Anti-shake model predictive control method and system for a variable mode system

Abstract

The present invention provides a anti-shake model predictive control method and system for a variable-mode system, belonging to the field of hybrid system control. In order to solve the problem that the traditional anti-shake variable-mode control algorithm is difficult to balance the anti-shake control performance and the stabilization control performance, resulting in problems such as a significant reduction in the convergence speed and a sharp increase in the overshoot in the stabilization control performance of the control system. The present invention includes establishing a variable-mode control system model and designing a cost function, designing linear inequality conditions for stability based on the average dwell time variable-mode system stability criterion and the multi-Lyapunov function method and calculating the cost upper bound, designing linear inequality conditions that satisfy the system constraints and calculating the system control performance cost upper bound, and finally obtaining the multi-mode state feedback control gain according to the designed receding horizon optimization algorithm and applying it to the control system. The present invention improves the comprehensive performance of the system, broadens the application objects and applicable scope of such methods, and has good engineering application value.

Description

Technical Field

[0001] The present invention relates to the technical field of the control of hybrid systems, and more particularly, to an anti-shake model predictive control method and system for a variable mode system. Background Art

[0002] As a special type of hybrid system, a variable mode system consists of multiple sub-modes and a mode switching signal that controls the behavior of these mode changes. This type of system is widely used in the control system modeling of actual physical objects such as unmanned aerial vehicles, mobile robots, and multi-agent platforms. According to the type of the mode switching signal, the variable mode system can be divided into time-dependent type and state-dependent type. Among them, the average dwell time switching signal is a typical time-dependent mode switching signal, that is, the number of mode changes within a certain time has an upper limit, and the average time required for consecutive multiple mode changes needs to exceed a certain value. This type of signal allows the system mode to switch quickly when necessary, and then compensates for the energy increase caused by the fast switching process by slowing down the mode change frequency.

[0003] However, in order to achieve system stability under frequent mode changes, the designed controller parameters usually jump instantaneously at the moment of mode change, which will cause a severe "jitter" phenomenon of the control input, resulting in problems such as a reduction in the actuator life. To overcome this defect, an anti-shake variable mode control method has been proposed in existing research, which reduces the impact of the controller parameter jump by extending the time required for the control gain change, imposing a maximum constraint on the control jitter, etc. Nevertheless, better anti-shake control performance usually leads to a decrease in the system stabilization control performance indexes (such as the convergence speed and overshoot). With the diversification of the system control objectives, the pursuit of different types of control performance limits the applicability of traditional anti-shake control algorithms to specific systems. Therefore, developing an optimization method that balances multiple types of control objectives to achieve the optimal control performance under comprehensive multiple objectives has become the main research direction of current anti-shake control.

[0004] As a powerful tool for handling multi-objective optimization and soft / hard constraints, model predictive control is widely used in variable-mode systems with state and control input constraints. At the same time, recent research has also combined the model predictive control scheme with the soft-switching idea in anti-shake variable-mode control to improve problems such as poor system performance caused by controller jitter. Related achievements have been applied to economic systems and wind energy conversion systems, achieving good results. For example, the existing patent "An Active Fault-Tolerant Control Method for Unmanned Aerial Vehicles with Jitter Suppression Performance" (Application No.: CN202211579411.1) relates to the field of unmanned aerial vehicle control technology. An unmanned aerial vehicle model in the form of a linearized discrete-time state-space expression is established; the FDI process with inaccurate observation information is modeled using the theory of hidden semi-Markov switching systems, and an anti-shake controller dependent on the observation mode is constructed; the anti-shake constraint conditions for the state of the unmanned aerial vehicle system are constructed; sufficient conditions for ensuring the mean-square stability of the unmanned aerial vehicle system under inaccurate FDI information are proposed; sufficient conditions for the existence of a fault-tolerant controller with anti-shake performance for the discrete-time unmanned aerial vehicle system are proposed; the matrix inequality is solved to obtain the gain of the fault-tolerant controller for the unmanned aerial vehicle system; and the active fault-tolerant control of the quadrotor unmanned aerial vehicle is realized using the gain of the fault-tolerant controller for the unmanned aerial vehicle system.

