Network prediction control system and method based on network communication constraint

Abstract

The invention discloses a network prediction control system and method based on network communication constraints, and relates to the technical field of control systems.The method comprises the steps that state data of a network hopping system are obtained, and the state data are input into a prediction model for prediction calculation, according to the prediction model, a polyhedral model is adopted to describe a system jump phenomenon, a Markov chain is utilized to describe network delay, and 0-1 distribution represents DoS attacks; based on the prediction calculation result, adopting a multi-step mode dependence state feedback control law to generate a control instruction; and outputting the control instruction to an actuator so as to adjust the system state of the network hopping system. According to the method, the prediction model considering the network communication constraint is established, so that the stable control of the network jump system is realized.

Description

Technical Field

[0001] The present application relates to the technical field of networked control systems, and in particular to a network predictive control system and method based on network communication constraints. Background Art

[0002] With the rapid development of network technology, networked control systems (NCS) have been widely used in the field of industrial automation. Compared with the traditional point-to-point connection mode, NCS uses the network as a transmission medium, changes the signal transmission form between nodes, and connects the control system components located in different physical spaces, thereby breaking through the limitations of control location and control range, and realizing remote terminal control and resource sharing. However, the introduction of the network also brings uncertain factors such as network-induced delay, data packet loss, and denial of service attacks (DoS attacks), which have a great impact on the performance of the control system and may cause system performance degradation or even system crash.

[0003] Traditional network predictive control strategies are usually designed based on deterministic and static system models, and lack consideration of network characteristics. Therefore, they show limitations in dealing with network uncertainties and attack problems and are difficult to meet the needs of modern industrial control systems. Summary of the invention

[0004] The main purpose of this application is to provide a network predictive control system and method based on network communication constraints, aiming to solve the technical problem of how to improve the control performance and stability of the network jump system under network communication constraints.

[0005] To achieve the above objectives, an embodiment of the present application provides a network predictive control method based on network communication constraints, the method comprising: Acquire the state data of the network hopping system, and input the state data into the prediction model for prediction calculation, wherein the prediction model adopts a polyhedron model to describe the system hopping phenomenon, uses a Markov chain to describe the network delay, and a 0-1 distribution represents a DoS attack; Based on the prediction calculation results, a multi-step mode-dependent state feedback control law is adopted to generate a control instruction; The control instruction is output to the actuator to adjust the system state of the network hopping system.

[0006] In one embodiment, before the step of inputting the state data into the prediction model for prediction calculation, the step includes: Acquiring sampling data of the state vector, control input and system mode of the network hopping system; Based on the sampled data, determining matrix parameters of a time-varying system matrix and a time-varying input matrix; According to the sampling data and the matrix parameters, a state space equation of a discrete time stochastic switching system is constructed, wherein the state space equation is:

[0007] in, represents the system state vector; Represents system control input; Represents the system mode; Represent a time-varying system matrix with appropriate dimensions; represents a time-varying input matrix with appropriate dimensions; Indicates the initial system state; represents the initial mode; represents the time step in the discrete time domain; The prediction model is constructed by combining the state space equation with the polyhedron model, the network delay model based on Markov chain, and the DoS attack model based on 0-1 distribution.

[0008] In one embodiment, the step of combining the state space equation with the polyhedron model, the network delay model based on Markov chain, and the DoS attack model based on 0-1 distribution to construct the prediction model includes: Assumption 1: When the system state of the discrete-time stochastic switching system is completely measurable and the predictive controller acting on the discrete-time stochastic switching system has a control signal , so that the discrete-time random switching system remains stable at all times; According to the state space equation and the sampled data, the feedback signal of the predictive controller and control signals It is expressed as:

[0009] in, is the channel delay from the sensor to the prediction controller, is the channel delay from the prediction controller to the actuator; Based on the state space equation and the predictive controller, a discrete time random switching system considering time delay is obtained. The discrete time switching system considering time delay is expressed as:

[0010] in, represents the initial state, represents the initial delay, represents a nonlinear relationship, represents the total delay, i.e. .

[0011] In one embodiment, after the step of obtaining a discrete-time stochastic switching system considering time delay based on the state-space equation and the predictive controller, the method further includes: Based on the second assumption, the discrete-time switching system considering delay is updated to limit the total delay. The second assumption sets the channel delay from the sensor to the predictive controller and the channel delay from the predictive controller to the actuator to be respectively and The total delay at this time satisfies the following conditions:

[0012] in, Representatives in The minimum total delay at a given moment, Representatives in The maximum value of the total delay at a given moment; Assuming that the time delay follows a Markov random process, the random process is defined as The state space is a finite set The Markov chain, Decide Switching between delay values; When the total delay belongs to the state space set , constructing a Markov transition probability of a discrete delay jump, wherein the Markov transition probability is used to describe the random characteristics of the delay; Based on the Markov transition probability, the network delay influence in the discrete-time switching system considering delay is updated to obtain an updated discrete-time random switching system considering delay.

[0013] In one embodiment, after the step of obtaining the discrete-time random switching system considering the time delay, the following steps are included: Based on the discrete-time random switching system considering time delay, a set of DoS attacks is constructed, and the set of DoS attacks is expressed as:

[0014] in, is the number of times the discrete-time random switching system with time delay has been subjected to DoS continuous attacks, Indicates The start time of the DoS attack, Indicates The end time of the DoS attack; Determine the DoS attack time set of the discrete-time random switching system considering delay within the system operation time period, and calculate the discrete-time random switching system with delay at the The duration of the DoS attack; Based on the DoS attack time set and the attack duration, a 0-1 distribution is used to indicate whether the discrete-time random switching system with delay considered is under a DoS attack at any given time, wherein 1 indicates that the system is under attack and 0 indicates that the system is not under attack.

[0015] In one embodiment, the step of obtaining the status data of the network hopping system and inputting the status data into the prediction model for prediction calculation includes: Acquire the state vector of the network hopping system in real time through sensors; The state vector is input into the prediction model, and prediction calculation is performed to obtain a system state prediction result for at least one future time step.

