Stability analysis and control method and system of discrete time network control system

Abstract

The invention belongs to the field of control science and engineering, and particularly discloses a stability analysis and control method and system for a discrete time network control system, and the method comprises the following steps: dividing a time delay interval of the system into a plurality of time delay sub-intervals which are not intersected, and enabling each sub-interval to correspond to a time delay mode, the time delay mode comprises a stable mode and an unstable mode; constructing a discrete time switching system model composed of a plurality of modes, designing a corresponding state feedback controller gain for each time delay mode, and designing a mode-related variable gain controller; in combination with a modal average residence time condition and multi-Lyapunov function construction, an exponential stability criterion capable of processing an unstable modal and a controller design method are provided. The method provided by the invention can effectively reduce the analysis conservative property, improves the robustness and dynamic performance of the system, and is suitable for time delay system control in a complex network environment.

Description

Technical Field

[0001] This application belongs to the field of control science and engineering, and more specifically, relates to a stability analysis and control method and system for discrete-time network control systems. Background Technology

[0002] Networked control systems (NCSs) are a type of feedback closed-loop control system that connects controllers, actuators, and sensors through a communication network. Due to their flexible structure and convenient deployment, they are widely used in industrial automation, autonomous driving, remote control, and smart grids.

[0003] However, uncertainties introduced by the network, such as communication latency, packet loss, and network congestion, can cause complex dynamic time delays in the system. Among these, multi-source induced time-varying delays become a key factor affecting system stability and performance.

[0004] Most current studies assume that time delays follow a pattern of "variation within a fixed boundary," using Lyapunov functionals and linear matrix inequalities (LMI) to analyze system stability. Although some progress has been made, the traditional analytical framework fails when network-induced time delays exhibit dynamic characteristics such as "segmented changes, alternating time periods, and abrupt deterioration," especially when there are cases where "the system is unstable within some time delay intervals."

[0005] Therefore, there is an urgent need for a general method that can model, analyze, and design controllers for multiple different time delay modes (including stable and unstable modes). Summary of the Invention

[0006] To address the shortcomings of existing technologies, the purpose of this application is to provide a stability analysis and control method and system for discrete-time network control systems, which can unify the analysis of stable and unstable modes and is applicable to the design of control systems with piecewise variable time-delay structures.

[0007] To achieve the above objectives, in a first aspect, this application provides a stability analysis and control method for discrete-time network control systems, applicable to scenarios with multi-source induced time-varying time delays, comprising the following steps: S10, the system's time delay interval is divided into multiple non-overlapping time delay sub-intervals, each sub-interval corresponding to a time delay mode, the time delay mode including stable mode and unstable mode; S20. Based on the time delay mode, construct a discrete-time switching system model consisting of multiple modes, where each mode corresponds to a subsystem. Design a corresponding state feedback controller gain for each time delay mode to form a variable gain controller related to the time delay mode. S30, introduce the modal correlation mean residence time condition, construct multiple Lyapunov functionals, and derive sufficient conditions to satisfy the global uniform exponential stability of the system; S40, obtain the stability analysis method in the form of linear matrix inequality, and solve the controller gain in each time delay mode based on the linear matrix inequality conditions to realize the switching control strategy for time delay mode.

[0008] The beneficial effects of this application are as follows: (1) This application has wide applicability and is applicable to discrete-time network control systems containing stable and unstable time delay modes. It can effectively cope with complex dynamic time delay environments caused by multi-source network disturbances (such as congestion, packet loss, etc.) and significantly expand the engineering application scope of the control method; (2) By designing a time delay mode-related variable gain controller, the controller parameters can be dynamically switched according to the current time delay mode, thereby improving the dynamic response performance of the system under stable mode and maintaining closed-loop stability under unstable mode, thus enhancing the robustness and control performance of the system as a whole; (3) This application introduces the modal mean residence time (MDADT) mechanism and multiple Lyapunov functional construction, which effectively reduces the conservatism of the analysis. The proposed stability criterion can be transformed into the form of linear matrix inequality (LMI), which is convenient to solve and implement using mature tools such as MATLAB, and has good engineering operability.

[0009] As a further preferred embodiment, in step S10, the division of the time delay mode is based on network-induced communication delay, data packet loss, and segment change characteristics caused by routing changes.

[0010] As a further preferred embodiment, in step S20, the switching signal of the switching system is a quasi-alternating switching signal, which satisfies that there is no continuous switching between stable and unstable modes.