[0005] However, within the framework of variable-mode model predictive control, considering imposing constraints on the control jitter performance or incorporating it into the cost function, and obtaining the optimal comprehensive performance through a multi-objective optimization scheme of anti-shake / stabilization performance, is an effective but currently less studied idea. Therefore, for the average dwell time variable-mode system, the present invention proposes a multi-objective function that incorporates stabilization performance and anti-shake performance into the cost function, and an anti-shake variable-mode model predictive control algorithm that simultaneously optimizes the comprehensive control performance of the system in the weighted sense. The relevant research results have relatively important significance in promoting the development of variable-mode system control theory and facilitating the practical application of anti-shake variable-mode control theory. Summary of the Invention

[0006] The technical problems to be solved by the present invention are:

[0007] To solve the problem that traditional anti-shake variable-mode control algorithms are difficult to balance anti-shake performance and stabilization performance, resulting in problems such as a significant reduction in convergence speed and a sharp increase in overshoot in the stabilization performance of the control system.

[0008] The technical solutions adopted by the present invention to solve the above technical problems:

[0009] The present invention provides an anti-shake model predictive control method for a variable-mode system, including the following steps:

[0010] S100. Establish a variable-mode control system model and design a cost function, including describing the variable-mode control system as a system composed of multiple sub-modes and variable-mode signals, given the form of the state feedback controller, and respectively designing the cost function for the stabilization control performance and the anti-shake control performance of the variable-mode control system;

[0011] S200. Design linear matrix inequality conditions that can ensure the stability of the variable-mode control system, and calculate the upper bound of the cost of the system's stabilization control performance, including relying on the stability criterion of the average dwell time variable-mode control system, based on the multi-Lyapunov function method, designing linear matrix inequality conditions to ensure the stability of the system, and giving the upper bound of the cost of the system's stabilization control performance;

[0012] S300. Design linear matrix inequality conditions that can meet the system constraints, and calculate the upper bound of the cost of the system's anti-shake control performance, including considering the state constraints and control constraints of the variable-mode control system, deriving linear matrix inequality conditions that can make the state and controller input of the variable-mode control system meet the constraints, and determining the upper bound of the cost of the anti-shake control performance;

[0013] S400. Design a receding horizon optimization algorithm, including establishing a receding horizon optimization problem based on the cost function and linear matrix inequality conditions designed in steps S200 and S300, selecting a solver to solve the problem, obtaining the multi-mode state feedback control gain and applying it to the variable-mode control system.

[0014] Further, in step S100, it includes:

[0015] Establish a variable-mode control system model:

[0016] x(k + 1) = A σ(k) x(k) + B σ(k) u(k) (1)

[0017] where, is the state vector, is the control input vector; σ(k) is the switching signal, indicating the current sub-mode; A σ(k) and B σ(k) are both system state matrices, and k is the sampling time;

[0018] The system control gain under the model predictive control framework is:

[0019] u k+n|k = K σ(k) x k+n|k (2)

[0020] where, x k+n|k and u k+n|kare the predicted system state and control input of the variable-mode control system at time k + n, respectively, and K σ(k) is the control gain;

[0021] The cost function J(k) of the variable-mode control system is:

[0022] J(k) = J stab (k) + J bump (k) (3)

[0023] where is the system stabilization performance, and Q and R are both weight coefficients;

[0024] is the system anti-shake performance, represents the maximum value of the square of the two-norm of the change in the system control input.

[0025] Furthermore, in step S200, it includes: giving the stability condition of the average dwell time variable-mode system. For the variable-mode system shown in Equation (1), given positive constants 0 < λ < 1, μ ≥ 1, if there exists a function V σ(k) and two types of K ∞ functions κ 1 and κ 2 , for the system sub-mode j = i + , i + represents the next mode after mode i of the variable-mode system, and the corresponding V j (x j ) and V i (x j ), V j (x j ) and V i (x j ) represent the Lyapunov functions of the state x j in mode j and mode i respectively, and the following inequalities hold:

[0026] κ 1 (|x k |) ≤ V σ(k) (x k ) ≤ κ 2 (|x k |) (4)

[0027] V σ(k) (x k+1 ) - V σ(k) (x k ) ≤ -(1 - λ)V σ(k) (x k ) (5)

[0028] V j (xj ) ≤ μV i (x j ) (6)

[0029] Then the system is globally uniformly asymptotically regionally stable for switching signals that satisfy the average dwell time condition:

[0030]

[0031] where τ a represents the average dwell time of the system, is the minimum average dwell time of the system;

[0032] Design linear matrix inequality conditions that can ensure the stability of the system by combining Theorem 1:

[0033] Theorem 1. Consider the variable-mode control system shown in Equation (1). Given positive constants 0 < λ < 1, μ ≥ 1, if there exist positive scalars γ 1 > 0, positive definite matrices G, S σ(k) > 0 and matrix W σ(k) = K σ(k) G such that the following linear matrix inequalities hold:

[0034]

[0035] μP σ(k) (k) - P σ(k-1) (k - 1) ≥ 0 (10)

[0036] Then the system is globally uniformly asymptotically regionally stable for the variable-mode system that satisfies the average dwell time condition , and the upper bound of the stabilization performance cost of the system is γ 1 .

