A generalized switching control method and system with both anti-asynchronous capability and interference suppression performance

Abstract

The present invention provides a generalized switching control method and system with both anti-asynchronous capability and interference suppression performance, belonging to the field of generalized switching system control technology. In order to solve the problem that the modal asynchronous characteristics and the influence of external interference are not fully considered in the existing generalized switching control methods. In response to the problems of modal asynchrony and external interference, the present invention designs a state feedback switching controller with stability and H∞ performance guarantee based on the generalized switching system framework and the multi-Lyapunov function method. Compared with the traditional non-modal asynchronous method and the traditional method that does not consider asynchrony, the modal asynchronous method proposed in the present invention has better practicality and application potential, and shows better convergence performance in simulation; and considering the actual situation with interference, the designed controller not only guarantees stability, but also guarantees H∞ performance, and provides the L2 gain expression form of the closed-loop system; it expands the existing generalized switching system theoretical system and has high engineering application value.

Description

Technical Field

[0001] The present invention relates to the technical field of generalized switching system control, and in particular to a generalized switching control method and system with both anti-asynchronous capability and interference suppression performance. Background Art

[0002] Generalized switching systems, as hybrid systems that combine differential and algebraic equations, offer significantly improved modeling capabilities and application potential compared to traditional switching systems. In recent years, generalized switching systems have garnered widespread attention, and related research findings have been applied to practical scenarios such as mobile robots, multi-constrained manipulators, and large-scale circuit systems.

[0003] Controller design is a hot topic in the study of generalized switched systems. For generalized switched systems, switched controllers often offer better control performance and lower conservatism than non-switched controllers. However, because identifying the current mode of the system requires time, controller switching in real systems often lags behind system switching, a phenomenon known as asynchrony. The presence of asynchrony can affect system control performance and, in severe cases, can lead to system instability. To overcome this drawback, existing studies have proposed methods for anti-asynchrony control of generalized switched systems. However, it is worth noting that these methods often assume that the asynchrony times of different modes are consistent. While this assumption simplifies the derivation, it idealizes the actual situation and introduces a certain degree of conservatism. Furthermore, anti-asynchrony control of generalized switched systems often assumes that the singular matrices of different modes of the system are identical or have equal ranks, which limits the scope of application of these methods. Summary of the Invention

[0004] The technical problems to be solved by the present invention are:

[0005] In order to solve the problem that the existing generalized switching control method does not fully consider the modal asynchronous characteristics and the influence of external interference.

[0006] The present invention is to solve the above technical problems using the following technical solutions:

[0007] The present invention provides a generalized switching control method with both anti-asynchronous capability and interference suppression performance, comprising the following steps:

[0008] S100. Design a generalized switching controller with asynchrony and interference; this includes constructing a generalized switching system model with interference, combining matrix theory to give a system equivalent form, and obtaining a switching controller expression that considers modal asynchrony;

[0009] S200, for a continuous-time generalized switching system, designing an anti-asynchrony switching controller with stability; including designing an anti-asynchrony stability lemma based on a multi-Lyapunov function method according to a mode-dependent average residence time switching signal; combining the generalized switching system model with interference in step S100 and the switching controller expression considering modal asynchrony, designing an anti-asynchrony switching controller with stability guarantee;

[0010] S300. Design an anti-asynchronous switching controller with stability and H∞ performance guarantee for continuous-time generalized switching systems with interference; including giving the system stability lemma considering modal asynchrony and interference and the system L2 gain expression form based on the multi-Lyapunov function method, and designing an anti-asynchronous switching controller with stability and H∞ performance guarantee.