[0011] As a further preferred embodiment, in step S20, the controller gain is dynamically switched according to the sub-interval to which the current time delay belongs, so as to improve the control performance and robustness of the system under different modes.

[0012] As a further preferred embodiment, in step S20, the controller design step includes setting adjustment parameters during the solution of the linear matrix inequality to balance the relationship between system response speed and control energy consumption.

[0013] As a further preferred option, in step S40, an extended multi-Lyapunov functional is introduced to avoid the occurrence of higher-order polynomials related to time-delay boundaries in the control conditions, thereby transforming the non-convex constraint into a solvable linear matrix inequality form.

[0014] As a further preferred embodiment, the method is applicable to systems with both stable and unstable time-delay modes, and can still achieve exponential stability of the closed-loop system in the presence of unstable modes.

[0015] Secondly, this application provides a stability analysis and control system for a discrete-time network control system, applicable to scenarios with multi-source induced time-varying delays, including: The time delay mode partitioning module is used to divide the time delay interval of the system into multiple non-overlapping time delay sub-intervals, each sub-interval corresponding to a time delay mode, wherein the time delay mode includes stable mode and unstable mode; The variable gain controller design module is used to construct a discrete-time switching system model consisting of multiple modes based on the time delay mode, wherein each mode corresponds to a subsystem, and a corresponding state feedback controller gain is designed for each time delay mode to form a time delay mode-related variable gain controller. The stability analysis and controller gain solution module is used to introduce the modal correlation mean residence time condition, construct multiple Lyapunov functionals, derive sufficient conditions to satisfy the global uniform exponential stability of the system, obtain the stability analysis method in the form of linear matrix inequalities, and solve the controller gain in each time delay mode based on the linear matrix inequality conditions to realize the switching control strategy for time delay modes.

[0016] Thirdly, this application provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the stability analysis and control method of the discrete-time network control system as described in any one of the above.

[0017] Fourthly, this application provides a computer-readable storage medium storing computer instructions thereon, which, when executed by a processor, implement the stability analysis and control method for a discrete-time network control system as described in any one of the above-mentioned methods.

[0018] It is understandable that the beneficial effects of the second, third and fourth aspects mentioned above can be found in the relevant descriptions in the first aspect above, and will not be repeated here. Attached Figure Description

[0019] Figure 1 A flowchart illustrating the stability analysis and control method for the discrete-time networked control system provided in this application; Figure 2 A flowchart illustrating the stability analysis and control method for a discrete-time networked control system provided in this application embodiment; Figure 3 Unstable time-delay mode example diagram provided for embodiments of this application; Figure 4 The state response curves for the multi-unstable time-delay modes provided in the embodiments of this application; Figure 5 The controller design provided in the embodiments of this application verifies the system status. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0021] It should be understood that, in the description of this application, the term "multiple" means two or more, unless otherwise expressly and specifically defined.

[0022] like Figure 1 As shown, this application provides a stability analysis and control method for discrete-time network control systems, applicable to scenarios with multi-source induced time-varying time delays, including the following steps: S10 divides the system's time delay interval into multiple non-overlapping time delay sub-intervals. Each sub-interval corresponds to a time delay mode, which includes stable and unstable modes.

[0023] S20: Based on the time delay mode, a discrete-time switching system model consisting of multiple modes is constructed, where each mode corresponds to a subsystem. For each time delay mode, a corresponding state feedback controller gain is designed to form a time delay mode-related variable gain controller.

[0024] S30 introduces the Mode-Dependent Average Dwell Time (MDADT) condition to construct a multiple Lyapunov functional; and derives sufficient conditions for satisfying the Global Unified Exponential Stability (GUES) of the system.

[0025] S40, Obtain the stability analysis method in the form of linear matrix inequality (LMI), and solve the controller gain in each time delay mode based on the LMI conditions to realize the switching control strategy for time delay mode.

[0026] The beneficial effects of this application are as follows: (1) This application has wide applicability and is applicable to discrete-time network control systems containing stable and unstable time delay modes. It can effectively cope with complex dynamic time delay environments caused by multi-source network disturbances (such as congestion, packet loss, etc.) and significantly expand the engineering application scope of the control method; (2) By designing a time delay mode-related variable gain controller, the controller parameters can be dynamically switched according to the current time delay mode, thereby improving the dynamic response performance of the system under stable mode and maintaining closed-loop stability under unstable mode, thus enhancing the robustness and control performance of the system as a whole; (3) This application introduces the modal mean residence time (MDADT) mechanism and multiple Lyapunov functional construction, which effectively reduces the conservatism of the analysis. The proposed stability criterion can be transformed into the form of linear matrix inequality (LMI), which is convenient to solve and implement using mature tools such as MATLAB, and has good engineering operability.