[0037] Furthermore, in step S300, it includes:

[0038] The given constraint form of the system is:

[0039] -[ω] α ≤ [Ex(k) + Hu(k)] α ≤ [ω] α (11)

[0040] where ω is the upper bound of the system state and control constraints, E and H are both weight coefficients, and the function [·] α represents the α-th element of the vector;

[0041] Make the system and the designed controller satisfy the state and control input constraints and have anti-shake performance by combining Theorem 2:

[0042] Theorem 2. Consider the variable-mode system shown in Equation (1). If there exist positive scalars γ 2 > 0, positive definite matrices Z, G, S σ(k) > 0, and a matrix W σ(k) = K σ(k) G such that Equation (9) in Theorem 1 and the following linear matrix inequalities hold:

[0043]

[0044] trace(Z) ≤ γ 2 (14)

[0045] where Ω is the system constraint matrix and satisfies [Ω] αα = ([ω] α ) 2 , and the function [·] αα represents the element in the α-th row and α-th column of the matrix;

[0046] Then the system satisfies the constraints shown in Equation (11), and the upper bound of the anti-shake performance cost of the system is γ 2 .

[0047] Furthermore, in step S300, it includes: establishing a receding horizon optimization problem based on linear matrix inequalities, selecting a solver to solve the optimization problem, and obtaining the system state feedback control gain K σ(k) and the control input u(k), which act on the variable-mode control system,

[0048] The optimization problem for controller design is established as:

[0049]

[0050] Select the Yalmip toolbox and the Sdpt3 solver to solve the linear matrix inequality. At each sampling time, solve the optimization problem shown in Equation (15) to obtain the state feedback control gain K σ(k) = W σ(k) G -1 and the control input u(k) = K σ(k) x(k), which act on the control system (1) to achieve receding horizon optimal control.

[0051] Furthermore, the anti-shake model predictive control method is used in the control system modeling of actual physical objects, including the flight control system of unmanned aerial vehicles, the motion control system of mobile robots, and the cooperative control system of multi-agent platforms.

[0052] The anti-shake model predictive control system of a variable mode system according to the present invention has program modules corresponding to the above steps, and executes the steps in the anti-shake model predictive control method of the variable mode system when running.

[0053] The present invention provides a computer-readable storage medium storing a computer program, which is configured to implement the steps of the anti-shake model predictive control method for a variable mode system when called by a processor.

[0054] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0055] The present invention considers the state variables and control input constraints of the system, and designs an anti-shake stabilization controller for the average dwell time variable mode system, which can theoretically ensure the stability of the system on the premise of meeting various constraints.

[0056] The present invention establishes a controller design method under the rolling horizon optimization framework, in which the system stabilization performance and anti-shake control performance are respectively considered in the cost function. By solving the linear matrix inequality conditions, the optimization of the two types of system performance is carried out simultaneously, and the control gain that can ensure the optimal comprehensive performance of the system is obtained.

[0057] Aiming at the defect that the existing anti-shake variable mode controller design method cannot balance the anti-shake control performance and the stabilization control performance, the present invention proposes an anti-shake variable mode model predictive control method that takes into account both types of control performances, improves the comprehensive performance of the system, broadens the application objects and scope of application of such methods, and has good engineering application value. Description of the Drawings

[0058] Figure 1 It is a flowchart of an anti-shake model predictive control method for a variable mode system in an embodiment of the present invention;

[0059] Figure 2 It is a variable mode signal diagram used in the simulation experiment in an embodiment of the present invention;

[0060] Figure 3 It is a comparative curve graph of the state responses of a variable mode system under the action of a traditional controller and the controller proposed in the present invention in an embodiment of the present invention;

[0061] Figure 4 It is a comparative curve graph of the control inputs of a variable mode system under the action of a traditional controller and the controller proposed in the present invention in an embodiment of the present invention;

[0062] Figure 5 It is a comparative curve graph of the control change amounts of a variable mode system under the action of a traditional controller and the controller proposed in the present invention in an embodiment of the present invention. Detailed Embodiments

[0063] To make the above objects, features, and advantages of the present invention more obvious and understandable, the following provides a detailed description of specific embodiments of the present invention in conjunction with the accompanying drawings.