[0011] Furthermore, in step S100, it includes:

[0012] The generalized switching system is:

[0013]

[0014]

[0015] in, are the system state, control input, control output and disturbance input respectively, σ(t) is the system switching signal, satisfying σ(t)∈L={1,2,…,N}, N is the number of system modes; for Matrix A i 、B i 、C i 、D i 、E i 、F i and G i is a known constant matrix, and there exists a constant r i Satisfy rank(E i ,B i ,F i )=rank(E i )=r i , r i is the matrix E i The rank of the modal i system state x degrees of freedom, satisfying r i ≤n x , where n x is the dimension of system state;

[0016] Considering the mode-dependent average dwell time signal, t k is the kth switching moment, t0 is the initial moment;

[0017] From matrix theory, we know that for There exists a non-singular matrix and So that:

[0018]

[0019]

[0020] in, The dimension is r i ×r i The identity matrix of is a non-singular matrix; let:

[0021]

[0022] in, are two state variables of the system; the generalized switching system has the following equivalent form:

[0023]

[0024]

[0025] Secondly, the state feedback asynchronous switching controller is given as follows:

[0026] u=K' c(t) x1 (8)

[0027] Among them, c(t)∈L is the controller mode, satisfying c(t)=σ(td σ(t) ), d σ(t) is the modal asynchrony time, K′ c(t) is the controller gain; for the initial mode, σ(td σ(t0) )=σ(t0),

[0028] Furthermore, in step S200, including:

[0029] Lemma 1 of the stability of asynchronous generalized switched systems based on the multi-Lyapunov function method is:

[0030] Nonlinear generalized switched systems Given a constant α σ(t) >0,β σ(t) >0,μ σ(t) ≥1, if there exists multiple Lyapunov functions V σ(t) and two types of K ∞ Functions κ1 and κ2, for asynchronous generalized switching system submodes i, j∈L, i≠j and any system mode switching time t k and The following inequality holds:

[0031]

[0032] Then the asynchronous generalized switching system satisfies the mode-dependent average residence time condition and the average residence time is τ i The switching signal is globally consistent and asymptotically stable, τ i Satisfies the following inequality:

[0033]

[0034] On this basis, based on the linear matrix inequality condition of Theorem 1, an anti-asynchronous switching controller with stability guarantee is designed:

[0035] Combined with the generalized switching control system of formula (1), given the constant α i >0,β i >0,μ i ≥1,δ ii >0,δ ij > 0, if there exists a real matrix X i T =X i >0, U i , So that the following inequality holds:

[0036]

[0037] in,

[0038] Then the system satisfies the modal dependence average residence time condition The switching signal is globally consistent and asymptotically stable, and the state feedback controller gain is

[0039] The solver solves the linear matrix inequality of Theorem 1 and obtains an asynchronous switching-resistant controller with stability guarantee.

[0040] Furthermore, in step S300, it includes:

[0041] Based on the multi-Lyapunov function method, Lemma 2 of system stability considering modal asynchrony and interference is given:

[0042] The nonlinear generalized switched system with constraints can be expressed as and y = g σ(t) (x,w), given a constant α σ(t) >0,β σ(t) >0,μ σ(t) ≥1, if there exists multiple Lyapunov functions V σ(t) , two types of K ∞For the functions κ1 and κ2 and the positive real number γ, for the constrained nonlinear generalized switched system submodes i, j∈L, i≠j, the following inequality holds:

[0043]

[0044] in,

[0045] Γ=y T y-γ 2 w T w (14)

[0046] Then the system satisfies the modal dependence average residence time condition and the average residence time is τ i The switching signal is globally consistent and asymptotically stable, τ i Satisfies the following inequality:

[0047]

[0048] The minimum L2-gain of a constrained nonlinear generalized switched system is:

[0049]

[0050] Among them, N 0i is the mode-dependent switching lower bound of the mode-dependent mean dwell time switching signal;

[0051] Combined with the system and controller descriptions given in step S100, an asynchronous switching-resistant controller with stability and H∞ performance guarantees is designed based on the following Theorem 2:

[0052] Combining the generalized switching control system of formula (1) and formula (2), given the constant α i >0,β i >0,μ i ≥1,δ ii >0,δ ij > 0, if there is a real matrix U i , and a positive real number γ, so that the following inequality holds:

[0053]

[0054]

[0055] in,

[0056]

[0057] Then the system satisfies the modal dependence average residence time condition The switching signal is globally consistent and asymptotically stable, and the minimum L2-gain of the system is The state feedback controller gain is

[0058] The solver solves the linear matrix inequality in Theorem 2 and obtains an asynchronous switching controller with stability and H∞ performance guarantees.

