the embodiments of the present application can change the original open-loop step number n s by adjusting the size of the prediction window m0., the new open-loop step number is defined as

[0186] When k∈(k s +h0,k s +h s ], the system satisfies:

[0187] V(x(k))≤V o (x(k s +h0+n s )|x(k s +h0)) (29)

[0188] where h s = h0+ [n s -m0] + . According to the formula, the above formula can be further scaled, and then we have:

[0189] V(x(k))≤δV(x(k s )) (30)

[0190] So far, the CPS system has experienced zero-order maintenance for h0time and open-loop operation for [n s -m0] + time, during which the CPS system does not satisfy the trigger condition (17). When k∈(k s ,k s +h s ], even if the data transmitted by the feedback channel is not lost, the event trigger will not be activated, i.e. Pr{θ(k)=1|x(k s ),ρ sc (k)=1}=0. Therefore, during the zero-order maintenance and open-loop operation phase, the system behavior has no randomness, i.e. E{V(x(k))|x(k s )}=V(x(k)) when k∈(k s ,k s +h s ]. At the time after that, the trigger satisfies the trigger condition, i.e. Pr{θ(k)=1|x(k s ),ρ sc (k)=1}=1, at this time, whether the controller is triggered depends on whether the sampled data transmitted by the feedback channel is lost, and whether the CPS closed loop depends on whether the sampled data transmitted by the feedback channel and the control data transmitted by the forward channel are transmitted successfully at the same time, i.e.

[0191]

[0192] At this time, the system behavior has uncertainty, and we need to use expectation to describe the system state.

[0193] This application's embodiments assume k s The next closed-loop time of the system is k. s+1 When k∈(k s +h s ,k s+1 At that time, we have:

[0194]

[0195] As can be seen from equation (32) above, as long as the value of q is reasonably adjusted so that 0 < qγ < 1, the above equation can converge to pδV(x(k) s Let: )) / (1-qγ),

[0196]

[0197] in, Based on the above formula, the expression can be rewritten as:

[0198] E{V(x(k s+1 ))|x(k s )}≤ξV(x(k s (34)

[0199] Where p / (1-qγ) is an increasing function of q and is greater than 1, therefore ξ≥δ. Furthermore, embodiments of this application also require the reasonable selection of parameters q1, q2, α, and δ to ensure that ξ<1.

[0200] Thus far, the embodiments of this application have demonstrated that the Lyapunov function of CPS decreases between two adjacent closed-loop times. Further discussion is needed regarding the relationship between k∈(k...) between two adjacent closed-loop times. s ,k s+1 The expected operating condition of the system. When k∈(k s ,k s+1 ),have:

[0201]

[0202] In summary, for any two adjacent closing times k∈(k) of the CPS closed-loop system, s ,k s+1 Within, all contain:

[0203] E{V(x(k))}<ξV(x(k s (36)

[0204] Taking the expected value from both sides simultaneously, we get:

[0205] E{V(x(k))}<ξE{V(x(k s ))},k∈(k s ,k s+1 (37)

[0206] Further recursion can be obtained:

[0207] E{V(x(k s ))}<ξ 2 E{V(x(k s-1 ))}<…<ξ s+1 E{V(x(k0))} (38)

[0208] where k0 represents the 0th time of closing loop of the system, the embodiment of the present application takes k0=0, then the behavior of the system at k0 time does not have randomness, thus:

[0209] E{V(x(k))}<ξ s+1 V(x(0)) (39)

[0210] Expanding the left and right sides of the above formula, it can be obtained:

[0211] E{x T (k)Px(k)}<ξ s+1 x T (0)Px(0) (40)

[0212] According to the lemma 1, scaling the left end of the formula, it has:

[0213] E{λ min (P)x(k) T x(k)}≤E{x(k) T Px(k)} (41)

[0214] That is:

[0215] λ min (P)E{||x(k)|| 2}≤E{x(k) T Px(k)} (42)

