Switching system output feedback control method based on dynamic event trigger mechanism and polling protocol

Abstract

The invention discloses a switching system output feedback control method based on a dynamic event trigger mechanism and a polling protocol, and relates to the technical field of networked switching system control. The method comprises the following steps: establishing a continuous time linear system model; designing a dynamic event triggering mechanism to save network resources, and applying the dynamic event triggering mechanism to a sensor-controller network channel; a polling protocol is adopted for communication scheduling, and data conflicts in a controller-actuator network channel are avoided; and designing a dynamic output feedback controller. Through the design of the dynamic event triggering mechanism, the polling protocol and the dynamic output feedback controller, the communication and control problems of the networked switching system under network congestion and data collision are solved. The core contribution of the method is that unnecessary communication is reduced, and network resources are saved; the data collision is avoided, and the communication reliability is improved. The technologies and methods provide important guarantee for safe and reliable operation of the networked switching system in a complex communication environment.

Description

Technical Field

[0001] The present invention relates to the technical field of the control of networked switching systems, and particularly to an output feedback control method for a switching system based on a dynamic event-triggering mechanism and a polling protocol. Background Art

[0002] As an important class of hybrid systems, switching systems can be used to describe systems with complex dynamic characteristics in actual engineering. Its characteristic is that the system consists of a finite number of dynamic models and a set of switching rules. Introducing network communication into the switching system, making the communication network embedded in the switching system as a system link, and components such as sensors, controllers, and actuators all operate in a network environment to provide data transmission between components. This type of system is called a networked switching system. With the rapid development of network technology, networked switching systems are increasingly widely used in industrial automation, intelligent transportation, remote medical treatment and other fields. However, networked switching systems face problems such as network congestion and data collision during actual operation, which may lead to a decline in system performance or even failure. Once a safety problem occurs in a networked control system, it will cause huge economic losses. Therefore, for networked switching systems, it is of great significance to study how to overcome the influence of other communication-limited problems on the premise of saving network resources.

[0003] To solve the above problems, researchers have proposed an event-triggering mechanism, which reduces unnecessary network transmissions by communicating only when the system state reaches a specific condition. Compared with the time-triggering mechanism, the event-triggering mechanism can effectively reduce the number of data transmissions and save network resources. The traditional static event-triggering mechanism uses a fixed threshold, while the dynamic event-triggering mechanism adjusts the triggering condition according to the dynamic state of the system, further improving the flexibility and efficiency of the system. In addition, according to the polling protocol, at each transmission moment, there is and only one communication node accessing the network for transmission, thus avoiding data conflicts. However, how to ensure the safe and reliable operation of a networked switching system under the polling protocol while adopting the event-triggering mechanism remains a major challenge. Summary of the Invention

[0004] The purpose of the present invention is to provide an output feedback control method for a switching system based on a dynamic event-triggering mechanism and a polling protocol to solve problems such as network congestion, data collision, and waste of communication resources existing in the prior art. This method optimizes the utilization of network resources through the combination of a dynamic event-triggering mechanism and a polling protocol to ensure the safe and reliable operation of a networked switching system.

[0005] To achieve the above purpose, the technical solution of the present invention is as follows:

[0006] Step 1. Establish a continuous-time linear system model: Construct a mathematical model of the networked switched system, including subsystem, sensor, controller, and actuator components.

[0007] Step 2. Design a dynamic event-triggering mechanism: Introduce a dynamic event-triggering mechanism in the sensor-controller network channel to reduce unnecessary communications.

[0008] Step 3. Adopt a polling protocol for communication scheduling: Use a polling protocol in the controller-actuator network channel to avoid data conflicts.

[0009] Step 4. Design a dynamic output feedback controller: Based on the dynamic event-triggering mechanism and the polling protocol, design a dynamic output feedback controller.

[0010] Step 5. Obtain an enhanced system: Verify the effectiveness of the designed control method through simulation or experiment, and optimize and adjust according to the actual operating conditions.

