Robust control method and system for multi-balance-point variable-mode system

Abstract

The invention provides a robust control method and system for a multi-balance-point variable-mode system, and belongs to the field of hybrid system control. The problems that an existing H-infinity controller is difficult to be used for a multi-balance-point variable-mode system, robust performance improvement of the multi-balance-point variable-mode system in practical application is limited, and resistance to external interference is weak are solved. According to the method, the generalization situation that subsystems have different balance points is considered, the stability and convergence area estimation method of the multi-balance-point variable-mode system is provided, and therefore more accurate control over complex variable-mode system behaviors is achieved; the H-infinity controller is designed for the problem of external interference generally existing in practical application, the resistance of the variable-mode system to external bad interference is remarkably enhanced, the stability and reliability of the system are ensured, a new view angle is provided for research of the variable-mode system, and the application range of the variable-mode system is widened. And powerful technical support is provided for practical application in related fields.

Description

Technical Field

[0001] The present invention relates to the technical field of control of hybrid systems, and in particular to a robust control method and system for a multi-equilibrium point variable mode system. Background Art

[0002] Variable modal system is a special type of hybrid control system, which contains multiple subsystems (modes) and variable modal signals. Variable modal system theory plays an important role in the modeling and control of physical systems with modal variation characteristics, and has been widely used in the fields of UAV flight control, robotic arm control, multi-agent system control, traffic management control, and chemical process control. In this context, in-depth research on the control methods and robust control techniques of variable modal systems is of great significance to ensure the stability of the control system and improve its anti-interference ability.

[0003] In the field of variable modal system research, system stability analysis and controller design are hot issues. Most existing studies focus on the situation where all subsystems have a common equilibrium point. In practical engineering applications such as power control, legged robots, and flapping-wing robots, each subsystem often has a different equilibrium point. The multi-equilibrium variable modal system is an extension of the conventional common equilibrium point variable modal system and a more general control system model. The existence of multiple equilibrium points makes the system behavior more complex. The existing control methods for variable modal systems are no longer applicable here. When discussing the stability of a multi-equilibrium variable modal system, it is unrealistic for the trajectory to converge to a certain point, but it is more reasonable to converge to a certain area. Although a small number of studies have explored the stability conditions of multi-equilibrium variable modal systems, no clear controller design method has been proposed. How to propose a stability analysis method suitable for multi-equilibrium variable modal systems and design controllers needs to be studied urgently.

[0004] The L2 gain of a variable modal system is a key indicator for evaluating its control performance. The L2 gain can quantify the anti-interference ability of the control system. In modern industrial control, aerospace, and autonomous driving, the L2 gain performance directly affects the safety and reliability of the entire system. In the past few decades, a large number of studies have been devoted to the L2 gain analysis of common equilibrium point variable modal systems, and remarkable results have been achieved. These studies proposed the bounded real lemma and designed the H ∞ The controller provides an effective solution for the stability and robust control of variable modal systems. However, these research results are also limited by the assumption of a common equilibrium point and are difficult to apply to multi-equilibrium variable modal systems. ∞ The research on controller design is still insufficient, which limits the improvement of robust performance of multi-equilibrium variable modal systems in practical applications. Therefore, the bounded real lemma of multi-equilibrium variable modal systems is studied, and a multi-equilibrium H∞ Variable mode controller has important theoretical value and practical significance in promoting the development of variable mode system control theory. Summary of the invention

[0005] The technical problems to be solved by the present invention are:

[0006] In order to solve the problem that the existing H∞ controller is difficult to use in multi-equilibrium point variable modal systems, which limits the improvement of the robust performance of multi-equilibrium point variable modal systems in practical applications and has weak resistance to external disturbances.

