A control method and system for a double switching time delay system based on an MSE switching strategy

Abstract

The present application belongs to the field of complex system modeling and control technology, and particularly relates to a control method, system and platform of a double switching time-delay system based on a minimum state expectation (MSE) switching strategy. The present application generates a state space expression of a variable double switching time-delay system according to a double switching time-delay system of the MSE switching; constructs an MSE switching strategy in combination with Lyapunov stability theory; performs stabilizing control on the variable double switching time-delay system in real time according to the constructed MSE switching strategy, so as to obtain a sufficient condition for exponential almost everywhere stabilization of the variable double switching time-delay system and a maximum time delay allowed by the system; moreover, the method and the obtained stabilizing condition of the present application are applicable to system modeling with complex switching dynamic characteristics, and have great theoretical and practical application value.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of complex system modeling and control, and particularly relates to a control method, system and platform for a double switching time-delay system based on an MSE switching strategy. BACKGROUND

[0002] At present, a switching system as a special hybrid system is composed of a series of continuous or discrete subsystems and a switching strategy that dominates the operation of the subsystems. According to different switching strategies, the switching system is divided into deterministic switching systems and random switching systems. With the rapid development of science and technology and complexity science, dynamic control systems are becoming more and more complex, and the pure use of deterministic switching systems or random switching systems for modeling complex control systems cannot accurately describe the internal operation mechanism. For example, a complex system with multiple working conditions, the switching between which is determined by deterministic control instructions, and the types of random faults under different working conditions may be different, which can be described by a Markov process. Therefore, this kind of complex system can be modeled as a double switching system that simultaneously exists deterministic switching and random switching, also known as a Markov jump linear system or a two-layer switching system. The double switching system is divided into fixed double switching systems and variable double switching systems according to the transition probability of the Markov process. At present, the research results on double switching systems mainly focus on fixed double switching systems, and there are few research results on variable double switching systems. The reason is that in the variable double switching system, different Markov jump linear subsystems are controlled by different Markov processes, so the ergodicity of the Markov process is no longer applicable in the variable double switching system. Obviously, the research on variable double switching systems is more challenging.

[0003] In addition, in recent years, switching time-delay systems have attracted the attention of many scholars due to their wide range of applications, such as network control systems and power electronic systems. A switching time-delay system refers to a system in which time delays exist in the subsystems of the switching system. Therefore, how to eliminate the influence of time delays or how to keep the system with good stability performance when the system has time delays is the research focus of switching time-delay systems. On the one hand, there is currently no research on double switching time-delay systems. On the other hand, most of the existing research on deterministic switching time-delay systems or random switching time-delay systems assumes that the size of the time delay is known to obtain sufficient conditions for system stability, and few documents solve the maximum time delay allowed by the system, i.e., the time delay upper bound. Therefore, the extended research on variable double switching time-delay systems is of great significance.

[0004] Compared with the time-delay random or deterministic switching system, in the double switching time-delay system, not only the influence of time-delay exists, but also the switching dynamics are more complex. Therefore, how to construct a suitable functional and switching strategy is crucial for the analysis and control of the double switching time-delay system. The existing construction of time-delay system functional has been more developed and mature methods, such as time-delay partition functional, augmented functional and the like. These methods applied to the double switching time-delay system will be able to greatly enrich the complex system theory. In addition, there are many methods for the design of switching strategy, such as the dwell time method, the average dwell time method, the continuous dwell time method and the like, but these methods have certain limitations, for example, for some systems with random mutations in internal structure or properties, the dwell time and the average dwell time will no longer be applicable; and for the continuous dwell time method, the switching number of the system will be limited in a finite time interval.

[0005] Therefore, in view of the above technical problems and defects, it is urgent to design and develop a double switching time-delay system control method, system and platform based on MSE switching strategy. SUMMARY

[0006] In order to overcome the deficiencies and difficulties existing in the prior art, the purpose of the present application is to provide a double switching time-delay system control method, system and platform based on MSE switching strategy, so as to realize the sufficient condition of variable double switching time-delay system exponential almost everywhere and the maximum time delay allowed by the system. Moreover, the method used by the present application and the obtained stabilization condition are applicable to the modeling of systems with complex switching dynamic characteristics, and have great theoretical and practical application value.

[0007] The first purpose of the present application is to provide a double switching time-delay system control method based on MSE switching strategy; the second purpose of the present application is to provide a double switching time-delay system control system based on MSE switching strategy; the third purpose of the present application is to provide a double switching time-delay system control platform based on MSE switching strategy; the first purpose of the present application is achieved in the following way: the method specifically comprises the following steps: generating a state space expression of a variable double switching time-delay system according to the MSE switching double switching time-delay system; constructing an MSE switching strategy in combination with Lyapunov stability theory; and performing real-time stabilization control on the variable double switching time-delay system according to the constructed MSE switching strategy.