[0064] Specific Embodiment 1: As shown in Figure 1 , the present invention provides a shake-proof model predictive control method for a variable mode system, including the following steps:

[0065] S100. Establish a variable mode control system model and design a cost function, including describing the system as a variable mode system composed of multiple sub-modes and variable mode signals, given the form of a state feedback controller, and respectively designing a cost function for the stabilization control performance and a cost function for the shake-proof control performance of the variable mode system. Specifically, it includes:

[0066] First, consider the following variable mode control system model:

[0067] x(k + 1) = A σ(k) x(k) + B σ(k) u(k) (1)

[0068] Wherein, is the state vector, is the control input vector; σ(k) is the switching signal indicating the current sub-mode; A σ(k) and B σ(k) are both system state matrices, and k is the sampling time;

[0069] In the present invention, the system control gain in the model predictive control framework adopts the following form:

[0070] u k+n|k = K σ(k) x k+n|k (2)

[0071] Wherein, x k+n|k and u k+n|k are respectively the predicted system state and control input at time k + n of the system at time k, and K σ(k) is the control gain;

[0072] On this basis, the cost function J(k) of the system can be expressed as:

[0073] J(k) = J stab (k) + J bump (k) (3)

[0074] Wherein, is the system stabilization performance, and Q and R are both weight coefficients; is the system shake-proof performance, represents the maximum value of the square of the two-norm of the change in the system control input;

[0075] S200. Design the linear matrix inequality conditions that can ensure the system stability, and calculate the upper bound of the cost of the stabilization control performance of the system, including relying on the average dwell time variable mode system stability criterion, and based on the multi-Lyapunov function method, design the linear matrix inequality conditions that can guarantee the system stability, and give the upper bound of the cost of the system stabilization control performance, specifically including:

[0076] First, give the stability conditions of the average dwell time variable mode system: For the variable mode system shown in Equation (1), given positive constants \(0 \lt \lambda \lt 1\) and \(\mu \geq 1\), if there exists a function \(V σ(k) (x)\) and two types of \(K ∞ functions \(\kappa 1 \) and \(\kappa 2 \), for the system sub-mode \(j = i + (i + represents the next mode after the variable mode system is in mode \(i\)), and the corresponding \(V j (x j )\) and \(V i (x j )\) represent the Lyapunov functions of the state \(x j \) in mode \(j\) and mode \(i\) respectively, the following inequalities hold:

[0077] \(\kappa 1 (|x k |) \leq V σ(k) (x k ) \leq \kappa 2 (|x k |) (4)

[0078] V σ(k) (x k+1 ) - V σ(k) (x k ) \leq -(1 - \lambda)V σ(k) (x k ) (5)

[0079] V j (x j ) \leq \mu V i (x j ) (6)

[0080] Then the system is globally uniformly asymptotically regionally stable for the switching signals that satisfy the average dwell time condition:

[0081]

[0082] where \(\tau a \) represents the average dwell time of the system, is the minimum average dwell time of the system;

[0083] On this basis, relying on Theorem 1, linear matrix inequality conditions that can guarantee the stability of the system are designed:

[0084] Theorem 1: Consider the variable-mode control system shown in Equation (1). Given positive constants 0 < λ < 1 and μ ≥ 1, if there exist positive scalars γ 1 > 0, positive definite matrices G, S σ(k) > 0, and a matrix W σ(k) = K σ(k) G such that the following linear matrix inequalities hold:

[0085]

[0086] μP σ(k) (k) - P σ(k-1) (k - 1) ≥ 0 (10)

[0087] Then the system is globally uniformly asymptotically regionally stable for the variable-mode system satisfying the average dwell time condition , and the upper bound of the stabilization performance cost of the system is γ 1 ;

[0088] S300. Design linear matrix inequality conditions that can satisfy the system constraints, and calculate the upper bound of the anti-shake control performance cost of the system, including considering the state constraints and control constraints of the system, deriving the linear matrix inequality conditions that can make the system state and controller input satisfy the constraints, and determining the upper bound of the anti-shake control performance cost, specifically including:

[0089] First, given the constraint form of the system as:

[0090] -[ω] α ≤ [Ex(k) + Hu(k)] α ≤ [ω] α (11)

[0091] where ω is the upper bound of the system state and control constraints, and both E and H are weight coefficients. The function [·] α represents the α-th element of the vector;

[0092] Next, Theorem 2 is given to make the system and the designed controller satisfy the state and control input constraints and have anti-shake performance:

[0093] Theorem 2: Consider the variable-mode system shown in Equation (1). If there exist positive scalars γ 2 > 0, positive definite matrices Z, G, S σ(k) > 0, and a matrix W σ(k) = K σ(k) G such that Equation (9) in Theorem 1 and the following linear matrix inequalities hold:

[0094]

[0095]

[0096] trace(Z)≤γ 2 (14)

[0097] Where Ω is the system constraint matrix and satisfies [Ω] αα =([ω] α ) 2 ,function[·] αα represents the element in the αth row and αth column of the matrix;

[0098] Then the system satisfies the constraint shown in formula (11), and the upper limit of the anti-shake performance cost of the system is γ 2 ;

[0099] S400, designing a rolling horizon optimization algorithm, including establishing a rolling horizon optimization problem based on the cost function and linear matrix inequality conditions designed in steps S200 and S300, selecting a suitable solver to solve the problem, obtaining a multi-modal state feedback control gain and acting on the control system, specifically including:

[0100] Establish a rolling horizon optimization problem based on linear matrix inequality, select a suitable solver to solve the optimization problem, and obtain the system state feedback control gain K σ(k) and control input u(k), acting on the variable mode control system,

[0101] First, the optimization problem of controller design can be formulated as:

[0102]

[0103] In the present invention, the Yalmip toolbox and Sdpt3 solver are selected to solve the linear matrix inequality, and the optimization problem shown in equation (15) is solved at each sampling time to obtain the state feedback control gain K σ(k) =W σ(k) G -1 And control input u(k) = K σ(k) x(k), acts on the control system (1) to achieve rolling optimization control.

[0104] Specific implementation scheme 2: The present invention provides an anti-shake model predictive control system for a variable mode system. The system has a program module corresponding to the above steps, and executes the steps in the anti-shake model predictive control method for the variable mode system during operation.

[0105] The other combinations and connection relationships of this embodiment are the same as those of the first embodiment.

[0106] 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 the anti-shake model predictive control method of a variable mode system when called by a processor.

[0107] The other combinations and connection relationships of this embodiment are the same as those of the first embodiment.

[0108] Simulation experiment

[0109] It is used to observe the control effect comparison of the system under the control of the controller designed by the present invention and the traditional controller, and to evaluate the simulation effect to verify the applicability and superiority of the algorithm.

[0110] A pitch attitude stabilization control is performed on an aircraft with three 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 variable mode system, and the system model is shown in formula (1), that is, x(k+1)=A σ(k) x(k)+B σ(k) u(k). The system state is defined as the aircraft's angle of attack α and pitch acceleration q, that is, x = [α, q] T ; Define the system control quantity as the pitch rudder deflection angle δ of the aircraft E and thrust vector throttle δ PTV , that is, u=[δ E ,δ PTV ] T In addition, the system matrices of the variable modal system are:

[0111]

[0112] The subscript numbers represent the submode numbers of the system.

[0113] The initial state of the system is x 0 =[2,-1.2] T ; The weight system in the cost function is Q = diag{10,10} and R = 10; the average residence time parameters of the system are μ = 1.5 and λ = 0.92; the constraint parameters are E = diag{1,1,0,0}, H = diag{0,0,1,1} and ω = [25,10,15,15] T , where the diag function represents a diagonal matrix composed of parameters. Therefore, the control goal in this experiment is to make the system state converge while taking into account the anti-shake performance of the controller while ensuring that the system state and control input meet the constraints.

[0114] After the variable modal system is established based on step S100 and the system parameters are given, the controller is designed according to Theorem 1, Theorem 2 and the optimization problem (15) given in steps S200, S300 and S400. Figure 2 The figure shows the average dwell time variable mode signal used in the simulation. In the simulation results, the system state response curve, control input curve and control variation curve under the action of the traditional variable mode model predictive controller and the proposed anti-shake variable mode model predictive controller are recorded, as shown in the figure. Figure 3 , Figure 4 and Figure 5 As shown in the figure. From the comparison with the traditional algorithm, it can be seen that the proposed algorithm shows better performance in overshoot and convergence speed, and the control jitter is effectively suppressed. The simulation results verify the effectiveness and advantages of the method described in the patent.