[0059] Furthermore, the generalized switching control method is used to perform pitch attitude stabilization control on an aircraft with two sub-modes, defining the system state as the aircraft's angle of attack x1 and pitch angular acceleration x2, the system control quantity as the aircraft's pitch rudder deflection angle u, the system external disturbance as w, and the system output as y.

[0060] Furthermore, in step S200 and step S300, the Yalmip toolbox and the Sdpt3 solver are selected to solve the linear matrix inequalities of Theorem 1 and Theorem 2 respectively.

[0061] A generalized switching control system with both anti-asynchronous capability and interference suppression performance is disclosed. The system has a program module corresponding to the above steps and executes the steps of the generalized switching control method with both anti-asynchronous capability and interference suppression performance during operation.

[0062] A computer-readable storage medium stores a computer program configured to implement the steps of a generalized switching control method having both anti-asynchronous capability and interference suppression performance when called by a processor.

[0063] Compared with the prior art, the present invention has the following beneficial effects:

[0064] The present invention provides a generalized switching control method and system with both anti-asynchronous capability and interference suppression performance. To address modal asynchrony and external interference issues, based on the generalized switching system framework and the multi-Lyapunov function method, a state feedback switching controller with stability and H∞ performance guarantee is designed. This expands the existing generalized switching system theory system and has high engineering application value.

[0065] Compared with traditional non-modal asynchronous methods and traditional methods that do not consider asynchronous operation, the modal asynchronous method proposed in this invention has better practicality and application potential, and shows better convergence performance in simulation.

[0066] The method proposed in the present invention takes into account the actual situation with interference. The designed controller not only ensures stability but also ensures H∞ performance, and provides the L2 gain expression form of the closed-loop system. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1Flowchart of a generalized switching control method with both anti-asynchronous capability and interference suppression performance according to an embodiment of the present invention;

[0068] Figure 2 The system mode and controller mode diagram in the embodiment of the present invention;

[0069] Figure 3 A comparison diagram of the state trajectories of the present invention and the traditional method in an embodiment of the present invention, wherein x1 and x2 are two state variables of the system respectively;

[0070] Figure 4 1 is a comparison diagram of the state response curves of the present invention and the traditional method in an embodiment of the present invention, wherein (a) and (b) are the state convergence effects of x1 and x2 respectively. DETAILED DESCRIPTION

[0071] 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.

[0072] Specific implementation plan 1: Combined Figure 1 and Figure 2 As shown, the present invention provides a generalized switching control method with both anti-asynchronous capability and interference suppression performance, comprising the following steps:

[0073] S100. Construct a control problem for a generalized switched system with asynchrony and interference. Specifically, write a model of a generalized switched system with interference and, combined with matrix theory, give a system equivalent form. Finally, give a switching controller expression that considers modal asynchrony.

[0074] First, consider the following generalized switching system:

[0075]

[0076] y=C σ(t) x+D σ(t) u+G σ(t) w (2)

[0077] in, are system state, control input, control output and disturbance input respectively,

[0078] σ(t) is the system switching signal, satisfying σ(t)∈L={1,2,…,N}, where N is the number of system modes; Matrix A i 、B i 、C i 、D i 、E i 、F i and G iis a known constant matrix, and there exists a constant r i Satisfy rank(E i ,B i ,F i )=rank(E i )=r i , r i It is called matrix E i The rank of the modal i system state x degrees of freedom, satisfying r i ≤n x , where n x is the dimension of system state;

[0079] The present invention considers the modal-dependent average dwell time signal, t k is the kth switching moment, t0 is the initial moment;

[0080] From matrix theory, we know that for There exists a non-singular matrix and So that:

[0081]

[0082]

[0083] Among them, I ri The dimension is r i ×r i The identity matrix, is a non-singular matrix;

[0084] make:

[0085]

[0086] in, are two state variables of the system; the generalized switching system has the following equivalent form:

[0087]

[0088] 0=A σ(t),21 x1+A σ(t),22 x2 (7)

[0089] Secondly, a state feedback asynchronous switching controller is given as follows:

[0090] u=K' c(t) x1 (8)