[0016] In one embodiment, the step of generating a control instruction based on the prediction calculation result by using a multi-step mode-dependent state feedback control law includes: Based on the DoS attack and the network delay, a multi-step mode-dependent state feedback control law is designed. The expression of the multi-step mode-dependent state feedback control law is:

[0017] in, represents the control gain of the system mode dependence; Constructing an objective function of predictive control, wherein the objective function is used to optimize the multi-step mode-dependent state feedback control law; The objective function is transformed into an LMI optimization problem, and an optimal control sequence is determined by solving the LMI optimization problem.

[0018] In one embodiment, the step of converting the objective function into an LMI optimization problem and determining the optimal control sequence by solving the LMI optimization problem comprises: When the objective function satisfies a random convergence condition, an optimization problem in a finite time domain is obtained according to an upper bound of the objective function; After converting the optimization problem in the finite time domain into an LMI optimization problem, adding control input constraints and system state constraints, a solvable LMI optimization problem is obtained; The solvable LMI optimization problem is solved using an LMI tool to obtain an optimal control sequence.

[0019] In one embodiment, the step of outputting the control instruction to the actuator to adjust the system state of the network hopping system includes: When there is no DoS attack, the control input is executed in the order of control instructions corresponding to the optimal control sequence; During a DoS attack, a cache control sequence in the cache is selected to execute a control input.

[0020] The embodiment of the present application also provides a network prediction control system based on network communication constraints, the system comprising: A predictive controller unit, configured to receive system state measurements from sensors and reference inputs after network delay compensation, and calculate an optimal control sequence; A sensor unit, used to monitor the current state of the controlled object and return the monitoring result to the prediction controller; A buffer unit, used to store and process received control instructions to reduce the impact caused by network delay; The actuator unit is used to execute the control input on the controlled object according to the control instruction corresponding to the optimal control sequence received.

[0021] The embodiment of the present application discloses a network predictive control method based on network communication constraints, by acquiring the state data of the network jump system, inputting the state data into the prediction model for predictive calculation, wherein the prediction model uses a polyhedron model to describe the system jump phenomenon, uses a Markov chain to describe the network delay, and a 0-1 distribution represents a DoS attack; based on the prediction calculation results, a multi-step modal-dependent state feedback control law is used to generate control instructions; the control instructions are output to the actuator to adjust the system state of the network jump system. By establishing a prediction model that takes into account network communication constraints, the present application can accurately describe the system jump phenomenon, the random characteristics of the network delay, and the random characteristics of the DoS attack. Based on the prediction model, the control instructions are obtained and the control input is executed, so as to achieve stable control of the network jump system and improve the control performance and stability of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 It is a flowchart of a first embodiment of a network predictive control method based on network communication constraints involved in an embodiment of the present application; Figure 2 It is a structural block diagram of a networked control system under DoS attack and delay according to a first embodiment of a network predictive control method based on network communication constraints involved in an embodiment of the present application; Figure 3 A schematic diagram of a DoS attack sequence according to a first embodiment of a network prediction control method based on network communication constraints according to an embodiment of the present application; Figure 4 It is a schematic diagram of a network predictive control system based on network communication constraints in the second embodiment involved in the embodiment scheme of the present application; Figure 5 A schematic diagram of a single simulation result of controller I of the third embodiment of the network predictive control method based on network communication constraints involved in the embodiment of the present application; Figure 6 This is a schematic diagram of 100 numerical simulation results of the third embodiment of the network predictive control method based on network communication constraints under the action of controller I involved in the embodiment of the present application; Figure 7 This is a schematic diagram of 100 numerical simulation results of the third embodiment of the network predictive control method based on network communication constraints under the action of controller II involved in the embodiment scheme of the present application.

[0023] The purpose, features and advantages of this application will be further described in conjunction with the embodiments and with reference to the accompanying drawings. DETAILED DESCRIPTION

[0024] It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0025] With the rapid development of network technology, networked control systems (NCS) have been widely used in the field of industrial automation. Compared with the traditional point-to-point connection mode, NCS uses the network as a transmission medium, changes the signal transmission form between nodes, and connects the control system components located in different physical spaces, thereby breaking through the limitations of control location and control range, and realizing remote terminal control and resource sharing. However, the introduction of the network also brings uncertain factors such as network-induced delay, data packet loss, and denial of service attacks (DoS attacks), which have a great impact on the performance of the control system and may cause system performance degradation or even system crash.

[0026] Traditional network predictive control strategies are usually designed based on deterministic and static system models, and lack consideration of network characteristics. Therefore, they show limitations in dealing with network uncertainties and attack problems and are difficult to meet the needs of modern industrial control systems.

[0027] In order to solve the above-mentioned defects existing in the related art, the embodiment of the present application proposes a network predictive control method based on network communication constraints. The method obtains the state data of the network jump system and inputs the state data into the prediction model for predictive calculation, wherein the prediction model uses a polyhedron model to describe the system jump phenomenon, uses a Markov chain to describe the network delay, and a 0-1 distribution represents a DoS attack; based on the prediction calculation results, a multi-step modal-dependent state feedback control law is used to generate control instructions; the control instructions are output to the actuator to adjust the system state of the network jump system. By establishing a prediction model that takes into account network communication constraints, the present application can accurately describe the system jump phenomenon, the random characteristics of network delay, and the random characteristics of DoS attacks. Based on the prediction model, the control instructions are obtained and the control input is executed, so as to achieve stable control of the network jump system and improve the control performance and stability of the system.

[0028] For ease of understanding, the technical solutions in the embodiments of the present application will be described below in conjunction with the drawings in the embodiments of the present application.

[0029] The network predictive control method based on network communication constraints of the first embodiment proposed in this application can be found in Figure 1 The method comprises steps S10 to S30: Step S10: Acquire the status data of the network hopping system, and input the status data into the prediction model for prediction calculation, wherein the prediction model adopts a polyhedron model to describe the system hopping phenomenon, uses a Markov chain to describe the network delay, and a 0-1 distribution represents a DoS attack.