[0008] Further, the state space expression is specifically:

[0009]

[0010] x(0)=x0 (2)

[0011] Wherein: is the system state vector, is a deterministic switching signal and ρ(t, η(t)) is a stochastic switching signal; is a constant matrix with appropriate dimensions, is a continuous time-varying time delay and satisfies

[0012] Further, the MSE switching strategy is constructed by combining the Lyapunov stability theory, and further comprises the following steps: generating a controller gain matrix of the variable double switching time delay system in real time.

[0013] Further, the MSE switching strategy is constructed, and specifically a time-state dependent hybrid switching strategy.

[0014] Further, the expression of the switching strategy is specifically:

[0015]

[0016] wherein: is the value of the deterministic switching signal η(t) at the t k moment.

[0017] Further, the variable double switching time delay system is stably controlled in real time according to the constructed MSE switching strategy, and further comprises the following steps:

[0018] constructing an easy barrier system model;

[0019] verifying the effectiveness of the MSE switching strategy in real time according to the easy barrier system model;

[0020] verifying the correctness of the system exponential stabilization control sufficient condition in real time.

[0021] Further, the effectiveness of the MSE switching strategy is verified in real time according to the easy barrier system model, and further comprises the following steps:

[0022] constructing a functional containing a triple integral term and an exponential term, and combining the generalized free matrix integral inequality and the quadratic function negative definite lemma to process the time delay part in the system in real time.

[0023] The second object of the present application is achieved in that the system specifically comprises:

[0024] an expression generation unit configured to generate a state space expression of the variable double switching time delay system according to the MSE switching double switching time delay system;

[0025] a switching strategy construction unit configured to construct an MSE switching strategy by combining the Lyapunov stability theory;

[0026] a stabilizing control unit, configured to perform real-time stabilizing control on the variable double-switching time-delay system according to the constructed MSE switching strategy.

[0027] Further, the state space expression is specifically:

[0028]

[0029] x(0)=x0 (2)

[0030] wherein: x(t) is a system state vector, u(t) is a control input, η(t)∈{1,2,...,m} is a deterministic switching signal, and ρ(t,η(t))∈{1,2,...,n} is a random switching signal; is a constant matrix with a proper dimension, is a continuous time-varying time delay and satisfies

[0031] In the switching strategy construction unit, further provided are:

[0032] a first generation module, configured to generate a controller gain matrix of the variable double-switching time-delay system in real time;

[0033] The constructed MSE switching strategy is specifically a time-state-dependent hybrid switching strategy.

[0034] The expression of the switching strategy is specifically:

[0035]

[0036] wherein: η(t) is a value of the deterministic switching signal η(t) at t k

[0037] In the stabilizing control unit, further provided are:

[0038] a first construction module, configured to construct an easy barrier system model;

[0039] an effectiveness verification module, configured to verify effectiveness of the MSE switching strategy in real time according to the easy barrier system model;

[0040] a correctness verification module, configured to verify correctness of a system exponential stabilizing control sufficient condition in real time;

[0041] a construction processing module, configured to construct a functional containing a triple integral term and an exponential term, and process time delay parts in the system in real time by combining a generalized free matrix integral inequality and a quadratic function negative definite lemma.

[0042] ​The third object of the present application is achieved by comprising: a processor, a memory, and a control platform control program of a double switching time-delay system based on MSE switching strategy;

[0043] Wherein the processor executes the control platform control program of the double switching time-delay system based on MSE switching strategy, the control platform control program of the double switching time-delay system based on MSE switching strategy is stored in the memory, and the control platform control program of the double switching time-delay system based on MSE switching strategy implements the control method steps of the double switching time-delay system based on MSE switching strategy.

[0044] The present application generates a state space expression of a variable double switching time-delay system according to the double switching time-delay system based on MSE switching by the method; constructs an MSE switching strategy in combination with Lyapunov stability theory; and performs stabilizing control on the variable double switching time-delay system in real time according to the constructed MSE switching strategy, so as to realize a sufficient condition of exponential almost everywhere stabilization of the variable double switching time-delay system and the maximum time delay allowed by the system. Moreover, the method and the obtained stabilizing condition used by the present application are applicable to system modeling with complex switching dynamic characteristics, and have great theoretical and practical application value.

[0045] That is, compared with a deterministic switching time-delay system or a random switching time-delay system, the present application firstly takes a double switching time-delay system as a research object, which is a powerful expansion of the research on a single switching time-delay system. A time-state-dependent hybrid MSE switching strategy is designed under which the switching times of the system are not limited, and the MSE switching strategy is more suitable for a double switching time-delay system.

[0046] By constructing a functional and using generalized free matrix integral inequality and Jensen's inequality method, a sufficient condition of exponential almost everywhere stabilization of the variable double switching time-delay system and the maximum time delay allowed by the system are obtained. The method and the obtained stabilizing condition used by the present application are applicable to system modeling with complex switching dynamic characteristics, and have great theoretical and practical application value. BRIEF DESCRIPTION OF DRAWINGS

[0047] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed in the embodiment description will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without any creative effort on the basis of these drawings.