[0091] Among them, c(t)∈L is the controller mode, satisfying c(t)=σ(td σ(t) ), d σ(t) is the modal asynchrony time, K′c(t) is the controller gain;

[0092] For the initial mode,

[0093] The control problem is: for the generalized switching system such as formula (1) and formula (2), solve the existence conditions of the state feedback asynchronous switching controller such as formula (8) to ensure the stability and H∞ performance of the closed-loop system;

[0094] S200. Designing an anti-asynchronous switching controller with stability guarantee for a continuous-time generalized switching system; specifically, providing an anti-asynchronous stability lemma based on a multi-Lyapunov function method based on a mode-dependent average dwell time switching signal; on this basis, combining the system and controller description forms provided in step S100, designing an anti-asynchronous switching controller with stability guarantee;

[0095] Firstly, the stability lemma of asynchronous generalized switched systems based on the multi-Lyapunov function method is given:

[0096] Lemma 1: Nonlinear generalized switched systems Given a constant α σ(t) >0,β σ(t) >0,μ σ(t) ≥1, if there exists multiple Lyapunov functions V σ(t) and two types of K ∞ Functions κ1 and κ2, for system submodes i, j∈L, i≠j and any system mode switching time t k and The following inequality holds:

[0097]

[0098]

[0099] Then the system satisfies the modal dependence average residence time condition and the average residence time is τ i The switching signal is globally consistent and asymptotically stable, τ i Satisfies the following inequality:

[0100]

[0101] On this basis, an anti-asynchronous switching controller with stability guarantee is designed based on the linear matrix inequality conditions of Theorem 1.

[0102] Theorem 1: Consider the generalized switching control system shown in formula (1), given a constant α i >0,β i >0,μ i≥1,δ ii >0,δ ij > 0, if there is a real matrix U i , So that the following inequality holds:

[0103]

[0104] in,

[0105]

[0106] Then the system satisfies the modal dependence average residence time condition The switching signal is globally consistent and asymptotically stable, and the state feedback controller gain is

[0107] Select the Yalmip toolbox and Sdpt3 solver to solve the linear matrix inequality of Theorem 1, and you can get an anti-asynchronous switching controller with guaranteed stability.

[0108] S300. Designing an anti-asynchrony switching controller with stability and H∞ performance guarantees for a continuous-time generalized switching system with interference; specifically, providing a system stability lemma considering modal asynchrony and interference based on a multi-Lyapunov function method, and providing a system L2 gain expression form; on this basis, combining the system and controller description forms provided in step S100, designing an anti-asynchrony switching controller with stability and H∞ performance guarantees;

[0109] First, based on the multi-Lyapunov function method, the system stability lemma considering modal asynchrony and interference is given:

[0110] Lemma 2: A nonlinear generalized switched system with constraints can be expressed as and y = g σ(t) (x,w), given a constant α σ(t) >0,β σ(t) >0,μ σ(t) ≥1, if there exists multiple Lyapunov functions V σ(t) , two types of K ∞ For functions κ1 and κ2 and a positive real number γ, for system submodes i, j∈L, i≠j, the following inequality holds:

[0111]

[0112] in,

[0113] Γ=y T y-γ 2 w T w (14)

[0114] Then the system satisfies the modal dependence average residence time condition and the average residence time is τ i The switching signal is globally consistent and asymptotically stable, τ i Satisfies the following inequality:

[0115]

[0116] And the minimum L2-gain of the system has the following form:

[0117]

[0118] Among them, N 0i is the mode-dependent switching lower bound of the mode-dependent mean dwell time switching signal;

[0119] On this basis, combined with the system and controller description given in step S100, the following Theorem 2 is used to design an asynchronous switching controller with stability and H∞ performance guarantee.

[0120] Theorem 2: Consider the generalized switching system as shown in formula (1) and formula (2), given a constant α i >0,β i >0,μ i ≥1,δ ii >0,δ ij > 0, if there is a real matrix U i , and a positive real number γ, such that the following inequality holds:

[0121]

[0122] in,

[0123]

[0124]

[0125] Then the system satisfies the modal dependence average residence time condition The switching signal is globally consistent and asymptotically stable and the minimum L2-gain of the system is The state feedback controller gain is

[0126] The Yalmip toolbox and Sdpt3 solver are used to solve the linear matrix inequality in Theorem 2, and an asynchronous switching controller with stability and H∞ performance guarantee is obtained.