[0030] In this embodiment, in the structural framework of the network predictive control system, the characteristics of DoS (Denial of Service) attacks and network delays are taken into account, the random characteristics of network constraints are linked to the theory of random processes, the Markov chain is used to describe the delay, the polyhedron model is used to describe the jumping system phenomenon, the network jumping system is mathematically modeled, and a prediction model is obtained.

[0031] The polyhedron model is a mathematical model that can effectively handle system uncertainty, nonlinearity, and time-varying properties. The polyhedron model represents the state space of the system by constructing a polyhedron and restricting the state of the system within this polyhedron. Therefore, the polyhedron model can be used to capture the jump phenomenon of the system and effectively represent the dynamic changes and behavioral diversity of the system.

[0032] Markov chain is a mathematical model used to describe the state transition in a random process, where the transition between states is random and the transition probability is constant in time. In network predictive control systems, network delay is a key random variable that may affect the performance and stability of the system.

[0033] Specifically, the Markov chain can view network delay as a random process, in which the transition probability between delay values ​​is fixed in time. This means that if the network delay value at the current moment is known, the network delay value at the next moment can be predicted, and the prediction is based on the network delay value at the current moment and the known transition probability. By using the Markov chain to describe the random characteristics of network delay, the randomness and uncertainty of network delay can be reflected, which helps to understand and predict delay changes in the network environment.

[0034] In network predictive control systems, DoS attacks are a common network threat that prevents legitimate users from accessing services by exhausting system resources. 0-1 distribution is usually used to represent binary random variables, that is, an event either occurs (value 1) or does not occur (value 0). When describing the random characteristics of DoS attacks, 0-1 distribution can be used to represent whether a DoS attack occurs or not.

[0035] Specifically, assuming that a DoS attack is a random event, a 0-1 distribution can be used to indicate whether an attack occurs. If an attack occurs at a certain point in time, it is considered a successful attack event and recorded as 1; if an attack does not occur at a certain point in time, it is considered a failed attack event and recorded as 0. By using a 0-1 distribution to describe the random characteristics of a DoS attack, the randomness and uncertainty of a DoS attack can be reflected, which helps to understand and predict DoS attack behaviors in a network environment.

[0036] In an optional scheme, the state vector, control input and system mode sampling data of the network jump system are obtained. Based on the sampling data, the matrix parameters of the time-varying system matrix and the time-varying input matrix are determined. According to the sampling data and the matrix parameters, the state space of the system is defined, and the state space equation of a discrete time random switching system is established. Among them, the state space equation of the discrete time random switching system is as follows: (1-1) in, represents the system state vector; Represents system control input; Represents the system mode; Represent a time-varying system matrix with appropriate dimensions; represents a time-varying input matrix with appropriate dimensions; Indicates the initial system state; represents the initial mode; Represents the time step in the discrete time domain. The state space equation is combined with the polyhedron model, the network delay model based on the Markov chain, and the DoS attack model based on the 0-1 distribution to build a prediction model.

[0037] in, , , for Euclidean space.

[0038] It should be noted that the network jump system can be regarded as a special type of discrete-time random switching system, which is a widely studied control system whose state or parameters can randomly switch between finite or countably infinite modes. The "jump" of the network jump system refers to the sudden change of system parameters or system state, which may be due to changes in network communication constraints or other external factors. These "jumps" may affect the performance and stability of the system, so it is necessary to consider the impact of network communication constraints on system performance in the control design.

[0039] In an optional implementation scheme, a state space equation of a discrete-time stochastic switching system is established, and the state space equation is combined with the polyhedron model, the network delay model based on the Markov chain, and the DoS attack model based on the 0-1 distribution. The steps of constructing the prediction model include: Assumption 1: For system (1-1), the system state of the discrete-time random switching system is completely measurable, and there is a control signal , so that the discrete-time random switching system can remain stable at every moment.

[0040] System Matrix With uncertainty and time-varying, modal In a finite state space The system matrix is ​​contained in a matrix consisting of The set of vertices In the following form: (1-2) in, (1-3) in, is the subsystem mode; Represents the system matrix The characteristic value of and .

[0041] like Figure 2As shown, Figure 2 Figure 1 is a block diagram of the NCS (Networked Control System) structure under DoS attack and network delay. At each sampling moment, the state signal and control signal are transmitted in the form of data packets. Channel and The transmission is carried out on the channel. Channel represents the sensor to predictive controller channel, The channel represents the channel from the predictive controller to the actuator. The network layer considers the time-varying delay and defines and Respectively Channel delay and Channel delay and use timestamp technology in data packets to obtain the real-time delay of the system.

[0042] It should be noted that time-varying delay refers to the uncertainty of the time required for a data packet to travel from the sender to the receiver in the network. This delay may vary with factors such as network congestion, bandwidth changes, signal processing time, etc. It is not a fixed value. In control systems, time-varying delay may cause system performance degradation or even cause system instability.

[0043] Time stamp technology refers to the technology of adding time stamps to data packets in network control systems in order to measure and compensate for the time delay experienced by data packets in network transmission. When a data packet is time stamped when it is sent, the receiving end can calculate the transmission delay of the data packet in the network by comparing the difference between the current time and the time stamp after receiving the data packet. This technology helps to achieve more accurate network delay estimation, thereby providing real-time delay information for the control system, so as to carry out effective delay compensation and control strategy adjustment.

[0044] Based on assumption 1, the feedback signal on the controller side is predicted and control signals It can be expressed as: (1-4) in, is the channel delay from sensor to predictive controller, To predict the channel delay from the controller to the actuator, is the control signal of the actuator front end after time delay, is the control signal of the time-delayed prediction controller, is the feedback signal from the sensor before the delay. It is the feedback signal of the time-delayed predictive controller.

[0045] Set total delay , the state delay signal As a variable, a predictive controller acting on a discrete-time stochastic switching system is proposed. The predictive controller is nonlinear and the expression of the predictive controller is as follows: (1-5) in, express and The nonlinear relationship between According to the state space equation and the predictive controller, combined with equations (1-1) to (1-5), a type of discrete time random switching system considering time delay can be obtained. The discrete time random switching system considering time delay is expressed as: (1-6) in, represents the initial system state, represents the initial delay, represents a nonlinear relationship, represents the total delay, i.e. .