[0216] According to the lemma 1, scaling the right end of the formula:

[0217] ξ s+1 x(0) T Px(0)≤ξ s+1 λ max (P)x(0) T x(0) (43)

[0218] That is:

[0219] ξ s+1 x(0) T Px(0)≤ξ s+1 λ max (P)||x(0)||2 (44)

[0220] Therefore, the above formula can be rewritten as:

[0221] λ min (P)E{||x(k)|| 2}<ξ s+1 λ max (P)||x(0)|| 2 (45)

[0222] That is, it can be proved that the closed-loop system has:

[0223]

[0224] where λ min (P), λ max (P) are the minimum and maximum eigenvalues of the matrix P, respectively, and the matrix P is a symmetric positive definite matrix in the Lyapunov function. The theorem is proved.

[0225] The design of the multi-objective optimization function is described in detail below.

[0226] The foregoing introduces event triggering at the controller end, which saves energy by reducing the number of data transmissions in the forward channel. At the same time, considering that the transmission power represents the energy consumption of the sending node, the embodiments of the application further save energy by reducing the transmission power of the sending end. In addition, the embodiments of the application also consider reducing the data transmission cost by reducing the selection probability α of the cellular network. Reducing the number of data transmissions in the forward channel means that a larger event triggering coefficient δ needs to be set, reducing the transmission power of the sending end will result in a larger value of the packet loss rate q, and reducing the probability α of the cellular network being used for data transmission will also result in a larger value of the packet loss rate q. According to the expression of the system decay rate ξ in the foregoing, ξ is proportional to q and is also proportional to δ, and a larger value of q and δ will result in a larger system decay rate ξ, that is, energy saving and cost compression are at the expense of system performance. However, according to the analysis in the foregoing, to ensure the stability of the closed-loop system, the values of q and δ are limited within a certain range, and changing the values of q and δ within their respective ranges can change the value of ξ, but the system remains stable. Therefore, the embodiments of the application construct a multi-objective optimization problem by taking the system decay rate ξ, the transmission power σ1, σ2 of the sending end, the event triggering coefficient δ, and the total data transmission cost f as optimization objectives, and by solving the optimization problem, the optimal transmission power, the optimal triggering coefficient, and the optimal cellular network selection probability can be obtained under the premise of ensuring system performance, so as to achieve the effect of obtaining better system performance with lower energy consumption and lower transmission cost.

[0227] According to the above analysis, the balance problem among communication energy saving, system performance, and data transmission cost can be converted into the following multi-objective optimization problem:

[0228]

[0229]

[0230]

[0231] 0 < δ < ξ

[0232] 0 < ξ ≤ ξ0

[0233] 0 ≤ σ1 ≤ σ 10

[0234] 0 ≤ σ2 ≤ σ 20

[0235] 0 ≤ α ≤ 1

[0236] q1 < q2 (47)

[0237] wherein ξ = pδ / (1-qγ) is the decay rate of the closed-loop system, and ξ0 < 1 is a pre-given upper bound of the system decay rate; is the communication packet loss rate; γ > 1 is related to the divergence rate of the open-loop system, and can be seen in the above formula; σ1 is the transmission power of the cellular network, and σ 10 is a pre-given upper bound of σ1; σ2 is the transmission power of the WiFi network, and σ 20 is a pre-given upper bound of σ2; δ is the event-triggering coefficient; α is the probability of using the cellular network to transmit data under the heterogeneous wireless communication mode; and f is the total cost of using the heterogeneous wireless communication network to transmit data.