[0007] The present invention adopts the following technical solutions to solve the above technical problems:

[0008] The present invention provides a robust control method for a multi-equilibrium point variable mode system, comprising the following steps:

[0009] S100, establishing a control system model of a multi-equilibrium-point variable modal system, describing the multi-equilibrium-point variable modal system as a multi-equilibrium-point variable modal system with multiple equilibrium points and external interference, and then expanding the existing definition of stability and L2 gain of the variable modal system;

[0010] S200, based on the multi-Lyapunov function method, assigning a Lyapunov function about the center of the convergence region to each mode with different equilibrium points, and giving a criterion for global consistent asymptotic regional stability according to the rate of change of the Lyapunov function, and using this criterion to evaluate the stability of the multi-equilibrium point variable mode system under the condition of average residence time;

[0011] S300, according to the influence of variable mode and multi-equilibrium point characteristics on the L,gain performance index of the multi-equilibrium point variable mode system, the L,gain analysis method of the multi-equilibrium point variable mode system is established, and then the bounded real lemma in the form of linear matrix inequality is proposed;

[0012] S400 , designing a H∞ variable modal controller of a multi-equilibrium variable modal system with a modal-dependent state feedback according to the bounded real lemma in the form of a linear matrix inequality proposed in step S300 .

[0013] Furthermore, in step S100, it specifically includes:

[0014] S110, the multi-equilibrium point variable modal system model is:

[0015]

[0016] in, is the state vector; is the control input vector; is the measured output vector; w is the disturbance input vector belonging to L2[0,∞); σ(t)=i is the variable mode signal, indicating that mode i is currently activated; A is the state matrix; B is the input matrix; C is the output matrix; D is the direct transfer matrix; E is the disturbance input matrix; F is the disturbance output matrix;

[0017] and represent the equilibrium state, balanced input and balanced output of mode i respectively;

[0018] S120, the stability of the expanded multi-equilibrium variable modal system is defined as:

[0019] For a multi-equilibrium variable mode system If there exists a positive constant δ and a KL-like function β, such that for all variable modal signals σ, the solution of the system satisfies Then the multi-equilibrium variable mode system is globally consistent and asymptotically stable:

[0020]

[0021] in,

[0022]

[0023] n represents the dimension of the state vector x; and R are Ω e The center and radius of

[0024] S130. The L2 gain of the expanded multi-equilibrium point variable mode system is defined as:

[0025] For a multi-equilibrium variable mode system, if under the initial condition x(t0), for If the following inequality holds, the multi-equilibrium variable mode system has an unweighted L2 gain γ:

[0026]

[0027] in, represents the deviation between the measured output and the current balanced output; C is a positive constant related to x(t0).

[0028] Furthermore, in step S200, it specifically includes:

[0029] For multi-equilibrium variable mode systems Assuming constants λ>0 and μ≥1, define the region in, and R are given constants;

[0030] Assume that the Lyapunov function and two Class functions k1 and k2 such that,

[0031]

[0032] V i (x)≤μ xj (x) (6)

[0033] in, Represents a collection of modalities;

[0034]

[0035] The average residence time τ of the variable mode system with multiple equilibrium points a The modal signal satisfying formula (8) is globally consistent and asymptotically stable, and has a stable region Ω e ;

[0036]

[0037] in, is the bound that the average residence time needs to meet;

[0038] The initial state x(0) is outside the stable region;

[0039] Assume t0 = 0, and Expressed as the variable mode moment on the interval [0, T); for In each interval have,

[0040]

[0041] According to formula (6), we can get:

[0042]

[0043] According to formula (9) and formula (10), we can get:

[0044]

[0045] From i=0 to i=N σ (T, 0)-1 iterations, we can get:

[0046]

[0047] Among them, N0 represents the threshold value when the system switches, which is used to ensure the minimum number of times the system remains in the mode after switching to the new mode;

[0048] If the average residence time τ a If formula (8) is satisfied, the state will eventually converge to the stable region.