[0048] Figure 1 A switching principle diagram of the variable double switching time-delay system of the present application;

[0049] Figure 2A model block diagram of the barrier system of the present application;

[0050] Figure 3 A schematic diagram of the MSE deterministic switching signal of the present application;

[0051] Figure 4 A schematic diagram of the random switching signal of the present application;

[0052] Figure 5 A schematic diagram of the seven-time state sample implementation of the variable double switching time delay system of the present application;

[0053] Figure 6 A schematic diagram of the control method flow of the double switching time delay system based on the MSE switching strategy of the present application;

[0054] Figure 7 A schematic diagram of the control system architecture of the double switching time delay system based on the MSE switching strategy of the present application;

[0055] Figure 8 A schematic diagram of the control platform architecture of the double switching time delay system based on the MSE switching strategy of the present application;

[0056] Figure 9 A schematic diagram of the computer readable storage medium architecture in an embodiment of the present application;

[0057] The object, function features and advantages of the present application will be further explained with reference to the embodiments and the accompanying drawings. DETAILED DESCRIPTION

[0058] In order to better understand the object, technical solution and advantages of the present application, the present application will be further explained with reference to the embodiments and the accompanying drawings, and the person skilled in the art can easily understand other advantages and functions of the present application from the content disclosed in the present specification.

[0059] The present application can also be implemented or applied through other different specific examples, and each detail in the present specification can be modified and changed in various ways based on different viewpoints and applications without departing from the spirit of the present application.

[0060] It should be noted that if the embodiments of the present application involve directional indications (such as up, down, left, right, front, back, etc.), the directional indications are only used to explain the relative position relationship, movement condition, etc. between the components in a certain specific posture (as shown in the drawings), and if the specific posture changes, the directional indications will also change accordingly.

[0061] In addition, if the description of "first", "second" and the like is involved in the embodiments of the present application, the description of "first", "second" and the like is only for the purpose of description, and cannot be understood as indicating or implying the relative importance of the indicated technical features or implicitly indicating the number of the indicated technical features. Therefore, the features limited by "first", "second" can be explicitly or implicitly included at least one of the features. Secondly, the technical solutions of various embodiments can be combined with each other, but it must be based on the realization of the ordinary skilled in the art, when the combination of technical solutions appears contradictory or cannot be realized, it should be considered that the combination of technical solutions does not exist, also not within the protection scope required by the present application.

[0062] Preferably, the control method of a double switching time delay system based on MSE switching strategy provided by the present application is applied in one or more terminals or servers. The terminal is a device capable of automatically performing numerical calculation and / or information processing according to pre-set or stored instructions, and its hardware includes but is not limited to microprocessor, application specific integrated circuit (ASIC), field-programmable gate array (FPGA), digital signal processor (DSP), embedded device, etc.

[0063] The terminal can be a desktop computer, a notebook computer, a palm computer, a cloud server and other computing devices. The terminal can interact with the user through a keyboard, a mouse, a remote controller, a touchpad or a voice control device.

[0064] The present application is to realize a control method, system, platform and storage medium of a double switching time delay system based on MSE switching strategy.

[0065] As shown in Figure 6 The flow chart of the control method of a double switching time delay system based on MSE switching strategy provided by the present application is shown in the figure.

[0066] In the present embodiment, the control method of a double switching time delay system based on MSE switching strategy can be applied in a terminal with display function or a fixed terminal, and the terminal is not limited to personal computer, smart phone, tablet computer, desktop computer or all-in-one computer with camera, etc.

[0067] The control method of the double-switching time-delay system based on the MSE switching strategy can also be applied to a hardware environment composed of a terminal and a server connected to the terminal through a network. The network includes but is not limited to a wide area network, a metropolitan area network or a local area network. The control method of the double-switching time-delay system based on the MSE switching strategy of the embodiment of the application can be executed by the server, can be executed by the terminal, or can be executed by the server and the terminal together.

[0068] For example, for a terminal that needs to control the double-switching time-delay system based on the MSE switching strategy, the terminal can directly integrate the control function of the double-switching time-delay system based on the MSE switching strategy provided by the method of the application, or install a client for implementing the method of the application. For another example, the method provided by the application can also run on a device such as a server in the form of a software development kit (SDK), and provide an interface of the control function of the double-switching time-delay system based on the MSE switching strategy in the form of the SDK, so that a terminal or other device can implement the control function of the double-switching time-delay system based on the MSE switching strategy through the provided interface.

[0069] The application will be further described below with reference to the accompanying drawings.

[0070] As shown in Figures 1-9 The application provides a control method of a double-switching time-delay system based on an MSE switching strategy, and the method specifically includes the following steps: S1, generating a state space expression of a variable double-switching time-delay system according to the double-switching time-delay system based on the MSE switching strategy; S2, constructing an MSE switching strategy in combination with Lyapunov stability theory; and S3, performing stabilizing control on the variable double-switching time-delay system in real time according to the constructed MSE switching strategy.

