Generalized switching control method and system with asynchronous resistance and interference suppression performance

Abstract

The invention provides a generalized switching control method and system with asynchronous resistance and interference suppression performance, and belongs to the technical field of generalized switching system control. The method aims to solve the problem that modal asynchronous characteristics and external interference influences are not fully considered in an existing generalized switching control method. Aiming at the problems of modal asynchronization and external interference, a state feedback switching controller with stability and H infinity performance guarantee is designed based on a generalized switching system framework and a multi-Lyapunov function method. Compared with a traditional non-modal asynchronous method and a traditional method without considering asynchronization, the modal asynchronous method provided by the invention has better practicability and application potential and shows better convergence performance in simulation; according to the invention, the design is simple, the actual situation containing interference is considered, the designed controller not only ensures the stability, but also ensures the H-infinity performance, and an L2 gain expression form of a closed-loop system is given; the theoretical system of an existing generalized switching system is expanded, and the method 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 having both anti-asynchronous capability and interference suppression performance. Background Art

[0002] As a hybrid system that combines differential equations with algebraic equations, generalized switching systems have significantly improved modeling capabilities and application potential compared to traditional switching systems. In recent years, generalized switching systems have received extensive attention, and related research results have been applied to practical scenarios such as mobile robots, multi-constrained manipulators, and large circuit systems.

[0003] Controller design is a hot topic in the study of generalized switched systems. For generalized switched systems, switched controllers often have better control effects and lower conservatism than non-switched controllers. However, since it takes time to identify the current mode of the system, the switching of the controller in the actual system often lags behind the switching of the system, which is also called asynchronous phenomenon. The existence of asynchronous phenomenon will affect the control performance of the system, and in severe cases, it may also cause system instability. In order to overcome this defect, anti-asynchronous control methods for generalized switched systems have been proposed in existing studies. However, it is worth noting that these methods often assume that the asynchronous time of different modes is consistent. Although this assumption simplifies the derivation, it idealizes the actual situation and brings a certain degree of conservatism. On the other hand, in the anti-asynchronous control of generalized switched systems, it is often assumed that the singular matrices of different modes of the system are the same or the ranks of the singular matrices are equal, which also limits the scope of application of the method. 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 modal asynchronous characteristics and external interference effects are not fully considered in the existing generalized switching control methods.

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

[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 of generalized switching controller with asynchrony and interference; including constructing a generalized switching system model with interference, combining matrix theory, giving the system equivalent form, and obtaining the switching controller expression considering modal asynchrony;

[0009] S200, for a continuous-time generalized switching system, designing an anti-asynchronous switching controller with stability; including designing an anti-asynchronous 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 form considering modal asynchrony, designing an anti-asynchronous 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; Based on the multi-Lyapunov function method, the system stability lemma considering modal asynchrony and interference and the system L2 gain expression form are given to design 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; 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 satisfies r i ≤n x , where n x is the dimension of system status;

[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 There exists a non-singular matrix and So that:

[0018]

[0019]

[0020] in, The dimension is r i × 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] Where 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] Further, in step S200, it includes:

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

[0030] Nonlinear Singular Switched Systems Given a constant α σ(t) >0,β σ(t) >0,μ σ(t) ≥1, if there are 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, the anti-asynchronous switching controller with stability guarantee is designed based on the linear matrix inequality condition of Theorem 1:

[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] Further, in step S300, including:

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

[0042] The constrained nonlinear generalized switched system is 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 are multiple Lyapunov functions V σ(t) , two types of K ∞For functions κ1 and κ2 and a positive real number γ, for a constrained nonlinear generalized switched system submode 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 switching 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 description form given in step S100, an anti-asynchronous switching controller with stability and H∞ performance guarantee 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 of Theorem 2 and obtains an asynchronous switching-resistant controller with stability and H∞ performance guarantees.

[0059] Furthermore, the generalized switching control method is used to perform pitch attitude stability 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, the system has a program module corresponding to the above steps, and executes the steps in 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, wherein the computer program is 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 invention discloses a generalized switching control method and system with both anti-asynchronous capability and interference suppression performance. Aiming at the problems of modal asynchrony and external interference, a state feedback switching controller with stability and H∞ performance guarantee is designed based on the generalized switching system framework and the multi-Lyapunov function method, which expands the existing generalized switching system theoretical system and has high engineering application value.

[0065] Compared with the traditional non-modal asynchronous method and the traditional method that does not consider asynchronous, the modal asynchronous method proposed in the present 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 an L2 gain expression form of the closed-loop system. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1It is a flow chart of a generalized switching control method having both anti-asynchronous capability and interference suppression performance in 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 : is a comparison diagram of the state trajectories of the present invention and the traditional method in the 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 the 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: Combine 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 the control problem of generalized switching system with asynchrony and interference; specifically, write the generalized switching system model with interference, and combine matrix theory to give a system equivalent form; finally, give a switching controller expression form considering 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, They are system state, control input, control output and disturbance input.