[0049] Furthermore, in step S300, it specifically includes:

[0050] S310, for a multi-equilibrium variable modal system, let constants λ>0, μ≥1 and γ i >0, and define the area in, and R are given constants;

[0051] Assumption Function and two Functions k1 and k2 such that,

[0052]

[0053] V i (x)≤μV j (x) (14)

[0054] in,

[0055] And Can get,

[0056]

[0057] in,

[0058] Then the multi-equilibrium variable mode system is globally consistent and asymptotically stable under the variable mode signal with the average residence time satisfying formula (8), and has a stability of no more than γ * The unweighted L2 gain of

[0059]

[0060] S320, based on the L2 gain condition of the multi-equilibrium variable mode system in step S310, a bounded real lemma in the form of a linear matrix inequality is proposed:

[0061] For a multi-equilibrium variable mode system, let λ>0, μ≥1, η>1 and γ i >0 are all given constants; if the constant ∈ i ≥0 and positive definite matrix P i >0, So that,

[0062] P i ≤μP j (17)

[0063]

[0064] in,

[0065] Then the multi-equilibrium variable mode system is globally consistent asymptotically stable in the stable region for the variable mode signal that satisfies formula (8), and has formula (16) that does not exceed γ * The unweighted L2 gain of

[0066]

[0067] in, is the center of the minimum covering circle of all equilibrium points; R MVH >0, is the radius of the minimum covering circle.

[0068] Furthermore, a recursive randomized algorithm is used to solve the minimum covering circle.

[0069] Furthermore, in step S400, it specifically includes:

[0070] For a multi-equilibrium variable mode system, set λ>0, μ≥1 and γ i >0 is a given constant; if there is a constant ∈ i ≥0 and matrix X i >0,W i , so that,

[0071] X j ≤μX i (20)

[0072]

[0073] Where Ψ=A i X i +B i W i +(A i X i +B i W i ) T +λX i ;

[0074] Then there exists a set of modally dependent state feedback H ∞ Controller u(t) = K i x(t), so that the multi-equilibrium variable mode system is globally consistent and asymptotically stable when the variable mode signal satisfies formula (8), and the convergence region is Ω e , and the formula (16) does not exceed γ * The unweighted L2 gain of .

[0075] The present invention provides a robust control system for a multi-equilibrium point variable mode system. The system has a program module corresponding to the above steps and executes the steps in the above robust control method for the multi-equilibrium point variable mode system during operation.

[0076] The present invention provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, wherein the computer program is configured to implement steps of a robust control method for a multi-equilibrium point variable mode system when called by a processor.

[0077] Compared with the prior art, the present invention has the following beneficial effects:

[0078] ① Aiming at a type of variable modal system model in which each subsystem has different equilibrium points, the present invention proposes the concept of global consistent asymptotic regional stability and provides a numerically verifiable stability criterion applicable to multi-equilibrium point variable modal systems; the stability analysis method adopted by the present invention extends the common equilibrium point variable modal system in existing research to a more generalized multi-equilibrium point situation, thus expanding the scope of application of the stability analysis and controller design method of the variable modal system;

[0079] ② In order to cope with the external interference problems encountered in actual control systems, the designed H∞ controller significantly improves the robustness of the variable mode system; and the multi-equilibrium point H∞ variable mode control method proposed in the present invention improves the system's resistance to external interference, improves the safety and reliability of the control system, and has high engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] Figure 1 It is a flow chart of a robust control method of a multi-equilibrium point variable mode system in an embodiment of the present invention;

[0081] Figure 2 Schematic diagram of the state trajectory of a multi-equilibrium variable modal system with GUARS guarantee in an embodiment of the present invention, wherein GUARS is globally consistent asymptotic regional stability;

[0082] Figure 3 A schematic diagram of solving the minimum covering circle of all equilibrium points of a multi-equilibrium point variable mode system in an embodiment of the present invention;

[0083] Figure 4 A variable mode signal diagram used in a simulation experiment in an embodiment of the present invention;

[0084] Figure 5 The multi-balance point variable mode controller and the multi-balance point H in the embodiment of the present invention when the system has interference ∞ The state response comparison curve of the variable mode controller, where x1 and x2 represent the two state variables of the system respectively;

[0085] Figure 6 It is a deviation comparison curve diagram between the measured output and the current balanced output of the multi-balance point variable mode controller and the multi-balance point H∞ variable mode controller when there is interference in the system in an embodiment of the present invention. DETAILED DESCRIPTION

[0086] In the description of the present invention, it should be noted that the terminology nouns in the various embodiments, such as "up", "down", "front", "back", "left", "right", etc., which indicate directions, are only for simplifying the description of the positional relationship based on the drawings in the specification, and do not mean that the referred elements and devices must be operated according to the specific directions and defined operations and methods and structures in the specification. Such directional nouns do not constitute a limitation on the present invention.