[0011] Furthermore, the establishment of the system model in Step 1 is in the specific form of:

[0012]

[0013] where \(x(t)\in\mathbb{R}^{n}\) n and \(u(t)\in\mathbb{R}^{m}\) q are the state vector and control input of the system respectively, and \(y(t)\in\mathbb{R}^{p}\) s is the measured output. describes the rate of change of the system state with time. \(A\in\mathbb{R}^{n\times n}\) σ(t) \(B\in\mathbb{R}^{n\times m}\) n×n , \(C\in\mathbb{R}^{p\times n}\) σ(t) are matrices with appropriate dimensions. The switching signal \(\sigma(t)\) maps time \(t\) to a set of subsystem indices n×q where σ(t) \(H = \{1,2,\cdots,N\}\) s×n represents the total number of subsystems. When \(\sigma(t)=l\) and \(l\in H\), subsystem \(l\) is activated. where denotes the total number of subsystems. When \(\sigma(t)=l\) and \(l\in H\), subsystem \(l\) is activated.

[0014] Furthermore, the application of the dynamic event-triggering mechanism in the sensor-controller network channel in Step 2 to save network resources is in the specific form of:

[0015] \(l\) k+1 \(h = l\) k \(h+\inf\{l_h|\eta(l\) k \(h + \iota_h)+\theta(\alpha_y\) T \((l\) k \(h+\iota_h)\Omega\) σ(t) \(y(l\) k \(h+\iota_h)\)

[0016] -e T (l k (l + ιh)Ω σ(t) e(l k e(l + ιh)) ≤ 0}

[0017] where l k h is the current event triggering time, and l k+1 h is the next triggering time after l k h, and y(l k h) and y(l k (l + ιh) are the most recently transmitted output and the currently sampled output respectively, and e(l k (l + ιh) = y(l k h) - y(l k (l + ιh) is the error vector. θ > 0 is a given constant, and α is a given triggering threshold. Ω σ(t) > 0 is the event-triggering weight matrix. The internal dynamic variable η(t) satisfies the following conditions:

[0018]

[0019] where β ∈ (0, 1) is a given scalar.

[0020] Further explanation:

[0021] (1) Compared with the fixed triggering threshold, the dynamic event-triggering mechanism can adjust the triggering threshold according to the changes in the system state and output error by introducing the dynamic variable η(t) and adjusting the parameter θ, so as to optimize the system behavior and avoid over-triggering or under-triggering.

[0022] (2) Introducing the mode-dependent event-triggering weight matrix Ω σ(t) and the variable threshold α increases the design freedom and flexibility. Adjusting the parameter θ can affect the weights of the output and error in the triggering condition. A larger θ value will make the system more sensitive to changes, resulting in more frequent event triggers, thus improving the responsiveness, but also increasing the use of communication and network resources.

[0023] (3) It can be seen from the formula that the time interval between two consecutive triggering events is not less than the sampling interval h,

[0024] because the triggering time is consistent with the sampling time, effectively preventing the occurrence of Zeno behavior.

[0025] Furthermore, the polling protocol is used in the controller-actuator network channel in step 3 to avoid data collisions and conflicts and optimize the utilization of network resources. Define the periodic function ω(t) ∈ {1, 2,..., m}, where Let \(n\) denote the number of nodes in the network, and \(\omega(t)\) denote the nodes that can be accessed at time \(t\). The update rule of the polling protocol is as follows:

[0026] \(\omega(t)=\text{mod}(\omega(t - dt),m)+1\)

[0027] where \(dt\) is the time interval and \(\text{mod}\) represents the modulo operation. This rule ensures that the nodes access the network channels in sequence.

[0028] Denote where is the selected control signal that can access the controller - actuator network channel at transmission time \(t\). Denote as the control signal after transmission. The rule for scheduling and updating \(u(t)\) using the polling protocol is as follows:

[0029]

[0030] That is where is the Kronecker delta function.

[0031] Further explanation:

[0032] When \(\Lambda\) ω = \(I\), the update rule simplifies to the traditional form, that is This means that all nodes transmit their data at each moment.