[0127] Specific implementation scheme 2: The present invention provides a generalized switching control system with both anti-asynchronous capability and interference suppression performance. The system has a program module corresponding to the above steps, and executes the steps in the above-mentioned generalized switching control method with both anti-asynchronous capability and interference suppression performance during operation.

[0128] The other combinations and connection relationships of this embodiment are the same as those of the first embodiment.

[0129] Specific implementation scheme three: The present invention provides a computer-readable storage medium, which stores a computer program. The computer program is configured to implement the steps of a generalized switching control method with both anti-asynchronous capability and interference suppression performance when called by a processor.

[0130] The other combinations and connection relationships of this embodiment are the same as those of the first embodiment.

[0131] Simulation experiment

[0132] In this experiment, a pitch attitude stabilization control is performed on an aircraft with two sub-modes. Since the aerodynamic parameters of the aircraft are different at different flight altitudes and flight speeds, the system model changes. The aircraft is modeled as a generalized switching system, and the system model is shown in Equations (1) and (2). The system state is defined as the aircraft's angle of attack x1 and pitch angular acceleration x2, and x = [x1 x2] T , the system control quantity is the pitch rudder angle u of the aircraft, the external disturbance of the system is w, the system output is y, and the system matrix is ​​as follows:

[0133]

[0134] The subscript numbers represent the submode numbers of the system.

[0135] The initial state of the system is x0 =

[55] T , the interference input is w(t)=0.1e -2t , the system mode and controller mode are as follows Figure 2 After the system model and controller form are given based on step S100, the controller design for this system is carried out according to Theorem 1 and Theorem 2 given in step S200 and step S300. The state trajectory comparison diagram and state response curve comparison diagram of the proposed modal asynchronous method and the traditional method are shown in Figure 3 and Figure 4 As shown in the figure, the proposed method has superior convergence performance and is effectively resistant to asynchrony and interference. Traditional methods, on the other hand, may experience large overshoot, long convergence times, and even instability. Simulation results validate the effectiveness and advantages of the method described in the patent.

[0136] Although the present invention is disclosed as above, the scope of protection disclosed by the present invention is not limited thereto. Those skilled in the art of the present invention 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 scope of protection of the present invention.

Claims

1. A generalized switching control method with both anti-asynchronous capability and interference suppression performance, characterized in that: The following steps are involved: S100, Design of generalized switching controller with asynchrony and interference; This includes constructing a generalized switching system model with disturbances, combining it with matrix theory to give a system equivalent form, and obtaining a switching controller expression that takes modal asynchrony into account. S200, for a continuous-time generalized switching system, designing an anti-asynchrony switching controller with stability; including designing an anti-asynchrony stability lemma based on a multi-Lyapunov function method according to a mode-dependent average residence time switching signal; combining the generalized switching system model with interference in step S100 and the switching controller expression considering modal asynchrony, designing an anti-asynchrony switching controller with stability guarantee; Lemma 1 of the stability of asynchronous generalized switched systems based on the multi-Lyapunov function method is: Nonlinear generalized switched systems , given a constant , , , if there are multiple Lyapunov functions and two categories function and , for the asynchronous generalized switched system submode and any system mode switching moment and , the following inequality holds: ； Then the asynchronous generalized switching system satisfies the mode-dependent average residence time condition and the average residence time is The switching signal is globally consistent and asymptotically stable. Satisfies the following inequality: ； in, is the system state; Is the system switching signal, satisfying , is the number of system modes; is the kth switching moment; , , is a given constant; S300: Design of a stable and H∞-guaranteed asynchronous switching controller for continuous-time generalized switched systems with disturbances. This includes a multi-Lyapunov function approach, which provides a stability lemma for the system considering modal asynchrony and disturbances, as well as a formulation for the system's L2 gain, and designs a stable and H∞-guaranteed asynchronous switching controller. Based on the multi-Lyapunov function method, Lemma 2 of system stability considering modal asynchrony and interference is given: The nonlinear generalized switched system with constraints can be expressed as and ,in 、 They are the control output and disturbance input respectively, and the given constants are , , , if there are multiple Lyapunov functions , two categories function and and positive real numbers , for the submodes of nonlinear generalized switched systems with constraints , the following inequality holds: ； in, ； Then the system satisfies the modal dependence average residence time condition and the average residence time is The switching signal is globally consistent and asymptotically stable. Satisfies the following inequality: ； The minimum L2-gain of a constrained nonlinear generalized switched system is: ； in, is the lower bound of the mode-dependent switching of the mode-dependent mean dwell time switching signal.