[0071] The state space expression is specifically as follows:

[0072]

[0073] x(0)=x0 (2)

[0074] Wherein: is a system state vector, is a control input, η(t)∈{1,2,...,m} is a deterministic switching signal, and ρ(t,η(t))∈{1,2,...,n} is a random switching signal; is a constant matrix with a proper dimension, is a continuous time-varying time delay and satisfies

[0075] The method for constructing the MSE switching strategy based on Lyapunov stability theory also includes the following steps:

[0076] S21. Real-time generation of the controller gain matrix for the variable dual-switching time-delay system.

[0077] The MSE switching strategy is specifically a time-state dependent hybrid switching strategy.

[0078] The specific expression for the switching strategy is as follows:

[0079]

[0080] in: For the deterministic switching signal η(t) at t k The value at time.

[0081] The real-time stabilization control of the variable double-switching time-delay system based on the constructed MSE switching strategy further includes the following steps: S31, constructing a fault-prone system model; S32, verifying the effectiveness of the MSE switching strategy in real time based on the fault-prone system model; S33, verifying the correctness of the sufficient conditions for exponential stabilization control of the system in real time. The real-time verification of the effectiveness of the MSE switching strategy based on the fault-prone system model further includes the following steps: S321, constructing a functional containing a triple integral term and an exponential term, and combining the generalized free matrix integral inequality and the negative definite lemma of quadratic functions to process the time-delay component within the system in real time.

[0082] Specifically, in this embodiment of the invention, a stabilization method for a dual-switching time-delay system based on MSE switching is provided, the method comprising the following steps:

[0083] Step 1: Give the state-space expression of the variable double-switching time-delay system. Step 2: Design a time-state dependent hybrid MSE switching strategy based on Lyapunov stability theory. Step 3: Prove that the exponential stability of the variable double-switching time-delay system is almost everywhere under the designed MSE switching strategy. Step 4: Verify the effectiveness of the designed MSE switching strategy and the correctness of the sufficient condition for the almost everywhere exponential stability of the system through a fault-prone system model simulation example. Step 2 designs a novel time-state dependent hybrid switching strategy. The specific steps are as follows: Step 2-1: According to Lyapunov stability theory, if a control system tends to stabilize, its internal "energy" will decrease over time, meaning the system's state will gradually approach the system's equilibrium point. Since different Markov jump subsystems in the variable double-switching time-delay system are governed by different Markov processes, the following assumption is proposed:

[0084] Assumption 1: The j-th Markov jump subsystem of the variable double-switching time-delay system is at time t k-1is activated, and the expectation of the Markov jump subsystem satisfies the following relationship: k is activated, and the expectation of the Markov jump subsystem satisfies the following relationship:

[0085]

[0086] Assumption 2: The ith mode of the jth Markov jump subsystem of the variable double switching time-delay system is activated at time t k-1 is activated at time t k is activated, and satisfies the following relationship:

[0087]

[0088] Step 2-2, combining assumptions 1 and 2, the following switching strategy is proposed:

[0089]

[0090] Here is the value of the deterministic switching signal η(t) at time t k .

[0091] The step three constructs a functional containing a triple integral term and an exponential term, and the time delay part in the system is processed by the generalized free matrix integral inequality and the quadratic function negative lemma. Finally, based on the probability equation of the Markov process and the designed MSE switching strategy, the system is proved to be exponentially almost everywhere stable. The specific steps are as follows:

[0092] Step 3-1, first define the Lyapunov-Krasovskii functional as follows:

[0093]

[0094] Where:

[0095]

[0096]

[0097]

[0098]

[0099] Step 3-2, the derivative of the above functional is:

[0100]

[0101]

[0102]

[0103]

[0104] Step 3-3, Let And using generalized free matrix integral inequality and Jensen's inequality method, we can get:

[0105]

[0106] Step 3-4, by the negative definite lemma of quadratic function, we have Therefore, the following inequality holds:

[0107]

[0108] Step 3-5, suppose is a random switching signal ρ(t,η k ) on the switching time sequence in the time interval [t k , t k+1 ) and let According to the following inequality holds:

[0109]

[0110] Generally, for the following inequality holds:

[0111]

[0112] In the above formula, is the activation number of the i-th mode of the j-th Markov jump subsystem in the time interval [t k , t).

[0113] Step 3-6, suppose {(0,η0),(t1,η1),...,(t k ,η k )} is the switching sequence of the deterministic switching signal η(t) on [0,t] and satisfies Suppose for a given constant the stationary distribution and the transition rate there is a constant κ such that the following inequality holds:

[0114]

[0115]

[0116] Step 3-7, using the probability equation of Markov process, we can get:

[0117]

[0118] Step 3-8, taking mathematical expectation on both sides of the above inequality can obtain:

[0119]

[0120] Step 3-9, using And let The following inequality is established:

[0121]

[0122] Step 3-10, finally

[0123]

[0124] From the above formula, the variable double switching time delay system is exponentially almost everywhere stabilized under the control gain matrix And the designed MSE switching strategy.