[0033] Furthermore, the dynamic output feedback controller in step 4 does not require direct access to the system state. Because in practical applications, it is difficult or impossible to obtain the system state. The dynamic output feedback controller dynamically adjusts the control input according to the output \(y(l\) k \(h)\) to make it more practical in the actual system. The specific form is:

[0034]

[0035] where \(x\) c (t)\in\mathbb{R} m is the controller state, and \(A\) cσ(t) , \(B\) cσ(t) , \(C\) cσ(t) are gain matrices to be determined.

[0036] Furthermore, the enhanced system model in step 5 is verified by simulation experiments. The specific form of the enhanced system model is:

[0037]

[0038] where the enhanced state

[0039] The focus of the present invention is to design a dynamic event-triggering mechanism, a dynamic output feedback controller, a polling protocol, and a switching signal based on the mode-dependent average dwell time to collaboratively ensure that the networked switching system remains mean-square exponentially stable.

[0040] The beneficial effects of the present invention lie in that by combining the dynamic event-triggering mechanism and the polling protocol, the communication efficiency and control performance of the networked switching system are significantly optimized. Specifically, the dynamic event-triggering mechanism can adjust the triggering conditions in real time according to the system state, thereby minimizing the unnecessary communication between the sensor and the controller while ensuring the control accuracy, effectively alleviating the network congestion problem. In addition, the polling protocol avoids data collisions and conflicts by orderly scheduling the communication between the controller and the actuator, ensuring the reliable transmission of control signals. This comprehensive solution not only improves the utilization rate of network resources but also enhances the stability and robustness of the system in complex communication environments, especially suitable for application scenarios with limited network resources and high real-time requirements. Brief Description of the Drawings

[0041] Figure 1 is the control block diagram of the continuous-time networked switching system in the present invention;

[0042] Figure 2 is the schematic diagram of the system state mode in the present invention;

[0043] Figure 3 is the schematic diagram of the system output mode in the present invention;

[0044] Figure 4 is the schematic diagram of the system switching signal sequence in the present invention;

[0045] Figure 5 is the schematic diagram of the event-triggering release interval time in the present invention;

[0046] Figure 6 is the schematic diagram of the switching system control state trajectory under the polling protocol in the present invention. Detailed Embodiments

[0047] The exemplary embodiments disclosed by the present invention will be described in more detail below with reference to the drawings.

[0048] Example: As Figure 1 shown, the present invention provides an output feedback control method for a switching system based on a dynamic event-triggering mechanism and a polling protocol, and the specific implementation steps are as follows.

[0049] Step 1. Establish a continuous-time linear system model: Construct a mathematical model of the networked switching system, including subsystems, sensors, controllers, and actuator components.

[0050] Step 2. Design a dynamic event-triggering mechanism: Introduce a dynamic event-triggering mechanism in the sensor-controller network channel to reduce unnecessary communication.

[0051] Step 3. Adopt a polling protocol for communication scheduling: Use the polling protocol in the controller-actuator network channel to avoid data conflicts.

[0052] Step 4. Design a dynamic output feedback controller: Based on the dynamic event-triggering mechanism and the polling protocol, design a dynamic output feedback controller.

[0053] Step 5. Obtain an enhanced system: Verify the effectiveness of the designed control method through simulation or experiments, and optimize and adjust according to the actual operating conditions.

[0054] Step 1: Establish a system model in the following specific form:

[0055]

[0056] where \(x(t)\in\mathbb{R}\) n and \(u(t)\in\mathbb{R}\) q are the state vector and control input of the system respectively, and \(y(t)\in\mathbb{R}\) s is the measured output. describes the rate of change of the system state over time. \(A\) σ(t) \(\in\mathbb{R}\) n×n , \(B\) σ(t) \(\in\mathbb{R}\) n×q , \(C\) σ(t) \(\in\mathbb{R}\) s×n are matrices with appropriate dimensions. The switching signal \(\sigma(t)\) maps time \(t\) to a set of subsystem indices where represents the total number of subsystems. When \(\sigma(t)=l\) and \(l\in\mathcal{H}\), subsystem \(l\) is activated.