[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 satisfies r i ≤n x , where n x is the dimension of system status;

[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 There exists a non-singular matrix and So that:

[0081]

[0082]

[0083] Among them, I ri The dimension is r i × i The identity matrix of 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] Where 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 thus obtained: 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, for the continuous-time generalized switching system, designing an anti-asynchronous switching controller with stability guarantee; specifically, relying on the mode-dependent average residence time switching signal, giving an anti-asynchronous stability lemma based on the multi-Lyapunov function method; on this basis, combining the system and controller description form given 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 are 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 stability guarantee;

[0108] S300, for a continuous-time generalized switching system with interference, designing an anti-asynchronous switching controller with stability and H∞ performance guarantee; specifically, based on a multi-Lyapunov function method, a system stability lemma considering modal asynchrony and interference is given, and a system L2 gain expression form is given; on this basis, combined with the system and controller description form given in step S100, an anti-asynchronous switching controller with stability and H∞ performance guarantee is designed;

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

[0110] Lemma 2: A nonlinear generalized switching 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 are 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 form 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 a generalized switching system such as the generalized switching control system 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] By using the Yalmip toolbox and the Sdpt3 solver to solve the linear matrix inequality in Theorem 2, an asynchronous switching controller with stability and H∞ performance guarantee can be 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, wherein the computer-readable storage medium stores a computer program, and the computer program is 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.

[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. Due to the different aerodynamic parameters of the aircraft at different flight altitudes and flight speeds, its 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 performed 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 It can be seen that the proposed method has superior convergence performance and can effectively resist asynchronous and interference effects; while the traditional method may have a large overshoot and a long convergence time, and may even be unstable. The simulation results verify the effectiveness and advantages of the method described in the patent.

[0136] 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 generalized switching control method with both anti-asynchronous capability and interference suppression performance, characterized in that: The following steps are involved: S100, design generalized switching controller with asynchrony and interference; This includes constructing a generalized switching system model with disturbances, combining matrix theory, giving 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-asynchronous switching controller with stability; including designing an anti-asynchronous 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 form considering modal asynchrony, designing an anti-asynchronous switching controller with stability guarantee; S300, Design an anti-asynchronous switching controller with stability and H∞ performance guarantee for continuous-time generalized switching systems with interference; Based on the multi-Lyapunov function method, the system stability lemma considering modal asynchrony and interference and the system L2 gain expression form are given, and an anti-asynchronous switching controller with stability and H∞ performance guarantee is designed.

2. A generalized switching control method having 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: y=C σ(t) x+D σ(t) u+G σ(t) w (2) 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; 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 satisfies r i ≤n x , where n x is the dimension of system status; Considering the mode-dependent average dwell time signal, t k is the kth switching moment, t0 is the initial moment; From matrix theory, we know that There exists a non-singular matrix and So that: in, The dimension is r i × i 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: 0=A σ(t),21 x1+A σ(t),22 x2 (7) Secondly, the state feedback asynchronous switching controller is given as follows: u=K′ c(t) x1 (8) Where 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, 3. A generalized switching control method having both anti-asynchronous capability and interference suppression performance according to claim 2, characterized in that: In step S200, it includes: The stability Lemma 1 of asynchronous generalized switched systems based on the multi-Lyapunov function method is: Nonlinear Singular Switched Systems Given a constant α σ(t) >0,β σ(t) >0,μ σ(t) ≥1, if there are 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: 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: On this basis, the anti-asynchronous switching controller with stability guarantee is designed based on the linear matrix inequality condition of Theorem 1: 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 is a real matrix U i , 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. A generalized switching control method with both anti-asynchronous capability and interference suppression performance according to claim 3, characterized in that: In step S300, it includes: Based on the multi-Lyapunov function method, Lemma 2 of system stability considering modal asynchrony and interference is given: The constrained nonlinear generalized switched system is 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 are multiple Lyapunov functions V σ(t) , two types of K ∞ For functions κ1 and κ2 and a positive real number γ, for a constrained nonlinear generalized switched system submode i,j∈L,i≠j, the following inequality holds: in, C = y T y-g 2 w T w (14) 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: The minimum L2-gain of a constrained nonlinear generalized switching system is: Among them, N 0i is the mode-dependent switching lower bound of the mode-dependent mean dwell time switching signal; Combined with the system and controller description form given in step S100, an anti-asynchronous switching controller with stability and H∞ performance guarantee is designed based on the following Theorem 2: 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: 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 of Theorem 2 and obtains an asynchronous switching-resistant controller with stability and H∞ performance guarantees.

5. A 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 aircraft's angle of attack x1 and pitch angular acceleration x2, the system control quantity is the aircraft's pitch rudder deflection angle u, the system external disturbance is w, and the system output is y.

6. A 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 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 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 described in any one of claims 1 to 6 when called by a processor.

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