[0087] In the description of the present invention, it should be noted that the terms "first", "second", and "third" mentioned in the embodiments of the present invention are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first", "second", and "third" may explicitly or implicitly include one or more of the features.

[0088] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, specific embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0089] Specific implementation plan 1: Combine Figures 1 to 3 As shown, the present invention provides a robust control method for a multi-equilibrium point variable mode system, comprising the following steps:

[0090] S100, establishing a control system model of a multi-equilibrium-point variable modal system, including: describing the multi-equilibrium-point variable modal system as a multi-equilibrium-point variable modal system with multiple equilibrium points and external interference, and then expanding the existing definition of stability and L2 gain of the variable modal system to adapt to the situation of multiple equilibrium points, specifically including:

[0091] S110. Consider the following multi-equilibrium variable modal system model:

[0092]

[0093] in, is the state vector, is the control input vector, is the measured output vector, w is the disturbance input vector belonging to L2[0,∞); σ(t)=i is the variable mode signal, indicating that mode i is currently activated;

[0094] and Represent the equilibrium state, balanced input and balanced output of mode i respectively; A is the state matrix; B is the input matrix; C is the output matrix; D is the direct transfer matrix; E is the interference input matrix; F is the interference output matrix;

[0095] S120. Give the stability definition of a multi-equilibrium variable modal system: For a multi-equilibrium variable modal system If there exists a positive constant δ and a KL-like function β such that for all modal signals σ, the solution of the system satisfies Then the multi-equilibrium variable mode system is called globally consistent asymptotically stable (GUARS);

[0096]

[0097] in

[0098]

[0099] n represents the dimension of the state vector x, and R are Ω e The center and radius of

[0100] S130. Define the L2 gain of a multi-equilibrium point variable mode system: For a multi-equilibrium point variable mode system, if under the initial condition x(t0), for The following inequality holds:

[0101]

[0102] in represents the deviation between the measured output and the current balanced output; C is a positive constant related to x(t0); the multi-balance point variable mode system is said to have an unweighted L2 gain γ; T represents the matrix transpose;

[0103] S200, propose a stability criterion to evaluate the stability of a multi-equilibrium variable mode system, including: based on a multi-Lyapunov function method, assign a Lyapunov function about the center of the convergence region to each equilibrium point, and then give a criterion for global consistent asymptotic regional stability according to the rate of change of the Lyapunov function, and evaluate the stability of the multi-equilibrium variable mode system under the condition of average residence time by using the criterion, specifically including,

[0104] According to Theorem 1: Consider a multi-equilibrium variable modal system Assuming constants λ>0 and μ≥1, define the region in, and R are given constants;

[0105] Assume that there exists a Lyapunov function ( represents a collection of modes) and two Class functions k1 and k2 such that,

[0106] right

[0107]

[0108] V i (x)≤μV j (x) (6)

[0109] And

[0110]

[0111] The average residence time τ of the variable mode system with multiple equilibrium points a The modal signal GUARS satisfies formula (8) and has a stable region Ω e ;

[0112]

[0113] It can be shown that, considering the initial state x(0) is outside the stable region;

[0114] Assume t0 = 0, and let represents the variable mode moment on the interval [0, T); for In each interval have,

[0115]

[0116] According to formula (6), we can get:

[0117]

[0118] According to formulas (9) and (10), we can get:

[0119]

[0120] From i=0 to i=N σ (T, 0)-1 iterations, we can get:

[0121]

[0122] Among them, N0 represents a threshold when considering the system switching behavior, which is used to ensure that the system stays in the mode for at least the minimum number of times after switching to the new mode; if the average residence time condition is met, the GUARS of the system can be guaranteed;