[0057] Let \(\sigma = 2\), then \(A\) σ(t) are \(A\) 1 and \(A\) 2 , \(B\) σ(t) are \(B\) 1 and \(B\) 2 , \(C\) σ(t) are \(C\) 1 and \(C\) 2 respectively:

[0058]

[0059] \(C\) 1 =[1 0], \(C\) 2 =[1 0].

[0060] In addition, set the initial value of the system \(x(0)=[3 5]\)T , the system state mode and output mode are respectively represented by Figure 2 and Figure 3 as shown, and the system switching signal sequence is represented by Figure 4 as shown.

[0061] Step 2: Apply the dynamic event-triggering mechanism in the sensor-controller network channel to save network resources. The specific form is:

[0062] l k+1 h = l k h + inf{lh|η(l k h + ιh) + θ(αy T (l k h + ιh)Ω σ(t) y(l k h + ιh)

[0063] -e T (l k h + ιh)Ω σ(t) e(l k h + ιh)) ≤ 0}

[0064] where, l k h is the current event-triggering moment, l k+1 h is the next triggering moment after l k h, y(l k h) and y(l k h + ιh) are the most recently transmitted output and the currently sampled output respectively, and e(l k h + ιh) = y(l k h) - y(l k h + ιh) is the error vector.

[0065] Let θ = 30, α = 0.01, β = 0.1. The internal dynamic variable η(t) satisfies the following conditions:

[0066]

[0067] Furthermore, as Figure 5 shown, after adopting the dynamic event-triggering mechanism, the number of data transmissions in the time interval [0, 2.5] is 11, and the average release interval is 0.1833 s. Compared with the static event-triggering mechanism with an average release interval of 0.1290 s, the triggering times are significantly reduced, effectively alleviating the network burden.

[0068] Step 3: Use the polling protocol in the controller-actuator network channel to avoid data collisions and conflicts and optimize the utilization of network resources. Define the periodic function ω(t) ∈ {1, 2,..., m}, where, Let \(m\) denote the number of nodes in the network, and \(\omega(t)\) denote the nodes accessible at time \(t\). The update rule of the polling protocol is:

[0069] \(\omega(t)=\text{mod}(\omega(t - dt),m)+1\)

[0070] where \(dt\) is the time interval and \(\text{mod}\) represents the modulo operation. This rule ensures that nodes access the network channels in sequence.

[0071] Denote \(n\in\{1,2,\cdots,m\}\), where is the selected control signal that can access the controller - actuator network channel at transmission time \(t\). Denote as the control signal after transmission. The rule for scheduling and updating \(u(t)\) using the polling protocol is as follows:

[0072]

[0073] That is where is the Kronecker delta function. Let \(\omega = 2\), then \(\Lambda\) 1 \(=\text{diag}\{1,0\}\), \(\Lambda\) 2 \(=\text{diag}\{0,1\}\).

[0074] When \(\Lambda\) ω \(=I\), the update rule simplifies to the traditional form, that is This means that all nodes transmit their data at each moment. As Figure 6 shown, after adopting the polling protocol, \(u\) 1 (t) and \(u\) 2 (t) alternate between active and inactive states; while in the traditional form, \(u\) 1 (t) and \(u\) 2 (t) always remain in the active state. This shows that the amount of data released in the controller - actuator network channel is significantly reduced, and data conflicts can be avoided through the polling protocol.

[0075] Step 4: The specific form of the dynamic output feedback controller is:

[0076]

[0077] where \(x\) c (t)\(\in\mathbb{R}\) m is the controller state, and \(A\) cσ(t) , \(B\) cσ(t) , \(C\) cσ(t) are gain matrices to be determined. Set the initial value \(x\) c (0)=

[35] T , then \(A\) cσ(t) are respectively \(A\)c1 and A c2 ,B cσ(t) are respectively B c1 and B c2 ,C cσ(t) are respectively C c1 and C c2 。When scheduling node 1:

[0078]

[0079] When scheduling node 2:

[0080]

[0081] Step 5: The specific form of enhancing the system model is:

[0082]

[0083] where the enhanced state

[0084] It should be noted that the content not detailed in the description of the present invention belongs to the prior art well-known to those skilled in the art.