[0125] That is, a new switching method is proposed and the sufficient condition for system stabilization is obtained under the influence of time delay, and the maximum time delay allowed by the system is obtained by solving the sufficient condition. The present application proposes a new type of time-state dependent hybrid MSE switching strategy, and under the switching strategy, the sufficient condition for the system to be exponentially almost everywhere stabilized is given and proved by constructing a functional. The switching strategy and the stabilization condition of the system designed by the present application are applicable to control systems with complex switching dynamic characteristics, and have very important practical significance for modeling and control of complex systems.

[0126] Specifically, for the MSE switching strategy designed for the variable double switching time delay system and the obtained system stabilization condition, the stabilization method of the double switching time delay system based on the MSE switching of the present embodiment comprises the following steps:

[0127] Step 1, the state space expression of the variable double switching time delay system is given.

[0128]

[0129] x(0)=x0

[0130] In the above formula, is the state vector of the system, is the control input, η(t)∈{1,2,...,m} is a deterministic switching signal, and ρ(t,η(t))∈{1,2,...,n} is a random switching signal. is a constant matrix with appropriate dimensions. is a continuous time-varying time delay and satisfies

[0131]

[0132] Step two, design the MSE switching strategy based on Lyapunov stability theory.

[0133] According to Lyapunov stability theory, if a control system tends to be stable, its internal "energy" will decrease over time, that is, the state of the system will gradually tend to the equilibrium point of the system. Since different Markov jump subsystems in the variable double switching time-delay system are governed by different Markov processes, the following assumptions are proposed:

[0134] Assumption 1: The jth Markov jump subsystem of the variable double switching time-delay system is activated at time t k-1 , the j+1th Markov jump subsystem is activated at time t k , and the expectation of the Markov jump linear subsystem satisfies the following relationship:

[0135]

[0136] Here, is the quadratic form related matrix in the derivative of the system functional. The above formula indicates that the Markov jump subsystem with smaller state expectation will be activated and run.

[0137] Assumption 2: The ith mode of the jth Markov jump subsystem of the variable double switching time-delay system is activated at time t k-1 , the i+1th mode of the jth Markov jump subsystem is activated at time t k , and the mode expectation of the Markov jump linear subsystem satisfies the following relationship:

[0138]

[0139] Considering that different Markov jump subsystems in the variable double switching time-delay system are governed by different Markov processes, and the switching between subsystem modes has different transition probabilities, in order to ensure that the switching between modes of different Markov jump subsystems follows the above formula, a decay factor less than 1 is multiplied on the right side of the above formula where ζ [j] < 0, Δ t = t k - t k-1 , then the following inequality holds:

[0140]

[0141] Combining Assumption 1 and Assumption 2, the following time-state dependent hybrid MSE switching strategy is proposed:

[0142]

[0143] Here

[0144] To determine the value of the certainty switching signal η(t) at time t k

[0145] Step three, prove the system is almost surely exponentially stable under the designed MSE switching strategy.

[0146] First, define the Lyapunov-Krasovskii functional as follows:

[0147]

[0148] Where

[0149]

[0150]

[0151]

[0152]

[0153] Take the derivative of the above Lyapunov-Krasovskii functional to get the following form:

[0154]

[0155]

[0156]

[0157] Let And use the generalized free matrix integral inequality and Jensen's inequality method to get the following inequality:

[0158]

[0159]

[0160] Where

[0161]

[0162]

[0163]

[0164]

[0165] ​

[0166] By the quadratic function negative lemma, we have Thus, we have the following inequality:

[0167]

[0168] (05) Assume is a stochastic switching signal and k is the switching time sequence of k on the time interval k+1 . Let According to the following inequality holds:

[0169]

[0170] In general, for the following inequality holds:

[0171]

[0172] In the above formula, is the activation number of the ith mode of the jth Markov jump subsystem on the time interval k .

[0173] Assume is the switching sequence of the deterministic switching signal k on k and satisfies Stationary distribution and transition rate There is a constant such that the following inequality holds:

[0174]

[0175]

[0176] Using the probability equation of Markov process, the following inequality holds:

[0177]

[0178] Taking the mathematical expectation on both sides of the inequality and using the MSE deterministic switching strategy, we have the following inequality:

[0179] Using

[0180]

[0181] The following inequality holds:

[0182]

[0183] Finally, we have

[0184]

[0185] From the above equation, the variable double-switching time-delay system is exponentially almost globally stabilized under the designed MSE switching strategy with the control gain matrix

[0186] Step four, solve the controller gain matrix of the variable double-switching time-delay system through the following linear matrix inequality:

[0187]

[0188]

[0189]

[0190]

[0191]

[0192] wherein

[0193]

[0194]

[0195]

[0196]

[0197]

[0198]

[0199]

[0200] In the above equation, is a symmetric positive definite real matrix; is an arbitrary matrix; is a given scalar. The V i [j] i [j] , the gain matrix