[0123] The state trajectory of the multi-equilibrium variable modal system with GUARS guarantee is as follows: Figure 2 As shown, the state trajectory starts from x(0) and evolves to the equilibrium point of the currently activated mode; when the average residence time condition is met, the state eventually converges to the stable region;

[0124] S300, establishing an L2 gain analysis method for a multi-equilibrium-point variable mode system, comprising: firstly, according to the L2 gain analysis method for a multi-equilibrium-point variable mode system, and the influence of variable mode and multi-equilibrium-point characteristics on the system L2 gain, based on the L2 gain analysis results, a bounded real lemma in the form of a linear matrix inequality is proposed, specifically including:

[0125] S310, according to Theorem 2: Consider a multi-equilibrium variable modal system, that is, formula (1), set constants λ>0, μ≥1 and γ i >0, and define the area in and R are given constants;

[0126] Assume there is a function and two Functions k1 and k2,

[0127] Make

[0128]

[0129] V i (x)≤μV j (x) (14)

[0130] in,

[0131] And Can get,

[0132]

[0133] in,

[0134] Then the multi-equilibrium variable mode system has GUARS under the variable mode signal under the average residence time satisfying formula (8) and has no more than γ * The unweighted L2 gain of

[0135]

[0136] S320. Based on the L2 gain condition of the above multi-equilibrium variable mode system, in order to ensure numerical verifiability, a bounded real lemma in the form of a linear matrix inequality is proposed. The bounded real lemma of the multi-equilibrium variable mode system is as follows;

[0137] According to Theorem 3: Consider a multi-equilibrium variable mode system, let λ>0, μ≥1, η>1 and γ i >0 are all given constants; if there is a constant ∈ i ≥0 and positive definite matrix P i >0, So that,

[0138] for

[0139] P i ≤μP j (17)

[0140]

[0141] Then the multi-equilibrium variable mode system has an average residence time τ a The variable mode signal that satisfies formula (8) is GUARS in the stable region, and has formula (16) not exceeding γ * The unweighted L2 gain of

[0142]

[0143] in, is the center of the minimum covering circle of all equilibrium points, R MVH >0, is the radius of the minimum covering circle;

[0144] The schematic diagram of solving the minimum covering circle of all equilibrium points is as follows Figure 3 As shown in the figure, the solution of the minimum covering circle adopts a recursive randomized algorithm; the basic idea is to solve the minimum covering circle on a smaller subset of equilibrium points, so that a small adjustment to this solution can cover the entire set of equilibrium points; the basic steps of the algorithm are as follows: ① Basic case, if the point set is empty or a circle containing three or less equilibrium points has been found, then these equilibrium points are directly used to calculate the minimum circle; ② Recursive step, randomly select a point p, assuming that the minimum covering circle of other points has been calculated, then point p is already in this circle, then it is the minimum covering circle of the entire set of equilibrium points; otherwise, point p must be on the boundary of the new minimum covering circle;

[0145] S400. Based on the bounded real lemma of multi-equilibrium variable modal system, design the modal-dependent state feedback H∞ variable modal controller of multi-equilibrium variable modal system, including:

[0146] According to Theorem 4: For a multi-equilibrium variable mode system, set λ>0, μ≥1 and γi>0 as given constants. If there exists a constant ∈ i ≥0 and matrix X i >0,W i , so that for

[0147] X j ≤μX i (20)

[0148]

[0149] Where Ψ=A i X i +B i W i +(A i X i +B i W i ) T +λX i , then there exists a set of modally dependent state feedback H ∞ Controller u(t) = K i x(t), so that the multi-equilibrium point variable mode system is GUARS when the variable mode signal satisfies formula (8), and the convergence area is Ω e , and has formula (16) not exceeding γ * The unweighted L2 gain of .

[0150] Specific implementation scheme 2: The present invention provides a robust control system for a multi-equilibrium point variable mode system, which has a program module corresponding to the above steps and executes the steps in the above-mentioned robust control method for a multi-equilibrium point variable mode system during operation.