[0046] In an optional implementation, after obtaining the steps of a discrete-time stochastic switching system considering time delay according to the state-space equation and the predictive controller, hypothesis 2 is established. (channel delay from sensor to predictive controller) and (predicted controller to actuator channel delay) are respectively and The total delay at this time satisfies the following conditions: (1-7) in, Representatives in The minimum total delay at a given moment, Representatives in The maximum total delay at a given moment.

[0047] It should be noted that Assumption 2 is based on Assumption 1 and imposes the following restrictions on the total delay: first, setting the upper and lower limits of the total delay; second, setting the delay to obey the Markov random process.

[0048] Although the delay caused by network communication is random, it is usually related to past delays and follows a certain probability distribution. Therefore, if the delay is assumed to follow a Markov random process, the random process is defined as The state space is a finite set The Markov chain, Decide When the total delay belongs to the state space set , construct the Markov transition probability of discrete delay jump, Markov transition probability is used to describe the random characteristics of delay. Based on Markov transition probability, update the network delay impact in the discrete time switching system considering delay, and obtain the updated discrete time random switching system considering delay.

[0049] It should be noted that Represents the set of positive integers.

[0050] Specifically, for , the Markov transition probability of discrete delay jump is defined as follows: (1-8) in, , , It means to find the probability.

[0051] Optionally, to better reflect engineering practice, we further consider the hard constraints on the control input variables and system state variables of the system (1-6): (1-9) (1-10) in, Represents the maximum value of the control input variable; Represents the maximum value of the system state variable.

[0052] In an optional implementation, after obtaining the step of a discrete-time random switching system taking into account the time delay, the DoS attack sequence is described and the DoS attack model is determined. Send a data packet, start of DoS attack and sampling time Due to the DoS attack, the system status signal will intermittently reach the predictive controller. The DoS attack sequence is as follows: Figure 3 As shown, the definition is the number of times the discrete-time random switching system with delay has been subjected to continuous DoS attacks.

[0053] At this time, for the sampling time Considering the time delay of the discrete-time random switching system, we construct a set of DoS attacks. The set of DoS attacks in the discrete time domain is expressed as: (1-11) in, is the number of times the discrete-time random switching system with time delay has been subjected to DoS continuous attacks, Indicates The start time of the DoS attack, Indicates The end time of the DoS attack. represents the set of positive integers, Represents the system running time in the discrete time domain.

[0054] Determine the DoS attack time set of the discrete-time random switching system with time delay within the system operation time period, and calculate the discrete-time random switching system with time delay in the The attack duration during this DoS attack.

[0055] Based on the DoS attack time set and attack duration, a 0-1 distribution is used to indicate whether the discrete-time random switching system with delay is under DoS attack at any given time, where 1 indicates that the system is under attack and 0 indicates that the system is not under attack.

[0056] Specifically, during the system operation period The DoS attack time set is recorded as: (1-12) System At this moment, the DoS attacker The attack duration during the DoS attack is expressed as: (1-13) Considering the case where the DoS attack energy is limited, the duration of the DoS attack is defined to satisfy the following inequality: (1-14) in, Indicates The duration from the start to the end of a DoS attack, Indicates the maximum duration of a DoS attack.

[0057] Optionally, in a network predictive control system, the state of the network hopping system changes over time, so a mathematical model is needed to describe this change. The prediction model in this embodiment is established based on a polyhedron model, a Markov chain, and a 0-1 distribution, and the prediction model can accurately describe the uncertainty factors in the network environment, such as network delay and DoS attacks.

[0058] Based on this prediction model, the system state prediction equation of the network hopping system can be determined. The system state prediction is a mathematical expression that defines the law of change of the system state over time. By establishing a state prediction equation, the future state of the network hopping system can be predicted, and the corresponding network prediction control strategy can be formulated according to the prediction results.

[0059] In an alternative implementation, according to the discrete-time random switching system (1-6) considering time delay, for any time , based on the state vector obtained at the sensor end , the system state prediction equation of the network jump system is expressed as: (1-15) in, and Respectively expressed in Moment based on state of step-by-step predicted states and predicted control inputs.

[0060] It should be noted that according to The state at a certain moment predicts the subsequent Step status, that is The state of the moment.

[0061] Based on the discrete-time random switching system (1-6) considering time delay, through multiple iterations, the system state prediction equation can be further expressed as: (1-16) Considering DoS attacks and delay characteristics, define the predictive control step size Satisfies the following expression: (1-17) That is, the prediction interval must be at least one time step longer than the control interval. Indicated in The maximum value of the total delay at time , that is, the upper bound of the total delay; Indicates the maximum duration of a DoS attack.

[0062] Optionally, the step of obtaining the state data of the network hopping system and inputting the state data into the prediction model for prediction calculation includes: obtaining the state vector of the network hopping system in real time through a sensor, inputting the state vector into the prediction model, performing prediction calculation, and obtaining a system state prediction result for at least one future time step.

[0063] It should be noted that the state data acquisition of the network hopping system is achieved through real-time monitoring and collection of the current state of the system, which is the basis for effective prediction and control. As a device for information collection, the sensor can capture the state vector of the system, which contains key information describing the dynamic behavior of the system. These state vectors are input into the prediction model, which will perform prediction calculations based on the random characteristics of historical data and network communication constraints to predict the system state within at least one time step in the future. By obtaining the results of the prediction calculation, the controller can know the future state of the system in advance, so as to make corresponding decisions and adjustments to deal with possible network delays or system uncertainties and ensure the stability and performance of the system.

[0064] Step S20: Based on the prediction calculation result, a multi-step modal-dependent state feedback control law is adopted to generate a control instruction.

[0065] Based on the existence of DoS attacks and network delays in network communications, the design adopts a multi-step mode-dependent state feedback control law. The expression of the multi-step mode-dependent state feedback control law is as follows: (1-18) in, represents the control gain of the system mode dependence.