[0238] The requirements of system performance, communication energy saving and data transmission cost are embodied in the above multi-objective optimization problem. In view of system energy saving, the application embodiments hope that the transmission power σ1, σ2 is as small as possible, and hope that the event triggering coefficient δ affecting the system closed loop interval is as large as possible. In view of transmission cost, the application embodiments hope that the probability α positively correlated with transmission cost is as small as possible. Smaller σ1, σ2 and α values will result in larger q values, and larger packet loss rates will result in that the receiving end is difficult to receive the data packet sent by the sending end, so the system performance cannot be guaranteed. Larger event triggering coefficient will result in larger time interval of adjacent two closed loops of the system, and the system is in open loop state for a long time, at this time the system performance cannot be guaranteed. Smaller system attenuation rate ξ indicates that the system converges to the origin faster, and the system performance is better. Therefore, in view of system performance, the application embodiments hope that the attenuation rate ξ is as small as possible under the constraint of its upper limit ξ0. Based on the above considerations, the application embodiments need to solve a multi-objective optimization problem to seek satisfactory decision variable σ1, σ2, δ, α values.

[0239] The application embodiments use the weighting method in the traditional optimization algorithm to convert multiple objective functions in the formula into a single objective function, as follows:

[0240]

[0241] Wherein, C = [c1 c2 c3 c4 c5] T is a non-negative weight vector, The size of the weight coefficient determines the importance of each objective function, which can be adjusted according to actual conditions. At this point, the multi-objective optimization problem of the formula can be rewritten as the following optimization problem:

[0242]

[0243]

[0244]

[0245] 0 < δ < ξ

[0246] 0 < ξ ≤ ξ0

[0247] 0 ≤ σ1 ≤ σ 10

[0248] 0 ≤ σ2 ≤ σ 20

[0249] 0 ≤ α ≤ 1

[0250] q1 < q2 (49)

[0251] Wherein, the system attenuation rate is ξ = pδ / (1-qγ), and the system packet loss rate is

[0252] The embodiment of the application uses a genetic algorithm (Genetic Algorithm, GA) to solve the above nonlinear programming problem, and can obtain optimal σ1, σ2, δ, α solutions under weight coefficients c1, c2, c3, c4, and c5. The algorithm flow is shown in Table 2. While satisfying ξ≤ξ0, the triggering coefficient δ is maximized to reduce the number of sending control signals at the controller end, the transmission power σ1 and σ2 are minimized to reduce the working energy consumption of the communication node, and the cellular network selection probability α is minimized to reduce the cost of system data transmission, and a compromise is made among communication energy saving, system performance, and data transmission cost.

[0253] Table 2 Genetic algorithm flow

[0254]

[0255]

[0256] The specific description of the setting is as follows.

[0257] Consider the linear constant discrete system model in the following form:

[0258] x(k+1)=Ax(k)+Bu(k)

[0259] Wherein,

[0260]

[0261] The initial state of the system is x0=(1.5 1) T , and the system sampling period is selected as T s =0.1.

[0262] The minimum quadratic cost function is solved by the control system toolbox in MATLAB software, and then the optimal gain matrix is obtained. The minimum quadratic cost function is:

[0263]

[0264] The optimal gain matrix is:

[0265] K=(0.2166 -1.0008)

[0266] Wherein,

[0267]

[0268] Given matrices A, B, and K, solving the linear inequalities using the LMI toolbox in MATLAB yields a feasible solution for β = 0.1223, γ = 1.0558, and matrix P.

[0269]

[0270] Once the value of parameter γ is determined, the optimization problem can be solved using GA. The upper bound of the attenuation rate ξ0 = 0.6, the cost of transmitting data via cellular network f1 = 16, the cost of transmitting data via WiFi network f2 = 2, the maximum number of generations in the genetic algorithm MaxGenerations = 100, and the population size PopulationSize = 50 are set. The objective function J of the optimization problem is used as the fitness function to evaluate the quality of individuals. After several iterations, a set of solutions to the optimization problem can be obtained.