[0027] In one embodiment, the technical solution to achieve the above objective can be as follows: Please see Figure 2 This embodiment proposes an adaptive hybrid triggering control method for cyber-physical systems that systematically considers network attack information, including the following steps: Step 1: Establish a time-delay mode partitioning and modeling method Consider the following discrete-time networked control system: (1) in, It is the system status. It is a control input. It is the initial state. and The system matrix is ​​known. The system is unstable without control input. Therefore, to stabilize the system, the following state feedback controller is designed: (2) in, For controller gain. Note that the sensor will register the system state. and its timestamp Encapsulated into a data packet The data packet is then transmitted to the controller via the communication channel to generate a control input data packet. Once the control input data packet is generated, it can be immediately transmitted to the data packet processor via the communication channel to drive the actuator. However, due to bandwidth limitations, network-induced latency is inevitable during data packet transmission. Therefore, the controller can be re-expressed as follows: (3) in It is time-varying and time-delayed, satisfying: (4) Among them, positive integers These are the upper and lower bounds of the time delay, respectively.

[0028] It is worth noting that changes in network-induced latency and packet loss throughout the entire time period will cause time lag intervals. It varies within different time-delay sub-intervals. Within each time-delay sub-interval, the system exhibits different characteristics. Figure 3 A system simulation case is given, with the following system parameters:

[0029] Consider dividing the time delay interval It consists of four sub-intervals: The graph shows that the system exhibits different characteristics in different time delay intervals, especially when the time delay in the system is within a certain range. At times, the system is unstable.

[0030] To achieve better control performance, it is necessary to analyze different time delay intervals. Assume the time delay interval can be divided into... Sub-intervals ( Then the delay It can be composed of a series of time-delay modes The specific time-delay mode function is represented as follows: (5) in, , ( () represents the time period corresponding to the time-delay mode. express arrive Integers between [a certain range].

[0031] Due to malicious packet loss, the system's latency may exceed its stability margin for certain periods; these latency modes are called unstable latency modes. We assume... ,in , That is, the system exists A stable time-delay mode and There are several unstable time-delay modes. Clearly, different time-delay modes will affect the dynamic behavior of the system. Specifically, for stable time-delay modes, the system often has a faster response speed and better control performance; while unstable time-delay modes will significantly weaken the stability and dynamic performance of the system, and may even make the system unstable.

[0032] Step 2: Establish a time-delay mode-dependent switching system model While a fixed-gain controller (3) designed based on the worst-case time-delay boundary can guarantee system stability, its control performance is too conservative and its flexibility is poor. To overcome these limitations, this embodiment designs a variable-gain controller based on time-delay modes. This controller can dynamically adjust its parameters according to the current time-delay mode, thereby achieving adaptive control for different time-delay modes. For each time-delay mode, a corresponding controller gain is designed. The details are as follows: (6) This variable gain strategy enables the controller to dynamically adjust its parameters according to the current time-delay mode, thereby effectively utilizing a larger control margin under stable time-delay modes and improving the overall dynamic performance and robustness of the system.

[0033] Based on the above analysis, the discrete-time networked control system (1) with a variable gain controller is equivalent to a switching system with multiple time delays, as described below: (7) in, It is a time-delay mode function. When At the switching moment , No. Each subsystem is working.

[0034] Step 3: Obtain the stability criterion based on the modal correlation mean residence time Based on switched system theory, a globally consistent exponential stability analysis method for systems with multiple time-delay modes is derived. The specific steps are as follows: Step 3.1 Define the modal correlation mean residence time condition. For stable time-delay modes, a minimum residence time is set to ensure that the system has enough time to converge within that mode; while for unstable time-delay modes, a maximum residence time is set to prevent them from continuously affecting the dynamic performance of the system.

[0035] Definition 1 (Slow Mode Correlation Mean Dwell Time): For any time series and ,definition For the first The number of times each subsystem is activated within this time interval. For the first The total runtime of each subsystem. There are two constants. and This makes it possible for all ,have: (8) in It is a switching signal The slow-mode correlation mean dwell time.