[0201] ​​This embodiment presents a stabilization method for a variable dual-switching time-delay system based on an MSE switching strategy, utilizing Matlab 2015b software. Figure 2 Taking the fault-prone system shown as an example, the invention's time-state dependent hybrid MSE switching strategy and the obtained sufficient condition that the variable double-switching delay system exponent is almost always stable are verified:

[0202] (01) In Figure 2 In the fault-prone system shown, the left side represents the supervisor that generates a deterministic switching signal, which is used to select the controller in the controller set. The right side represents the controlled object. When the system experiences random mutations in its internal physical properties or external random disturbances, the fault-prone system will exhibit both fault-free and fault-free modes, with the transition between these modes governed by a Markov process. The system parameters are selected as follows:

[0203]

[0204]

[0205]

[0206] (02) The transition matrix of the Markov process is selected as follows:

[0207]

[0208] The stationary distribution is:

[0209] D [1] =[1 / 3 2 / 3]D [1] =[3 / 41 / 4]

[0210] (03) Selecting the attenuation factor The maximum allowable time delay of the variable double-switching time-delay system can be obtained by solving the linear matrix inequality using Matlab 2015b. At the same time, the solution obtained The control gain matrix can be calculated. and The matrices are as follows:

[0211]

[0212]

[0213]

[0214]

[0215] The results show that: from the matrix and its stationary distribution D[1] A deterministic switching signal such as Figure 3 , Figure Four is a random switching signal, Figure Five The seven sample implementations of the variable double switching time delay system under the MSE deterministic switching signal and the random switching signal are shown as follows. Figure Five It can be known that the variable double switching time delay system is exponentially almost everywhere stabilized under the designed MSE switching signal and the controller.

[0216] To achieve the above object, the application further provides a control system of a double switching time delay system based on an MSE switching strategy, as shown in Figure 7 The system specifically comprises:

[0217] An expression generating unit is configured to generate a state space expression of the variable double switching time delay system according to the MSE switching double switching time delay system.

[0218] A switching strategy constructing unit is configured to construct the MSE switching strategy in combination with Lyapunov stability theory.

[0219] A stabilization control unit is configured to perform real-time stabilization control on the variable double switching time delay system according to the constructed MSE switching strategy.

[0220] Further, the state space expression is specifically:

[0221]

[0222] x(0)=x0 (2)

[0223] Wherein: is a system state vector, is a control input, η(t)∈{1,2,...,m} is a deterministic switching signal, and ρ(t,η(t))∈{1,2,...,n} is a random switching signal. is a constant matrix with a proper dimension, is a continuous time-varying time delay and satisfies

[0224]

[0225] The switching strategy constructing unit is further provided with:

[0226] A first generating module is configured to generate a controller gain matrix of the variable double switching time delay system in real time.

[0227] The constructed MSE switching strategy is specifically a time-state dependent hybrid switching strategy.

[0228] The expression of the switching strategy is specifically:

[0229]

[0230] wherein: is the value of the deterministic switching signal η(t) at time t k

[0231] The stabilizing control unit is further provided with a first construction module for constructing an obstacle system model.

[0232] An effectiveness verification module is configured to verify the effectiveness of the MSE switching strategy in real time according to the obstacle system model; and a correctness verification module is configured to verify the correctness of the system exponential stabilization control sufficient condition in real time.

[0233] A construction processing module is configured to construct a functional containing a triple integral term and an exponential term, and to process the time delay part in the system in real time by combining a generalized free matrix integral inequality and a quadratic function negative definite lemma.

[0234] In the system scheme embodiment of the present application, the method steps involved in the control of the double-switching time delay system based on the MSE switching strategy are described above, and will not be repeated here.

[0235] To achieve the above object, the present application further provides a control platform of a double-switching time delay system based on the MSE switching strategy, as shown in Figure 8 which comprises a processor, a memory and a control platform control program of the double-switching time delay system based on the MSE switching strategy.

[0236] The processor executes the control platform control program of the double-switching time delay system based on the MSE switching strategy, which is stored in the memory, to realize the method steps of the control of the double-switching time delay system based on the MSE switching strategy, such as: S1, generating a state space expression of a variable double-switching time delay system according to the double-switching time delay system based on the MSE switching; S2, constructing the MSE switching strategy in combination with the Lyapunov stability theory; and S3, performing stabilizing control on the variable double-switching time delay system in real time according to the constructed MSE switching strategy.

[0237] The specific steps are described above, and will not be repeated here.

[0238] ​In the embodiment of the present application, the processor built in the control platform of the double switching time delay system based on MSE switching strategy can be composed of integrated circuits, for example, can be composed of a single packaged integrated circuit, or can be composed of multiple packaged integrated circuits with same function or different functions, including one or more central processing units (CPU), microprocessors, digital processing chips, graphic processors and combinations of various control chips, etc. The processor connects various components by various interfaces and lines, executes programs or units stored in the memory, and calls data stored in the memory, to execute various functions of the double switching time delay system based on MSE switching and process data.