[0271] When the mobile device moves to the location At this time, since there is no WiFi deployed in these locations, information can only be transmitted via cellular networks (BS), i.e., α = 1. The iterative process for solving the optimization problem at this point is as follows: Figure 7 As shown, the two variables are q1 and ξ, so the packet loss rate q = q1 = 0.3304, the expected attenuation rate ξ = 0.4781, the triggering coefficient δ = 0.4649, and the data transmission cost f = 16 can be obtained.

[0272] When the mobile device moves to the location At this time, information can be transmitted via cellular BS or WiFi. The iterative process for solving the optimization problem is as follows: Figure 8 As shown, the four variables are q1, q2-q1, ξ, and α. Therefore, we can obtain the packet loss rate of cellular network q1 = 0.3000, the packet loss rate of WiFi network q2 = 0.7471, the parameter α = 0.4575, the packet loss rate of heterogeneous communication network q = 0.5425, the expected attenuation rate ξ = 0.4877, the triggering coefficient δ = 0.4555, and the data transmission cost f = 8.4055.

[0273] The simulation models involved in the embodiments of this application will be described in detail below.

[0274] Figures 9 to 15CPS model diagram, controller simulation model diagram, mobile device model diagram based on intelligent sensor, discrete state space parameter configuration diagram, TT model diagram, Bernoulli binary sequence generator parameter configuration diagram and ET model diagram, and finally ETC is realized through a MATLAB function module. Periodic sampling of the discrete state space is transmitted to the controller node, and the controller node calculates the control signal and then transmits data to the discrete state space, so as to realize closed-loop control of the entire system. Among them, ETC and time-triggered control (TTC) are both set at the sensor end, when CtrSwitch = 1, the system is an event-triggered and power-optimized closed-loop system; when CtrSwitch = -1, the system is a time-triggered optimal closed-loop system. The Bernoulli binary sequence generator is used to simulate the data packet loss caused by the wireless communication network, which generates a binary number with a random Bernoulli distribution, where 0 represents packet loss and 1 represents successful data transmission, and the transmission of signals on the line from the sensor to the controller is used to simulate the packet loss situation.

[0275] The event-triggered information physical system wireless resource optimization method provided in the application is verified by numerical simulation.

[0276] Specifically, the simulation results when the mobile device is located at are as follows:

[0277] According to the simulation model, the simulation results of Figure 16 and Figure 17 can be obtained by using the MATLAB software platform for simulation verification. The running conditions of the state trajectories x1 and x2 of the two systems are shown in Figure 16 , and the communication working conditions of the two systems are shown in Figure 16 . By comprehensively analyzing Figure 16 and Figure 17 , it can be found that when the controlled device moves to the position and the data transmission cost is fixed, the system based on the intelligent controller sacrifices part of the system performance in consideration of energy saving, but the performance difference with the system based on the optimal controller is not large, and it can still meet the demand. However, in terms of system energy consumption, the energy saving effect of the former is very obvious compared with the latter. In summary, the design of the intelligent controller can save computing resources, wireless network resources and battery energy on the premise of ensuring system performance.

[0278] Specifically, the simulation results when the mobile device is located at are as follows:

[0279] According to the simulation model, simulation verification is performed by using a MATLAB software platform, and simulation results of Figure 18 and Figure 19 are obtained. Operation conditions of state trajectories x1, x2 of the two systems are shown in Figure 18 , and communication working conditions of the two systems are shown in Figure 19 . It can be found from Figure 18 and Figure 19 that the system based on the intelligent controller sacrifices part of system performance for energy saving, but the performance difference between the two systems is not large, and the system performance can still meet the demand. However, in terms of system energy consumption, the energy saving effect of the former is very obvious compared with the latter. It can be found from the comparison between Figure 16 and Figure 17 that the system based on the heterogeneous communication network sacrifices part of system performance for compression cost, but the system performance difference between the two systems is not large, and the system performance can still meet the demand. However, in terms of transmission cost, the former compresses nearly half of the transmission cost compared with the latter. In summary, the design of the intelligent controller can save wireless computing resources, network resources and battery energy and compress data transmission cost on the premise of guaranteeing system performance.