[0151] The other combinations and connection relationships of this embodiment are the same as those of the first embodiment.

[0152] Specific implementation scheme three: The present invention provides a computer-readable storage medium, which stores a computer program, and the computer program is configured to implement the steps of a robust control method for a multi-equilibrium point variable mode system when called by a processor.

[0153] The other combinations and connection relationships of this embodiment are the same as those of the first embodiment.

[0154] Simulation experiment

[0155] A simulation study is conducted on a two-dimensional multi-equilibrium variable modal system with external disturbance. The external disturbance signal of the system is w = 30sin(0.5t)exp(-0.15t). First, a multi-equilibrium variable modal controller is designed based on Theorem 1 in step S200. Then, Theorem 4 is used to design the multi-equilibrium H ∞ Variable mode controller, this controller takes the anti-interference ability of the system into consideration during the design process, and enhances the robustness of the control system by optimizing the design of the non-weighted L2 gain. Both controllers are used in simulation numerical examples for testing. Figure 4 The figure shows the average residence time variable mode signal used in the simulation. In the simulation results, the multi-balance point variable mode controller and the multi-balance point H are recorded. ∞ The state response curve and output curve of the variable mode controller. Among them, the state response curve is as follows Figure 5 shown. Figure 6 The deviation between the measured output and the balanced output is given. At the moment of mode change, the deviation between the measured output and the balanced output has an instantaneous jump, which is mainly due to the instantaneous change of the balanced output. In addition, compared with the multi-balance point variable mode controller, the multi-balance point H ∞ The variable mode controller shows a more superior robust performance, especially in suppressing periodic external interference, because the anti-interference performance index is additionally considered in its design process. The simulation results verify the effectiveness and advantages of the description method adopted by the present invention.

[0156] Although the present invention is disclosed as above, the protection scope of the present invention is not limited thereto. Those skilled in the art may make various changes and modifications without departing from the spirit and scope of the present invention, and these changes and modifications will fall within the protection scope of the present invention.

Claims

1. A robust control method for a multi-equilibrium point variable mode system, characterized in that: The following steps are involved: S100, establishing a control system model of a multi-equilibrium-point variable modal system, describing the multi-equilibrium-point variable modal system as a multi-equilibrium-point variable modal system with multiple equilibrium points and external interference, and then expanding the existing definition of stability and L2 gain of the variable modal system; S200, based on the multi-Lyapunov function method, assigning a Lyapunov function about the center of the convergence region to each mode with different equilibrium points, and giving a criterion for global consistent asymptotic regional stability according to the rate of change of the Lyapunov function, and using this criterion to evaluate the stability of the multi-equilibrium point variable mode system under the condition of average residence time; S300, according to the influence of variable mode and multi-equilibrium point characteristics on the L2 gain performance index of the multi-equilibrium point variable mode system, an L2 gain analysis method of the multi-equilibrium point variable mode system is established, and then a bounded real lemma in the form of linear matrix inequality is proposed; S400, according to the bounded real lemma in the form of linear matrix inequality proposed in step S300, design the H of the mode-dependent state feedback of the multi-equilibrium point variable mode system ∞ Variable mode controller.

2. The robust control method for a multi-equilibrium point variable mode system according to claim 1, characterized in that: In step S100, it specifically includes: S110, the multi-equilibrium point variable modal system model is: in, is the state vector; is the control input vector; is the measured output vector; w is the disturbance input vector belonging to L2[0,∞); σ(t)=i is the variable mode signal, indicating that mode i is currently activated; A is the state matrix; B is the input matrix; C is the output matrix; D is the direct transfer matrix; E is the disturbance input matrix; F is the disturbance output matrix; and represent the equilibrium state, balanced input and balanced output of mode i respectively; S120, the stability of the expanded multi-equilibrium variable modal system is defined as: For a multi-equilibrium variable mode system If there exists a positive constant δ and a KL-like function β, such that for all variable modal signals σ, the solution of the system satisfies Then the multi-equilibrium variable mode system is globally consistent and asymptotically stable: in, n represents the dimension of the state vector x; and R are Ω e The center and radius of S130. The L2 gain of the expanded multi-equilibrium point variable mode system is defined as: For a multi-equilibrium variable mode system, if under the initial condition x(t0), for If the following inequality holds, the multi-equilibrium variable mode system has an unweighted L2 gain γ: in, represents the deviation between the measured output and the current balanced output; C is a positive constant related to x(t0).