[0066] The objective function of the predictive control is constructed, and the objective function is used to optimize the multi-step modal-dependent state feedback control law. The objective function is converted into an LMI optimization problem, and the optimal control sequence is determined by solving the LMI optimization problem.

[0067] Specifically, in combination with the model predictive control theory, the expected objective function expression in the infinite time domain proposed in this embodiment is: (1-19) in, and is a positive definite symmetric weight constant matrix of appropriate dimension, represents the mathematical expectation, Represents a quadratic form.

[0068] It should be noted that Model Predictive Control (MPC) is a control strategy, the core of which is to use the system's prediction model to optimize control actions, so as to achieve the optimization of system performance while satisfying various network communication constraints. This control strategy first measures the current state of the system in real time through sensors, and then inputs these state data into the prediction model, which predicts the behavior of the system in the future based on the dynamic characteristics of the system. Next, based on these prediction results, MPC solves an optimization problem that aims to minimize a cost function that includes system performance indicators and constraints. During the optimization process, MPC not only considers the current system state, but also future control actions and system responses, so that control strategies can be planned in advance.

[0069] When implementing control, MPC uses a rolling horizon strategy, which means that in each control cycle, although the optimization problem will obtain a control input sequence for a period of time in the future, only the first element in the sequence, that is, the control action of the next control cycle, is actually executed. Subsequently, the system enters the next control cycle, re-measures the current state, updates the prediction model, and re-solves the optimization problem. This rolling optimization method enables MPC to adapt to changes in system states and the impact of external disturbances in real time, thereby maintaining system stability and high performance.

[0070] Specifically, we further combine the expected objective function (1-19) in the infinite time domain and the following constraints to construct the optimization problem: It is expressed as:

[0071] (1-20) in, represents the invariant set of time-varying terminal constraints, and the prediction time domain step size is step, then the control prediction step length is step, that is, the prediction step size is always larger than the control step size.

[0072] By solving the above optimization problem , we can get the following optimal predictive control sequence: (1-21) exist time, Indicates that there is no DoS attack at this time, and the executor is based on the delay The value from the optimal predictive control sequence Select Control input. time, Indicates that there is a DoS attack at this time, defining the time Indicates The moment before the DoS attack occurs. value, the executor executes the predictive control sequence from the most recently updated and select control input In the next At this moment, the controller will re-solve the optimization problem based on the newly received system state and prediction information to obtain the optimal prediction control sequence. Therefore, the improvement of the prediction controller is as follows: (1-22) In network predictive control systems, the objective function of predictive control needs to consider the state constraints and control input constraints of the network jump system.

[0073] It should be noted that the state constraint refers to the restriction of the system state within a certain range, while the control input constraint refers to the restriction of the control signal applied to the system.

[0074] Since the optimization problem (1-20) involves solving the control variables at infinite future times , which is generally difficult to solve accurately. Therefore, it is necessary to transform the optimization problem (1-20) into a solvable optimization problem.

[0075] First, we need to find the objective function By optimizing this upper bound of the objective function, we can approximate the expected objective function in the infinite time domain. . The original optimization problem is transformed into an LMI optimization problem, so that it can be solved using the LMI tool in MATLAB. In order to achieve the design of a networked predictive controller under DoS attacks and time delays, the following conditions must be met one by one, and the controller must be further designed.

[0076] It should be noted that the LMI tool is a toolbox in MATLAB software for solving linear matrix inequality problems. It provides various solvers that can effectively solve LMI problems. By using the LMI tool, the optimal control sequence can be obtained, which can be used to adjust the state of the network jump system to achieve the optimal control effect.

[0077] Optionally, the objective function is converted into an LMI optimization problem, and the step of determining the optimal control sequence by solving the LMI optimization problem includes: when the objective function satisfies a random convergence condition, an optimization problem in a finite time domain is obtained according to an upper bound of the objective function. After converting the optimization problem in the finite time domain into an LMI optimization problem, control input constraints and system state constraints are added to obtain a solvable LMI optimization problem. The solvable LMI optimization problem is solved using an LMI tool to obtain an optimal control sequence.

[0078] Specifically, when the objective function satisfies the random convergence condition, an optimization problem in a finite time domain is obtained according to the upper bound of the objective function, wherein the random convergence condition includes the following conditions 1 to 3: Condition 1: Let , and consider the random Lyapunov function of system mode and time delay dependence: (1-23) (1-24) when When , under the multi-step mode-dependent state feedback control law (1-18), in order to ensure that the system can stably converge to the desired state, the closed-loop system must satisfy the following random convergence conditions: (1-25) According to formula (1-25), from arrive It is expressed as: (1-26) According to the mean square stability theorem, if the system satisfies the closed-loop mean square stability, it means that ,therefore . Superimposing the above inequalities (1-26) yields: (1-27) Then, the upper bound of the objective function in infinite time domain can be regarded as an objective function with a terminal invariant set in finite time domain: (1-28) Condition 2: From arrive The objective function satisfies the following inequality: (1-29) Condition 3: When When the time-varying terminal constraint invariant set It is expressed as: (1-30) Then, when the objective function satisfies the random convergence condition, that is, combining conditions 1 to 3 and formula (1-27), the upper bound of the objective function can be obtained as: (1-31) According to the above conditions 1 to 3, the objective function and the upper bound of the objective function, the optimization problem in the finite time domain can be obtained as follows:

[0079] (1-32) Theorem 1.1: For the discrete-time stochastic switching system (1-6) under DoS attack and time delay, if , , The set of positive definite symmetric matrices Existence, positive definite matrix , If the following inequality holds, then the system (1-6) is stochastically convergent.

[0080] (1-33) in,

[0081] Through the following proof process, we obtain the above conditions 1 to 3 and formula (1-33), and prove Theorem 1.1: when season , by differentiating equation (1-23) and equation (1-24), we get: (1-34) If for any Formula (1-25) satisfies condition 1 if and only if formula (1-34) satisfies the following formula: (1-35) make Substituting into formula (1-35) we get: (1-36) in, Representation Matrix The inverse of.