[0239] The memory is used to store program codes and various data, is installed in the control platform of the double switching time delay system based on MSE switching strategy, and realizes high-speed and automatic access of programs or data during running. The memory includes read-only memory (ROM), random access memory (RAM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), one-time programmable read-only memory (OTPROM), electrically-erasable programmable read-only memory (EEPROM), compact disc read-only memory (CD-ROM) or other optical disc memory, disk memory, tape memory, or any other computer readable medium capable of carrying or storing data.

[0240] To achieve the above object, the present application further provides a computer readable storage medium, as shown in the drawings, the computer readable storage medium stores a control platform control program of the double switching time delay system based on MSE switching strategy. Figure 9 The control platform control program of the double switching time delay system based on MSE switching strategy realizes the steps of the control method of the double switching time delay system based on MSE switching strategy, for example:

[0241] S1, generating a state space expression of the variable double switching time delay system according to the MSE switching double switching time delay system; S2, constructing the MSE switching strategy in combination with the Lyapunov stability theory; S3, performing the stabilizing control on the variable double switching time delay system in real time according to the constructed MSE switching strategy.

[0242] The specific details of the steps have been described above, and will not be repeated here.

[0243] In the description of the embodiments of the present application, it should be noted that any process or method described in the flowchart or otherwise described herein can be understood as representing a module, a segment or a portion of code including one or more executable instructions for implementing specific logical functions or processes, and the scope of the preferred embodiments of the present application includes additional implementations in which the functions can be performed in an order other than that shown or discussed, including in a substantially simultaneous manner or in a reverse order in accordance with the functions involved, which should be understood by those skilled in the art to which the embodiments of the present application belong.

[0244] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a list of executable instructions for implementing logical functions, which can be embodied in any computer-readable medium for use by or in conjunction with an instruction execution system, device or apparatus, such as a computer-based system, a system including a processing module or other system that can fetch instructions from an instruction execution system, device or apparatus and execute the instructions. For the purposes of this specification, a "computer-readable medium" can be any device that can contain, store, communicate, propagate or transport a program for use by or in conjunction with an instruction execution system, device or apparatus or in conjunction with these instruction execution systems, devices or apparatuses. More specific examples (non-exhaustive list) of computer-readable media include the following: electrical connections having one or more wires (electronic devices), portable computer disks (magnetic devices), random access memories (RAM), read-only memories (ROM), erasable programmable read-only memories (EPROM or flash memories), fiber optic devices, and portable compact disk read-only memories (CDROMs).

[0245] In addition, the computer-readable medium can even be paper or other suitable medium on which the program can be printed, as the program can be electronically obtained, for example, by optical scanning of the paper or other medium, followed by electronic copying, and then stored in computer memory.

[0246] In the embodiments of the present application, in order to achieve the above-mentioned purpose, the present application further provides a chip system comprising at least one processor, when program instructions are executed in the at least one processor, the chip system is caused to execute the steps of the control method of the double switching time delay system based on the MSE switching strategy, for example: S1, generating a state space expression of a variable double switching time delay system according to a double switching time delay system based on MSE switching; S2, constructing an MSE switching strategy in combination with Lyapunov stability theory; S3, performing stabilizing control on the variable double switching time delay system in real time according to the constructed MSE switching strategy. The specific details of the steps have been described above, and will not be described here.

[0247] Those skilled in the art can appreciate that the units and algorithm steps of each example described in combination with the embodiments disclosed herein can be realized in electronic hardware or a combination of computer software and electronic hardware. Whether the functions are realized in hardware or software depends on the specific application and design constraints of the technical solution. The skilled person can use different methods to realize the described functions for each specific application, but such implementation should not be considered beyond the scope of the present application. Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working processes of the above-described system, device and unit can refer to the corresponding processes in the foregoing method embodiments, which will not be described here.

[0248] The present application generates a state space expression of a variable double switching time delay system according to a double switching time delay system based on MSE switching; constructs an MSE switching strategy in combination with Lyapunov stability theory; and performs stabilizing control on the variable double switching time delay system in real time according to the constructed MSE switching strategy, so as to realize the sufficient condition of exponential almost everywhere stabilization of the variable double switching time delay system and the maximum time delay allowed by the system. Moreover, the method used by the present application and the obtained stabilizing condition are applicable to system modeling with complex switching dynamic characteristics, and have great theoretical and practical application value.

[0249] That is, compared with deterministic switching time delay systems or random switching time delay systems, the present application firstly takes a double switching time delay system as a research object, which is a powerful expansion of the research on single switching time delay systems. A time-state-dependent hybrid MSE switching strategy is designed, under which the switching times of the system are not limited, and the MSE switching strategy is more suitable for double switching time delay systems.

[0250] By constructing a functional and using generalized free matrix integral inequality and Jensen's inequality method, a sufficient condition of exponential almost everywhere stability and the maximum time delay allowed by the system of variable double switching time delay system are obtained. The method and the obtained stability condition are applicable to the modeling of systems with complex switching dynamic characteristics, and have great theoretical and practical value.