[0280] Referring to Figure 20 , the embodiment of the application further provides an event-triggered information physical system wireless resource optimization system, which comprises an optimization processing module 101, a multi-objective optimization function construction module 102 and a calculation module 103 connected in sequence; the optimization processing module 101 is used for obtaining the corresponding relationship between the packet loss rate of the information physical system and the transmission power of the sending end, the selection probability of the cellular network based on the bit error rate; and introducing an event triggering mechanism at the controller end to optimize the data transmission times between the controller and the actuator; the multi-objective optimization function construction module 102 is used for analyzing the stability of the closed-loop system after the introduction of the event triggering mechanism, and obtaining the constraint condition for stabilizing the closed-loop system; and taking the constraint condition as a constraint, and taking the system decay rate, the transmission power of the sending end, the event triggering coefficient and the total data transmission cost as a target function, a multi-objective optimization function is constructed; the calculation module 103 is used for solving the multi-objective optimization function by using a genetic algorithm, and obtaining the optimal triggering coefficient, the optimal transmission power and the optimal cellular network selection probability under the premise of guaranteeing system performance.

[0281] According to the technical scheme, the embodiment of the application provides a wireless resource optimization method and system for an event-triggered cyber-physical system, which comprises the following steps: obtaining a corresponding relationship between a packet loss rate of the cyber-physical system and a transmission power of a sending end and a selection probability of a cellular network based on a bit error rate; introducing an event-triggering mechanism at a controller end to optimize a data transmission frequency between the controller and an actuator; analyzing stability of a closed-loop system after the event-triggering mechanism is introduced, and obtaining constraint conditions for stabilizing the closed-loop system; taking the constraint conditions as constraints, and taking a system decay rate, the transmission power of the sending end, an event-triggering coefficient and a total data transmission cost as objective functions to construct a multi-objective optimization function; and solving the multi-objective optimization function by using a genetic algorithm to obtain an optimal triggering coefficient, an optimal transmission power and an optimal cellular network selection probability under the premise of ensuring system performance.

[0282] The application studies the balance among communication energy saving, system performance and data transmission cost of a unit-level CPS in a heterogeneous wireless network and proposes a wireless resource optimization method for an event-triggered cyber-physical system. First, the packet loss rate is related to the transmission power of the sending end and the selection probability of the cellular network according to the bit error rate, and it is known that the packet loss rate is inversely proportional to the transmission power of the sending end and inversely proportional to the selection probability of the cellular network, that is, the system performance and the communication energy saving are contradictory to each other, and the system performance and the data transmission cost are also contradictory to each other. Then, the event-triggering is introduced at the controller end to reduce the data transmission frequency between the controller and the actuator, and save the battery energy, network resources and computing resources. Next, it is proved that the closed-loop system remains overall stability after the event-triggering mechanism is introduced, and constraint conditions for stabilizing the closed-loop system are obtained. The constraint conditions are taken as constraints, and the system decay rate, the transmission power of the sending end, the event-triggering coefficient and the total data transmission cost are taken as objective functions to construct a multi-objective optimization function, and the multi-objective optimization function is solved by using a genetic algorithm to obtain an optimal triggering coefficient, an optimal transmission power and an optimal cellular network selection probability under the premise of ensuring system performance. Finally, it is verified by numerical simulation that the wireless resource optimization method for the event-triggered cyber-physical system can balance the system performance, the communication energy saving and the data transmission cost.

[0283] Those skilled in the art can understand that the above embodiments are specific examples for implementing the application, and in actual application, various changes can be made in form and details without departing from the spirit and scope of the application. Any person skilled in the art can make various changes and modifications without departing from the spirit and scope of the application, and therefore the protection scope of the application should be limited by the scope defined by the claims.