3. The robust control method for a multi-equilibrium point variable mode system according to claim 2, characterized in that: In step S200, it specifically includes: For multi-equilibrium variable mode systems Assuming constants λ>0 and μ≥1, define the region in, and R are given constants; Assume that the Lyapunov function and two κ ∞ Class functions k1 and k2 such that, V i (x)≤μV j (x) (6) in, Represents a collection of modalities; The average residence time τ of the variable mode system with multiple equilibrium points a The modal signal satisfying formula (8) is globally consistent and asymptotically stable, and has a stable region Ω e ; in, is the bound that the average residence time needs to meet; The initial state x(0) is outside the stable region; Assume t0 = 0, and Expressed as the variable mode moment on the interval [0, T); for In each interval have, According to formula (6), we can get: According to formula (9) and formula (10), we can get: From i=0 to i=N σ (T, 0)-1 iterations, we can get: Among them, N0 represents the threshold value when the system switches, which is used to ensure the minimum number of times the system remains in the mode after switching to the new mode; If the average residence time τ a If formula (8) is satisfied, the state will eventually converge to the stable region.

4. The robust control method for a multi-equilibrium point variable mode system according to claim 3, characterized in that: In step S300, it specifically includes: S310, for a multi-equilibrium variable modal system, let constants λ>0, μ≥1 and γ i >0, and define the area in, and R are given constants; Assumption Function and two κ ∞ Functions k1 and k2 such that, V i (x)≤μV j (x) (14) in, And Can get, in, Then the multi-equilibrium variable mode system is globally consistent and asymptotically stable under the variable mode signal with the average residence time satisfying formula (8), and has a stability of no more than γ * The unweighted L2 gain of S320, based on the L2 gain condition of the multi-equilibrium variable mode system in step S310, a bounded real lemma in the form of a linear matrix inequality is proposed: For a multi-equilibrium variable mode system, let λ>0, μ≥1, η>1 and γi>0 be given constants; if the constant ∈ i ≥0 and positive definite matrix P i >0, So that, P i ≤μP j (17) in, Then the multi-equilibrium variable mode system is globally consistent asymptotically stable in the stable region for the variable mode signal that satisfies formula (8), and has formula (16) that does not exceed γ * The unweighted L2 gain of in, is the center of the minimum covering circle of all equilibrium points; R MVH >0, is the radius of the minimum covering circle.

5. The robust control method for a multi-equilibrium point variable mode system according to claim 4, characterized in that: The solution to the minimum covering circle adopts a recursive randomized algorithm.

6. The robust control method for a multi-equilibrium point variable mode system according to claim 4, characterized in that: In step S400, it specifically includes: For a multi-equilibrium variable mode system, set λ>0, μ≥1 and γ i > is a given constant; if there exists a constant ∈ i ≥0 and matrix X i >0,W i , so that, X j ≤μX i (20) where Ψ = A i X i + B i W i +(A i X i + B i W i ) T + λx i ; Then there exists a set of modally dependent state feedback H ∞ Controller u(t) = K i x(t), so that the multi-equilibrium variable mode system is globally consistent and asymptotically stable when the variable mode signal satisfies formula (8), and the convergence region is Ω e , and the formula (16) does not exceed γ * The unweighted L2 gain of .

7. A robust control system for a multi-equilibrium point variable mode system, characterized in that: The system has a program module corresponding to the steps of any one of claims 1 to 6, and executes the steps of the robust control method of the multi-equilibrium point variable mode system when running.

8. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and the computer program is configured to implement the steps of the robust control method for a multi-balance-point variable-mode system according to any one of claims 1 to 6 when called by a processor.

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