[0082] Using Schur's complement lemma, equation (1-36) is transformed into the following LMI optimization problem: (1-37) It should be noted that the Schur complement lemma is an important tool in matrix theory, providing a method to decompose a large matrix into several smaller matrices that are easier to handle and analyze. Specifically, for a given block matrix, if a submatrix can be found, called the Schur complement, then certain properties of the original matrix, such as positive definiteness or invertibility, can be determined by this Schur complement.

[0083] Next, the diagonal matrix Multiply both sides of equation (1-37). Based on Lemma 1.2, we know , we can get formula (1-33), and the proof of Theorem 1.1 is completed.

[0084] It should be noted that Indicates is a diagonal matrix with main diagonal elements.

[0085] Lemma 1.2: For a real symmetric positive definite matrix of appropriate dimension , , the following conditions hold:

[0086] Proof: Because ,so:

[0087] Specifically, according to condition 3, we know that time, is the invariant set of time-varying terminal constraints of the system (1-6) under the multi-step mode-dependent state feedback control law (1-18). This means that as long as , just satisfy , if and only if the following inequality is satisfied: If the following conditions are met: (1-39) Formula (1-38) can be guaranteed.

[0088] (1-38) It should be noted that when equation (1-35) is true, by moving its terms, we can see that equation (1-39) is also true. Therefore, equation (1-33) already contains this condition.

[0089] In the prediction time domain During this period, the inequality conditions (1-33) and (1-39) derived above guarantee the random convergence of the system under the multi-step mode-dependent state feedback control law (1-18) and that all predicted states will be in the terminal invariant set. The satisfaction of formula (1-39) also ensures that ,ensure Strictly decreasing, ensuring recursive feasibility while reducing the conservatism of the design.

[0090] According to the MPC principle, equation (1-29) of condition 2 and equation (1-30) of condition 3 can be expressed as: (1-40) (1-41) in, According to the predictive control principle, it can be deduced that , , , The system parameters are given by , composition.

[0091] Using Schur's complement lemma, equations (1-40) and (1-41) can be transformed into the following LMI optimization problems: (1-42) (1-43) After converting the finite time domain optimization problem into an LMI optimization problem, control input constraints and system state constraints are added to obtain a solvable LMI optimization problem.

[0092] Specifically, the control input constraints (1-9) and state constraints (1-10) are solved according to the multi-step modal-dependent state feedback control law (1-18) and converted into a solvable LMI form.

[0093] (1) Control input constraints: exist Moment, when arrive When , the control input constraint condition is equivalent to the following inequality: (1-44) in, Represents a symmetric term in a square matrix.

[0094] for , assuming the following inequality holds: (1-45) Combining equations (1-18) and (1-30), it can be proved that equation (1-45) satisfies the control input constraint. The proof is as follows: (1-46) Use Schur's complement lemma to transform equation (1-45), and then multiply the left and right sides of the transformed equation by the diagonal matrix , and combined with Lemma 1.2, then Equation (1-45) can be transformed into the following LMI: (1-47) (2) System state constraints: exist Moment, combined formula (1-40), when arrive , the system state constraint condition is equivalent to the following inequality: (1-48) when , assuming the following inequality holds: (1-49) Combining equations (1-18) and (1-30), we can see that equation (1-49) satisfies the system state constraint, as shown below: (1-50) Use Schur's complement lemma to transform equation (1-50) and multiply the left and right sides of the transformed equation by the diagonal matrix , and combined with Lemma 1.2, Equation (1-50) can be transformed into the following LMI: (1-51) according to And Theorem 1.1, after the above derivation, the MPC optimization problem with system state constraints and control input constraints can be further expressed as:

[0095] (1-52) Step S30: outputting the control instruction to the actuator to adjust the system state of the network hopping system.

[0096] In actual scenarios, predictive control methods usually require a high amount of computing for data analysis and prediction. However, traditional predictive control requires real-time solutions at every moment, which increases the computing burden of the system, causing the system to respond more slowly and even fail to meet real-time requirements.

[0097] Therefore, in the predictive control of the NCS system under DoS attack and delay studied in this embodiment, when there is no DoS attack, the predictive controller receives the latest state quantity and solves the optimization problem to obtain the optimal control sequence, and then executes the control input in sequence according to the control instruction sequence of the optimal control sequence, and transmits it to the cache through the network channel. During the DoS attack, the controller will not solve the optimization problem, and will select the appropriate cache control sequence to execute the control input according to the real-time state of the system through the cache control sequence in the cache, that is, select the control quantity suitable for the current system state to act on the controlled object.

[0098] Optionally, the step of outputting control instructions to the actuator to adjust the system state of the network hopping system includes: when there is no DoS attack, executing the control input in sequence according to the control instructions corresponding to the optimal control sequence; during the DoS attack, selecting the cache control sequence in the cache to execute the control input.

[0099] The network predictive control algorithm in this embodiment not only realizes active compensation of the system when DoS attacks and time delays occur, but also greatly reduces the computational burden of the control system.

[0100] Please refer to Figure 4 The second embodiment of the network predictive control system proposed in this application is based on network communication constraints. The system includes a predictive controller unit, a sensor unit, a buffer unit and an actuator unit. The above four units work together to achieve stable control of the controlled object under the condition of network communication constraints. Specifically: The predictive controller unit is used to receive the system state measurement values ​​from the sensor and the reference input after network delay compensation, calculate the optimal control sequence, and transmit it to the remote buffer through the network.

[0101] The sensor unit is used to monitor the current state of the controlled object and return the monitoring result to the prediction controller.

[0102] It should be noted that in a predictive control system, the controlled object may be any equipment, process or control system that requires state control.

[0103] The buffer unit is used to store and process the received control instructions to reduce the impact of network delay. Due to the existence of network delay, the buffer unit can temporarily store control instructions and data until they can be processed, thereby reducing the impact of network delay and ensuring the accuracy and timeliness of control instructions.

[0104] The actuator unit is used to execute the control input on the controlled object according to the control instruction corresponding to the optimal control sequence received.