Claims

1. A method for optimizing wireless resources in a cyber-physical system based on event triggering, characterized in that, include: Based on the bit error rate, the correspondence between the packet loss rate of the cyber-physical system and the transmission power of the transmitter and the selection probability of the cellular network is obtained; An event-triggered mechanism is introduced on the controller side to optimize the number of data transmissions between the controller and the actuator; The stability of the closed-loop system after the introduction of an event triggering mechanism is analyzed, and the constraints that make the closed-loop system stable are obtained. Using the aforementioned constraints as constraints, and taking the system attenuation rate, the transmission power of the transmitter, the event triggering coefficient, and the total data transmission cost as objective functions, a multi-objective optimization function is constructed. A genetic algorithm is used to solve the multi-objective optimization function to obtain the optimal triggering coefficient, optimal transmission power, and optimal cellular network selection probability under the premise of ensuring system performance. The construction of the multi-objective optimization function includes: The problem of balancing communication energy saving, system performance, and data transmission cost is transformed into a multi-objective optimization problem as shown in formula (4): 0 < δ < ξ 0<ξ≤ξ0 0≤σ1≤σ 10 0≤σ2≤σ 20 0≤α≤1 q1<q2 (4) Where ξ=pδ / (1-qγ) is the attenuation rate of the closed-loop system; ξ0<1 is a pre-given upper bound for the system attenuation rate; γ is the packet loss rate; γ > 1 is related to the divergence rate of the open-loop system; p is the probability of successful information transmission under heterogeneous wireless communication; ν1 and ν2 represent coefficients related to the parameters of cellular networks and WiFi networks, respectively; σ1 is the transmission power of the cellular network; σ 10 σ1 is a pre-defined upper bound; σ2 is the transmit power of the WiFi network; σ 20 σ² is a pre-defined upper bound; δ is the event triggering coefficient; α is the probability of using a cellular network to transmit data under heterogeneous wireless communication; f is the total cost of using a heterogeneous wireless communication network to transmit data; q1 is the packet loss rate of the cellular network; q2 is the packet loss rate of the WiFi network. After constructing the multi-objective optimization function, and before solving the multi-objective optimization function using a genetic algorithm, the following steps are also included: By using the weighted method in the optimization algorithm, the multiple objective functions in formula (4) are transformed into a single objective function, as shown in formula (5): Where C = [c1 c2 c3 c4 c5] T It is a non-negative weight vector. The magnitude of the weighting coefficients determines the importance of each objective function; Rewrite formula (4) as formula (6): 0 < δ < ξ 0<ξ≤ξ0 0≤σ1≤σ 10 0≤σ2≤σ 20 0≤α≤1 q1<q2 (6) Wherein, the system attenuation rate is ξ=pδ / (1-qγ), and the system packet loss rate is 2. The event-triggered wireless resource optimization method for cyber-physical systems according to claim 1, characterized in that, The method for obtaining the correspondence between the packet loss rate of a cyber-physical system and the transmission power of the transmitting end and the selection probability of the cellular network based on the bit error rate includes: The bit error rate is obtained based on the data bit error rate of the wireless channel; the data bit error rate is generated and obtained from inter-symbol interference and multipath interference in the wireless channel. Based on the bit error rate, the packet loss rate when transmitting data via cellular network, and the packet loss rate when transmitting data via WiFi network, the packet loss rate of the cyber-physical system is obtained. Based on the probability of successful information transmission under heterogeneous wireless communication methods, the packet loss rate when cellular networks send data, and the packet loss rate when WiFi networks send data, the correspondence between the packet loss rate of the cyber-physical system and the transmission power of the transmitting end and the selection probability of the cellular network is obtained.