[0251] The above-described embodiments only express several embodiments of the present application, and the description is more specific and detailed, but it should not be understood as a limitation on the scope of the patent of the present application. It should be noted that for ordinary skilled in the art, without departing from the concept of the present application, a number of modifications and improvements can be made, which are all within the scope of protection of the present application. Therefore, the protection scope of the patent of the present application should be subject to the appended claims.

Claims

1. A control method for a dual-switching time-delay system based on an MSE switching strategy, characterized in that... The method specifically includes the following steps: Based on the MSE-switched double-switched time-delay system, generate the state-space expression of the variable double-switched time-delay system; A time-state dependent switching strategy is constructed based on Lyapunov stability theory; specifically, the constructed MSE switching strategy is a time-state dependent hybrid switching strategy; the expression of the switching strategy is as follows: in: For the deterministic switching signal η(t) at t k The value at time; Based on the constructed MSE switching strategy, the variable dual-switching time-delay system is stabilized and controlled in real time.

2. The control method for a dual-switching time-delay system based on an MSE switching strategy according to claim 1, characterized in that... The state-space expression is specifically as follows: x(0)=x0 (2) in: Let be the system state vector. For the control input, η(t)∈{1,2,...,m} is the deterministic switching signal, and ρ(t,η(t))∈{1,2,...,n} is the random switching signal; For a constant matrix with appropriate dimensions, θ t It is a continuous time-varying time delay and satisfies 0 ≤ θ t ≤θ, 3. The control method for a dual-switching time-delay system based on an MSE switching strategy according to claim 1, characterized in that... The method of constructing the MSE switching strategy by combining Lyapunov stability theory also includes the following steps: The controller gain matrix of a variable dual-switching time-delay system is generated in real time.

4. The control method for a dual-switching time-delay system based on an MSE switching strategy according to claim 1, characterized in that... The step of performing real-time stabilization control on the variable dual-switching time-delay system based on the constructed MSE switching strategy further includes the following steps: Construct a fault-prone system model; Based on the fault-prone system model, the effectiveness of the MSE switching strategy is verified in real time; Real-time verification of the correctness of the sufficient conditions for the index-based stabilization control of the system.

5. The control method for a dual-switching time-delay system based on an MSE switching strategy according to claim 4, characterized in that... The step of verifying the effectiveness of the MSE switching strategy in real time based on the vulnerable system model also includes the following steps: A functional containing triple integral and exponential terms is constructed, and the time-delay part of the system is processed in real time by combining the generalized free matrix integral inequality and the negative definite lemma of quadratic functions.

6. A control system for a dual-switching time-delay system based on an MSE switching strategy, characterized in that... The system specifically includes: The expression generation unit is used to generate the state-space expression of the variable double-switched time-delay system based on the MSE-switched double-switched time-delay system. A switching strategy construction unit is used to construct an MSE switching strategy by combining Lyapunov stability theory; the switching strategy construction unit also includes: The first generation module is used to generate the controller gain matrix of the variable dual-switching time-delay system in real time. The MSE switching strategy is specifically a time-state dependent hybrid switching strategy. The specific expression for the switching strategy is as follows: in: For the deterministic switching signal η(t) at t k The value at time; The stabilization control unit is used to perform real-time stabilization control on the variable dual-switching time-delay system according to the constructed MSE switching strategy.

7. The control system for a dual-switching time-delay system based on an MSE switching strategy according to claim 6, characterized in that... The state-space expression is specifically as follows: x(0)=x0 (2) in: Let be the system state vector. For the control input, η(t)∈{1,2,...,m} is the deterministic switching signal, and ρ(t,η(t))∈{1,2,...,n} is the random switching signal; For a constant matrix with appropriate dimensions, θ t Continuous time-varying time delay and satisfying 0≤θ t ≤θ, The stabilization control unit is also provided with: The first building module is used to construct the vulnerable system model; The effectiveness verification module is used to verify the effectiveness of the MSE switching strategy in real time based on the vulnerable system model; The correctness verification module is used to verify the correctness of the sufficient conditions for the system's exponential stabilization control in real time. A processing module is constructed to build a functional containing triple integral terms and exponential terms, and to process the time-delay part of the system in real time by combining the generalized free matrix integral inequality and the negative definite lemma of quadratic functions.

8. A control platform for a dual-switching time-delay system based on an MSE switching strategy, characterized in that... include: Control program for the control platform of the processor, memory, and dual-switching time-delay system based on MSE switching strategy; The processor executes the control platform control program of the dual-switching time-delay system based on the MSE switching strategy. The control platform control program of the dual-switching time-delay system based on the MSE switching strategy is stored in the memory. The control platform control program of the dual-switching time-delay system based on the MSE switching strategy implements the control method steps of the dual-switching time-delay system based on the MSE switching strategy as described in any one of claims 1 to 7.

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