[0105] The network predictive control method based on network communication constraints of the third embodiment proposed in the present application also includes a mean square stability analysis of the system under the action of solving the optimization problem (1-52).

[0106] The mean square stability of the system under the action of solving the optimization problem (1-52) is given by the following theorem.

[0107] Theorem 1.3: Consider the uncertain system (1-6), if at the initial time For the initial state and initial delay The optimization problem (1-52) has a feasible solution. Then the optimization problem (1-52) is If there is a feasible solution at all times, the predictive control algorithm obtained based on Theorem 1.1 can ensure the mean square stability of the closed-loop system.

[0108] Proof: First, we prove the recursive feasibility of the control strategy. At this moment, assuming that there is an optimal solution to the optimization problem (1-52), the optimal solution is expressed as follows: (1-53) in,

[0109] According to the network prediction control strategy proposed in the above embodiment, when and When a DoS attack occurs, the optimal prediction control sequence in the cache is selected according to the DoS attack time and delay. , select the appropriate control quantity to act on the controlled object. Now define yes The feasible solution at this moment is as follows: (1-54) in,

[0110] By making the feasible solution Substituting into the optimization problem (1-52) all satisfies the constraints, indicating that is a feasible solution to the optimization problem. Therefore, if at the initial moment The optimization problem (1-52) has a feasible solution. Then the optimization problem (1-52) is There is a feasible solution at all times. Therefore, it can be proved that the proposed network predictive control strategy is recursively feasible.

[0111] Here is the proof of the stability of the closed-loop system: when , and make expectations on both sides of equation (1-25) to obtain: (1-55) Because the optimal solution satisfies the following constraints: (1-56) Combining equations (1-53), (1-54) and (1-56), we get: (1-57) According to the optimization principle, after optimization Will be in The time is further reduced. Therefore, we can further obtain: (1-58) Because the random process is a non-negative supermartingale process, based on formula (1-58) from arrive Summing gives: (1-59) so Greater than 0 and has an upper limit.

[0112] Therefore, we can get: (1-60) because and are all positive definite matrices, and we can further obtain: (1-61) therefore , proving that the closed-loop system is mean-square stable.

[0113] For example, in this embodiment, based on the state control equation (1-6) of NCS, a network predictive control strategy (1-52) is adopted to actively compensate the networked system, and the effectiveness and superiority of the proposed network predictive control strategy in the network hopping system under DoS attack and delay are verified through numerical simulation and comparative simulation.

[0114] Consider a discrete network hopping system with three modes:

[0115] By calculating the poles of the system matrix, we can see that all three systems are unstable. Consider the above control system and set the weight matrix coefficients to , , , , set the maximum time span of DoS attack according to the DoS model .

[0116] Assume that the minimum delay is , the maximum value is , then the transition probability of random delay is:

[0117] in, and .

[0118] Write the control algorithm program in MATLAB. Given the initial state vector of the system is By solving equation (1-52), the control gain of the system for the first time can be obtained as:

[0119] Exemplarily, the predictive controller of the network predictive control strategy designed based on the above embodiment is referred to as controller I. Figure 5 represents the single simulation result of controller I. Among them, Figure 5 (a)-(b) represent the system state and control input constraints under a single simulation. Figure 5 (c)-(d) represent the optimal values ​​of a single optimization problem and Curves,(c)-(d) represent the upper bound of the objective function. Figure 5 (e)-(g) represent the duration of DoS attack at each time of the system. , Delay and system modality , that is, (e)-(g) correspond to the DoS attack sequence, delay sequence, and system modal sequence, respectively.

[0120] from Figure 5 It can be seen that the network hopping system can achieve stable control of the system under the action of controller I in the case of system mode hopping, DoS attack and time delay.

[0121] In order to further fully discuss the effectiveness of the predictive controller, another predictive controller is introduced as a comparison object, referred to as controller II. The DoS sequence, delay sequence, and modal sequence in the same comparison simulation are the same for controller I and controller II. In order to eliminate uncertainty, both predictive controllers are simulated 100 times.

[0122] In order to make the simulation results more intuitive, the data of 100 simulation results are analyzed and processed. Figure 6 The red curve in (m) represents the average state response in 100 numerical simulations under the action of controller I; the green dotted line and the blue dotted line represent the best state response and the worst state response in 100 numerical simulation experiments, respectively. Figure 6(n) represents the system state response of the superposition of 100 numerical simulation results under the action of controller I. Figure 7 (p)-(q) are the system state response results in 100 numerical simulations under the action of controller II. Figure 6 and Figure 7 It can be clearly seen that the performance of controller I is better than that of controller II. In the results of 100 simulation experiments, when running for 30 time steps, under the action of controller II, the absolute value of the system state response was less than 0.01 only 3 times. Under the same conditions, when controller I was in action, the absolute value of the system state response was less than 0.01 92 times. Figure 6 and Figure 7 It can be seen from the comparison that when controller I is in effect, the system has higher stability against uncertainty. Figure 6 and Figure 7 The simulation results comparison of different controllers can be obtained in Appendix Table 1.

[0123] Appendix 1 System stability comparison results of controller Ⅰ and controller Ⅱ

[0124] Numerical simulation results show that the network predictive control strategy proposed in the present invention can not only actively compensate for the impact of DoS attacks and delays in real time, but also has obvious advantages in improving system response speed and stability.

[0125] The above are only preferred embodiments of the present application, and are not intended to limit the patent scope of the present application. Any equivalent structure or equivalent process transformation made using the contents of the present application specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent processing scope of the present application.

[0126] It should be noted that, in this article, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or system including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or system. In the absence of further restrictions, an element defined by the sentence "comprises a ..." does not exclude the existence of other identical elements in the process, method, article or system including the element.

[0127] Through the description of the above implementation methods, those skilled in the art can clearly understand that the above embodiment methods can be implemented by means of software plus a necessary general hardware platform, and of course by hardware, but in many cases the former is a better implementation method.

[0128] The above are only preferred embodiments of the present application, and are not intended to limit the patent scope of the present application. Any equivalent structure or equivalent process transformation made using the contents of the present application specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present application.