3. The event-triggered wireless resource optimization method for cyber-physical systems according to claim 2, characterized in that, The bit error rate is shown in formula (1): SER≈e -νσ (1) Where SER represents the bit error rate; ν is a coefficient related to wireless network parameters such as noise, attenuation, inter-symbol interference, and multiple access interference of the transmission channel; and σ is the transmission power of the transmitter. The bit error rates of cellular networks and WiFi networks are obtained using formula (1), and the bit error rates of cellular networks and WiFi networks are expressed as follows: Where ν1 and ν2 represent coefficients related to cellular network and WiFi network parameters, respectively, and σ1 and σ2 represent the transmission power of cellular network and WiFi network, respectively; The packet loss rate of the cyber-physical system is shown in formula (2): Where q is the packet loss rate of the cyber-physical system; p1 is the probability of the information transmission result occurring when data packets are sent via cellular base stations; p2 is the probability of the information transmission result occurring when data packets are sent via WiFi; and α is the selection probability of the cellular network.

4. The event-triggered wireless resource optimization method for cyber-physical systems according to claim 1, characterized in that, The introduction of an event-triggered mechanism on the controller side to optimize the number of data transmissions between the controller and the actuator includes: An event-triggered intelligent controller was designed for the closed-loop system, and the number of data transmissions between the controller and the actuator was optimized based on the triggering rules.

5. The event-triggered wireless resource optimization method for cyber-physical systems according to claim 4, characterized in that, The triggering rule is shown in formula (3): Where k is the current time; k s It is the system number The moment of the second closed loop; The trigger coefficient is a positive real number. δV(x(k s )) is the trigger threshold; It is the number of steps the actuator performs for zero-order hold; It is the number of steps the event trigger predicts for the future state of the system; x(k) is the state variable of the system at time k; V(x(k) is the number of steps the event trigger predicts for the future state of the system. s )) is the system in the first The Lyapunov function at the time of the second closed loop; V(x(k+m0)|x(k)) is the system state after the system has run m0 steps in the open loop at time k.

6. The event-triggered wireless resource optimization method for cyber-physical systems according to claim 1, characterized in that, The stability analysis of the closed-loop system after the introduction of an event-triggered mechanism includes: The Lyapunov function of the cyber-physical system is verified to decrease between two adjacent closed-loop times, and the expected operation of the system between two adjacent closed-loop times is analyzed.

7. The event-triggered wireless resource optimization method for cyber-physical systems according to claim 1, characterized in that, The step of using a genetic algorithm to solve the multi-objective optimization function includes: The nonlinear programming problem of the multi-objective optimization function is solved by using a genetic algorithm to obtain the optimal σ1, σ2, δ, α solutions with weight coefficients c1, c2, c3, c4, c5. While satisfying ξ≤ξ0, the triggering coefficient δ is maximized to reduce the number of control signals sent by the controller, the transmission power σ1 and σ2 is minimized to reduce the energy consumption of the communication node, and the cellular network selection probability α is minimized to reduce the cost of system data transmission. A trade-off is made among communication energy saving, system performance, and data transmission cost to achieve a balance among these three factors.

8. An event-triggered cyber-physical system (CPS) wireless resource optimization system, the system being used to implement the event-triggered CPS wireless resource optimization method as described in any one of claims 1 to 7, characterized in that, It includes an optimization processing module, a multi-objective optimization function construction module, and a calculation module connected in sequence; The optimization processing module is used to obtain the correspondence between the packet loss rate of the cyber-physical system and the transmission power of the transmitter and the selection probability of the cellular network based on the bit error rate; and to introduce an event triggering mechanism at the controller end to optimize the number of data transmissions between the controller and the actuator. The multi-objective optimization function construction module is used to analyze the stability of the closed-loop system after the introduction of the event triggering mechanism, and to obtain the constraints that make the closed-loop system stable. The aforementioned constraints are used as constraints, and the system attenuation rate, the transmission power of the transmitter, the event triggering coefficient, and the total data transmission cost are used as objective functions to construct a multi-objective optimization function; The computation module is used to solve the multi-objective optimization function using a genetic algorithm to obtain the optimal triggering coefficient, optimal transmission power, and optimal cellular network selection probability while ensuring system performance.

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