[0085] The above are only the preferred embodiments of the present invention, and do not limit the patent scope of the present invention. Any equivalent structural transformation or addition and replacement made by those skilled in the art within the technical scope disclosed in the present invention should be covered by the protection scope of the present invention.

Claims

1. A switching system output feedback control method based on dynamic event triggering mechanism and polling protocol, characterized in that The method reduces unnecessary communication in the sensor-controller network channel through a dynamic event trigger mechanism, saves network resources, and performs communication scheduling through a polling protocol to avoid data conflicts in the controller-actuator network channel. The method includes the following steps: Step 1. Establish a continuous-time linear system model: Construct a mathematical model of the networked switching system, including subsystems, sensors, controllers, and actuator components; Step 2. Design a dynamic event trigger mechanism: Introduce a dynamic event trigger mechanism in the sensor-controller network channel to reduce unnecessary communication; Step 3. Use polling protocol for communication scheduling: Use polling protocol in the controller-actuator network channel to avoid data conflicts; Step 4. Design a dynamic output feedback controller: Based on the dynamic event trigger mechanism and polling protocol, design a dynamic output feedback controller; Step 5. Derive the enhanced system: Verify the effectiveness of the designed control method through simulation or experiment, and optimize and adjust it according to the actual operating conditions.

2. The switching system output feedback control method based on dynamic event trigger mechanism and polling protocol according to claim 1 is characterized in that: The specific form of establishing the system model in step 1 is: Where x(t)∈R n and u(t)∈R q are the state vector and control input of the system, y(t)∈R s is the measured output, Describes the rate of change of the system state over time, A σ(t) ∈R n×n , B σ(t) ∈R n×q , C σ(t) ∈R s×n is a matrix of suitable dimension, the switching signal σ(t) maps time t to a set of subsystem indices in Represents the total number of subsystems. When σ(t) = l and l∈H, subsystem l is activated.

3. The switching system output feedback control method based on dynamic event triggering mechanism and polling protocol according to claim 1 is characterized in that: In step 2, a dynamic event trigger mechanism is introduced into the sensor-controller network channel, and the specific form is: l k+1 h=l k h+inf{lh|η(l k h+ιh)+θ(αy T (l k h+ιh)Ω σ(t) y(l k h+ιh)-e T (l k h+ιh)Ω σ(t) and(l k h+ιh))≤0} Among them, l k h is the current event triggering time, l k+1 h is l k The next triggering moment after h, y(l k h) and y(l k h+ιh) are the most recently transmitted output and the current sampled output, respectively, e(l k h+ιh)=y(l k h)-y(l k h+ιh) is the error vector, θ>0 is a given constant, α is a given trigger threshold, Ω σ(t) >0 is the event trigger weight matrix, and the internal dynamic variable η(t) satisfies the following conditions: in, β∈(0,1) is a given scalar.

4. The switching system output feedback control method based on dynamic event trigger mechanism and polling protocol according to claim 1 is characterized in that: In step 3, a polling protocol is used in the controller-actuator network channel, and the update rule is ω(t)=mod(ω(t-dt),m)+1 Among them, ω(t)∈{1,2,...,m} is a periodic function with a period of m, which represents the nodes accessible at time t. dt is the time interval, in is the selected control signal accessible to the controller-actuator network channel at transmission time t, For the control signal after transmission, the rules for updating u(t) using the polling protocol scheduling are as follows: Right now in is the Kronecker delta function.

5. The switching system output feedback control method based on dynamic event triggering mechanism and polling protocol according to claim 1 is characterized in that: The dynamic output feedback controller in step 4 is specifically in the form of: Among them, x c (t)∈R m is the controller status, A cσ(t) , B cσ(t) , C cσ(t) is the gain matrix that needs to be determined.

6. The switching system output feedback control method based on dynamic event triggering mechanism and polling protocol according to claim 1 is characterized in that: The enhanced system model in step 5 is verified by simulation experiment. The specific form of the enhanced system model is: The enhanced state

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