[0036] Definition 2 (mean residence time of fast modal correlation): For any time series and ,definition For the first The number of times each subsystem is activated within this time interval. For the first The total runtime of each subsystem. There are two constants. and This makes it possible for all ,have: (9) in It is a switching signal The fast modal correlation mean dwell time.

[0037] Step 3.2 Define the quasi-alternating switching signal In this embodiment, a stable time-delay mode can be arbitrarily switched to other time-delay modes, while an unstable time-delay mode can only be switched to a stable time-delay mode.

[0038] Definition 3: Assume a switching signal The following conditions must be met: 1) If ,So ; 2) If ,So .

[0039] Switching signals that meet the above conditions This is called a quasi-alternating switching signal.

[0040] Step 3.3 Obtain the stability conditions for switching systems Theorem 1: For , , ,and , , If multiple Lyapunov functions exist , and two categories function and , making (10) Therefore, the switching system (7) is globally consistent and exponentially stable, and has the following modally correlated mean residence time. (11) Step 4: Obtain LMI-based stability analysis and controller design methods Based on Lyapunov functionals and linear matrix inequalities, the global uniform exponential stability condition and controller design method for a switching system (7) with multiple time delay modes are derived.

[0041] Step 4.1 Constructing multiple Lyapunov functionals for Consider the following multiple Lyapunov functionals: (12) in

[0042] and , and , It is a positive definite matrix.

[0043] Step 4.2 Obtain the linear matrix inequality conditions that guarantee system stability Theorem 2: For a given scalar , ( ),as well as , ( ), and constants If a symmetric positive definite matrix exists , , and arbitrary matrices , , ,in , The following conditions are true for any and If all conditions are met, then the system (7) with a quasi-alternating switching signal that satisfies (11) is generally uniformly exponentially stable under the action of the quasi-alternating switching signal: (13) (14) in

[0044]

[0045]

[0046] Step 4.3 Obtain the controller design method Theorem 3: For a given scalar , ( ),as well as , ( ), and constants If a symmetric positive definite matrix exists , , and arbitrary matrices , , , ,in , The following conditions are true for any and If all conditions are met, then the system (7) with a quasi-alternating switching signal that satisfies (11) is generally uniformly exponentially stable under the action of the quasi-alternating switching signal: (15) (16) in

[0047] Furthermore, since the other definitions are the same as in Theorem 2, the parameters of the variable gain controller can be obtained through the following transformation: (17) The present application will now be described in detail with reference to specific embodiments.

[0048] This embodiment uses two numerical examples for testing.

[0049] Example 1: Consider system (7) as follows:

[0050] Figure 3 The paper shows that the system performance varies across different time delay intervals, and there are even time delay intervals that make the system unstable. Therefore, this example is used to verify the stability analysis method for multiple time delay modes established in this embodiment. Considering that the system has two unstable time delay modes, let... , That is, the system contains one stable time-delay mode and two unstable time-delay modes. The parameters are set as follows: , , , , , , , According to Theorem 2, the maximum allowable upper bound is: .

[0051] Therefore, by combining the modal correlation average residence time (11), we can obtain the time-delay modes. , The modal-dependent mean residence time conditions that need to be met are as follows:

[0052] To verify the correctness of the obtained modal correlation mean residence time, we selected... , as well as And define the time-delay mode function as:

[0053] Figure 4 The corresponding system state response curves are presented. The figures show that the system is stable under given quasi-alternating switching signals and modal-dependent average residence times. Therefore, the proposed method is effective.

[0054] Example 2: Consider testing the effectiveness of the controller design method through a truck-tractor system. Its linear continuous-time model near the equilibrium point is as follows:

[0055] in

[0056] and , , , , During the sampling period The discrete-time model of the truck-tractor system is shown below:

[0057] in, , .