Claims

1. A network predictive control method based on network communication constraints, characterized in that: The method comprises: Acquire the state data of the network hopping system, and input the state data into the prediction model for prediction calculation, wherein the prediction model adopts a polyhedron model to describe the system hopping phenomenon, uses a Markov chain to describe the network delay, and a 0-1 distribution represents a DoS attack; Based on the prediction calculation results, a multi-step mode-dependent state feedback control law is adopted to generate a control instruction; The control instruction is output to the actuator to adjust the system state of the network hopping system.

2. The method according to claim 1, characterized in that Before the step of inputting the state data into the prediction model for prediction calculation, the method includes: Acquiring sampling data of the state vector, control input and system mode of the network hopping system; Based on the sampled data, determining matrix parameters of a time-varying system matrix and a time-varying input matrix; According to the sampling data and the matrix parameters, a state space equation of a discrete time stochastic switching system is constructed, wherein the state space equation is: in, represents the system state vector; Represents system control input; Represents the system mode; Represent a time-varying system matrix with appropriate dimensions; represents a time-varying input matrix with appropriate dimensions; Indicates the initial system state; represents the initial mode; represents the time step in the discrete time domain; The prediction model is constructed by combining the state space equation with the polyhedron model, the network delay model based on Markov chain, and the DoS attack model based on 0-1 distribution.

3. The method according to claim 2, characterized in that The step of combining the state space equation with the polyhedron model, the network delay model based on Markov chain, and the DoS attack model based on 0-1 distribution to construct the prediction model includes: Assumption 1: When the system state of the discrete-time stochastic switching system is completely measurable and the predictive controller acting on the discrete-time stochastic switching system has a control signal , so that the discrete-time random switching system remains stable at all times; According to the state space equation and the sampled data, the feedback signal of the predictive controller and control signals It is expressed as: in, is the channel delay from the sensor to the prediction controller, is the channel delay from the prediction controller to the actuator; Based on the state space equation and the predictive controller, a discrete time random switching system considering time delay is obtained. The discrete time switching system considering time delay is expressed as: in, represents the initial state, represents the initial delay, represents a nonlinear relationship, represents the total delay, i.e. .

4. The method according to claim 3, characterized in that After the step of obtaining a discrete-time random switching system considering time delay based on the state-space equation and the predictive controller, the method further includes: Based on the second assumption, the discrete-time switching system considering delay is updated to limit the total delay. The second assumption sets the channel delay from the sensor to the predictive controller and the channel delay from the predictive controller to the actuator to be respectively and The total delay at this time satisfies the following conditions: in, Representatives in The minimum total delay at a given moment, Representatives in The maximum value of the total delay at a given moment; Assuming that the time delay follows a Markov random process, the random process is defined as The state space is a finite set The Markov chain, Decide Switching between delay values; When the total delay belongs to the state space set , constructing a Markov transition probability of a discrete delay jump, wherein the Markov transition probability is used to describe the random characteristics of the delay; Based on the Markov transition probability, the network delay influence in the discrete-time random switching system considering delay is updated to obtain an updated discrete-time random switching system considering delay.

5. The method according to any one of claims 3 to 4, characterized in that After the step of obtaining the discrete-time random switching system considering the time delay, the method further comprises: Based on the discrete-time random switching system considering time delay, a set of DoS attacks is constructed, and the set of DoS attacks is expressed as: in, is the number of times the discrete-time random switching system with time delay has been subjected to DoS continuous attacks, Indicates The start time of the DoS attack, Indicates The end time of the DoS attack; Determine the DoS attack time set of the discrete-time random switching system considering delay within the system operation time period, and calculate the discrete-time random switching system with delay at the The duration of the DoS attack; Based on the DoS attack time set and the attack duration, a 0-1 distribution is used to indicate whether the discrete-time random switching system with delay considered is under a DoS attack at any given time, wherein 1 indicates that the system is under attack and 0 indicates that the system is not under attack.

6. The method according to claim 1, characterized in that The step of obtaining the status data of the network hopping system and inputting the status data into the prediction model for prediction calculation comprises: Acquire the state vector of the network hopping system in real time through sensors; The state vector is input into the prediction model, and prediction calculation is performed to obtain a system state prediction result for at least one future time step.

7. The method according to claim 1, characterized in that The step of generating a control instruction based on the prediction calculation result by adopting a multi-step mode-dependent state feedback control law comprises: Based on the DoS attack and the network delay, a multi-step mode-dependent state feedback control law is designed. The expression of the multi-step mode-dependent state feedback control law is: in, represents the control gain of the system mode dependence; Constructing an objective function of predictive control, wherein the objective function is used to optimize the multi-step modal-dependent state feedback control law; The objective function is transformed into an LMI optimization problem, and the optimal control sequence is determined by solving the LMI optimization problem.

8. The method according to claim 7, characterized in that The step of converting the objective function into an LMI optimization problem and determining the optimal control sequence by solving the LMI optimization problem comprises: When the objective function satisfies the random convergence condition, an optimization problem in a finite time domain is obtained according to the upper bound of the objective function; After converting the optimization problem in the finite time domain into an LMI optimization problem, adding control input constraints and system state constraints, a solvable LMI optimization problem is obtained; The solvable LMI optimization problem is solved using an LMI tool to obtain an optimal control sequence.

9. The method according to claim 1, characterized in that The step of outputting the control instruction to the actuator to adjust the system state of the network hopping system includes: When there is no DoS attack, the control input is executed in the order of control instructions corresponding to the optimal control sequence; During a DoS attack, a cache control sequence in the cache is selected to execute a control input.

10. A network predictive control system based on network communication constraints, characterized in that: The system comprises: A predictive controller unit, configured to receive system state measurements from sensors and reference inputs after network delay compensation, and calculate an optimal control sequence; A sensor unit, used to monitor the current state of the controlled object and return the monitoring result to the prediction controller; A buffer unit, used to store and process received control instructions to reduce the impact caused by network delay; The actuator unit is used to execute the control input on the controlled object according to the control instruction corresponding to the optimal control sequence received.

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