2. The generalized switching control method with both anti-asynchronous capability and interference suppression performance according to claim 1, characterized in that: In step S100, it includes: The generalized switching system is: ； in, 、 、 、 are system state, control input, control output and disturbance input respectively, Is the system switching signal, satisfying , is the number of system modes; for ,matrix 、 、 、 、 、 and is a known constant matrix, and there exists a constant satisfy , is a matrix The rank of System Status Freedom, satisfaction ,in, is the dimension of system state; Considering the mode-dependent average dwell time signal, is the kth switching moment, is the initial moment; From matrix theory, we know that for , there exists a non-singular matrix and So that: ； in, The dimension is The identity matrix of 、 、 , is a non-singular matrix; let: ； in, , , are two state variables of the system; the generalized switching system has the following equivalent form: ； Secondly, the state feedback asynchronous switching controller is given as follows: ； in, is the controller mode, satisfying , is the modal asynchronous time, is the controller gain; for the initial mode, , .

3. The generalized switching control method with both anti-asynchronous capability and interference suppression performance according to claim 2, characterized in that: In step S200, it also includes: Based on the linear matrix inequality condition of Theorem 1, an anti-asynchronous switching controller with stability guarantee is designed: Combined with the generalized switching control system of formula (1), given the constant , , , , , if there exists a real matrix , , , so that the following inequality holds: ； in, ； Then the system satisfies the modal dependence average residence time condition The switching signal is globally consistent and asymptotically stable, and the state feedback controller gain is ; The solver solves the linear matrix inequality of Theorem 1 and obtains an asynchronous switching-resistant controller with stability guarantee.

4. The generalized switching control method with both anti-asynchronous capability and interference suppression performance according to claim 3, characterized in that: In step S300, it also includes: Combined with the system and controller descriptions given in step S100, an asynchronous switching-resistant controller with stability and H∞ performance guarantees is designed based on the following Theorem 2: Combining the generalized switching control system of formula (1) and formula (2), given the constant , , , , , if there exists a real matrix , , and positive real numbers , so that the following inequality holds: ； in, ； Then the system satisfies the modal dependence average residence time condition The switching signal is globally consistent and asymptotically stable, and the minimum L2-gain of the system is , the state feedback controller gain is ; The solver solves the linear matrix inequality in Theorem 2 and obtains an asynchronous switching controller with stability and H∞ performance guarantees.

5. The generalized switching control method with both anti-asynchronous capability and interference suppression performance according to claim 4, characterized in that: The generalized switching control method is used to perform pitch attitude stabilization control on an aircraft with two sub-modes, and the system state is defined as the angle of attack of the aircraft. and pitch angular acceleration , the system control quantity is the pitch rudder angle of the aircraft , the external interference of the system is , the system output is .

6. The generalized switching control method with both anti-asynchronous capability and interference suppression performance according to claim 5, characterized in that: In step S200 and step S300, the Yalmip toolbox and the Sdpt3 solver are selected to solve the linear matrix inequalities of Theorem 1 and Theorem 2 respectively.

7. A generalized switching control system with both anti-asynchronous capability and interference suppression performance, characterized by: The system has a program module corresponding to the steps of any one of claims 1 to 6, and executes the steps of the generalized switching control method having both anti-asynchronous capability and interference suppression performance during operation.

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 generalized switching control method with both anti-asynchronous capability and interference suppression performance according to any one of claims 1 to 6 when called by a processor.

Images