[0058] Consider a system with two stable time-delay modes, namely, .make , , Then the minimum residence time of the two time-delay modes can be calculated. .for , The maximum allowable upper bound obtained through Theorem 3 The corresponding controller gains are as follows:

[0059] Where C1 represents a time-delay mode-dependent variable-gain controller, and C2 represents a fixed-gain controller. The initial conditions of the system are: The minimum residence time for the two time-delay modes is set as follows: The time-delay mode function is:

[0060] Figure 5 The system's state response curves and switching signals are presented. As can be seen from the figures, the system based on the variable gain controller can quickly achieve stability. To further illustrate the superiority of the designed variable gain controller, four important performance indicators are given in Table 1: Time Multiplied by Absolute Error (STAE), Absolute Error Sum (SAE), Time Multiplied by Sum of Squared Errors (STSE), and Sum of Squared Errors (SSE). These four indicators play a crucial role in evaluating the fast convergence and steady-state performance of the control system because they quantify the dynamic behavior of the system error from different perspectives. The smaller the performance indicator, the better the control performance. Table 1 shows that the variable gain controller provides superior control performance compared to the fixed gain controller, further validating the advantages of introducing a time-delay modal correlation gain adjustment mechanism in improving system performance.

[0061] Table 1 Comparison of Control Performance

[0062] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A stability analysis and control method for discrete-time network control systems, applicable to scenarios with multi-source induced time-varying time delays, characterized in that, Includes the following steps: S10, the system's time delay interval is divided into multiple non-overlapping time delay sub-intervals, each sub-interval corresponding to a time delay mode, the time delay mode including stable mode and unstable mode; S20. Based on the time delay mode, construct a discrete-time switching system model consisting of multiple modes, where each mode corresponds to a subsystem. Design a corresponding state feedback controller gain for each time delay mode to form a variable gain controller related to the time delay mode. S30. Introducing the modal correlation mean residence time condition, constructing a multiple Lyapunov functional, and deriving sufficient conditions to satisfy the global uniform exponential stability of the system; S40, obtain the stability analysis method in the form of linear matrix inequality, and solve the controller gain in each time delay mode based on the linear matrix inequality conditions to realize the switching control strategy for time delay mode.

2. The stability analysis and control method for discrete-time network control systems as described in claim 1, characterized in that, In step S10, the time delay mode is divided based on network-induced communication delay, data packet loss, and segment change characteristics caused by routing changes.

3. The stability analysis and control method for discrete-time network control systems as described in claim 1, characterized in that, In step S20, the switching signal of the switching system is a quasi-alternating switching signal, which satisfies that there is no continuous switching between stable and unstable modes.

4. The stability analysis and control method for discrete-time network control systems as described in claim 1, characterized in that, In step S20, the controller gain is dynamically switched according to the sub-interval to which the current time delay belongs, so as to improve the control performance and robustness of the system under different modes.

5. The stability analysis and control method for discrete-time network control systems as described in claim 1, characterized in that, In step S20, the controller design step includes setting adjustment parameters during the solution of the linear matrix inequality to balance the relationship between system response speed and control energy consumption.

6. The stability analysis and control method for discrete-time network control systems as described in claim 1, characterized in that, In step S40, an extended multi-Lyapunov functional is introduced to avoid the occurrence of higher-order polynomials related to time-delay boundaries in the control conditions, thereby transforming the non-convex constraint into a solvable linear matrix inequality form.

7. The stability analysis and control method for discrete-time network control systems as described in claim 1, characterized in that, The method is applicable to systems with both stable and unstable time-delay modes, and can achieve exponential stability of the closed-loop system even in the presence of unstable modes.

8. A stability analysis and control system for a discrete-time network control system, applicable to scenarios with multi-source induced time-varying delays, characterized in that, include: The time delay mode partitioning module is used to divide the time delay interval of the system into multiple non-overlapping time delay sub-intervals, each sub-interval corresponding to a time delay mode, wherein the time delay mode includes stable mode and unstable mode; The variable gain controller design module is used to construct a discrete-time switching system model consisting of multiple modes based on the time delay mode, wherein each mode corresponds to a subsystem, and a corresponding state feedback controller gain is designed for each time delay mode to form a time delay mode-related variable gain controller. The stability analysis and controller gain solution module is used to introduce the modal correlation mean residence time condition, construct multiple Lyapunov functionals, derive sufficient conditions to satisfy the global uniform exponential stability of the system, obtain the stability analysis method in the form of linear matrix inequalities, and solve the controller gain in each time delay mode based on the linear matrix inequality conditions to realize the switching control strategy for time delay modes.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the stability analysis and control method for the discrete-time network control system as described in any one of claims 1 to 7.

10. A computer-readable storage medium storing computer instructions thereon, characterized in that, When the computer instruction is executed by the processor, it implements the stability analysis and control method of the discrete-time network control system as described in any one of claims 1 to 7.

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