[0115] 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 method for anti-shake model predictive control of a variable mode system, characterized in that: The following steps are involved: S100, establishing a variable mode control system model and designing a cost function, including describing the variable mode control system as a variable mode control system composed of multiple sub-modes and variable mode signals, given a state feedback controller form, and respectively designing a cost function of the stabilization control performance and a cost function of the anti-shake control performance of the variable mode control system; S200. Design linear matrix inequality conditions that can ensure the stability of variable mode control systems, and calculate the upper limit of the system's stabilization control performance cost, including relying on the stability criterion of variable mode control systems based on the average residence time, based on the multi-Lyapunov function method, designing linear matrix inequality conditions that ensure system stability, and giving the upper limit of the system's stabilization control performance cost; S300, designing a linear matrix inequality condition that can satisfy the system constraints, and calculating the upper limit of the anti-shake control performance cost of the system, including considering the state constraints and control constraints of the variable mode control system, deriving a linear matrix inequality condition that can make the variable mode control system state and controller input satisfy the constraints, and determining the upper limit of the anti-shake control performance cost; S400, designing a rolling horizon optimization algorithm, including establishing a rolling horizon optimization problem based on the cost function and linear matrix inequality conditions designed in steps S200 and S300, selecting a solver to solve the problem, obtaining a multi-modal state feedback control gain and applying it to a variable mode control system.

2. The anti-shake model predictive control method for a variable mode system according to claim 1, characterized in that: In step S100, it includes: Establish variable mode control system model: x(k+1)=A σ(k) x(k)+B σ(k) u(k) (1) in, is the state vector, is the control input vector; σ(k) is the switching signal, indicating the current sub-mode; A σ(k) and B σ(k) are all system state matrices, k is the sampling time; The system control gain under the model predictive control framework is: u k+n|k =K σ(k) x k+n|k (2) Among them, x k+n|k and u k+n|k are the system state and control input predicted by the variable mode control system at time k+n, respectively. σ(k) To control the gain; The cost function J(k) of the variable mode control system is: J(k)=J stab (k)+J bump (k) (3) in, is the system stabilization performance, Q and R are weight coefficients; For system anti-shake performance, It represents the maximum value of the square of the second norm of the system control input change.

3. The anti-shake model predictive control method for a variable mode system according to claim 2, characterized in that: In step S200, it includes: giving the stability condition of the average residence time variable mode system, for the variable mode system shown in formula (1), given a positive constant 0<λ<1, μ≥1, if there exists a function V σ(k) and two types of K ∞ Functions κ1 and κ2, for system submode j = i + ,i + represents the next mode of the variable mode system after mode i, and the corresponding V j (x j ) and V i (x j ), V j (x j ) and V i (x j ) represent the state x j For the Lyapunov function in mode j and mode i, the following inequality holds: κ1(|x k |)≤V σ(k) (x k )≤κ2(|x k |) (4) V σ(k) (x k+1 )-V σ(k) (x k )≤-(1-λ)V σ(k) (x k ) (5) V j (x j )≤μV i (x j ) (6) Then the system is globally consistent asymptotically stable for switching signals that satisfy the average dwell time condition: Among them, τ a represents the average residence time of the system, is the minimum average residence time of the system; Combined with Theorem 1, the linear matrix inequality condition that can ensure the stability of the system is designed: Theorem 1. Consider the variable mode control system shown in equation (1). Given a positive constant 0<λ<1, μ≥1, if there exists a positive scalar γ1>0, the positive definite matrix G,S σ(k) >0 and the matrix W σ(k) =K σ(k) G, so that the following linear matrix inequality holds: μP σ(k) (k)-P σ(k-1) (k-1)≥0 (10) The system satisfies the average residence time condition The variable modal system is globally consistent asymptotically stable, and the upper limit of the stabilization performance cost of the system is γ1.

4. The anti-shake model predictive control method for a variable mode system according to claim 3, characterized in that: In step S300, it includes: The constraints of the given system are in the form: -[ω] α ≤[Ex(k)+Hu(k)] α ≤[ω] α (11) Where ω is the system state and the upper limit of the control constraint, E and H are weight coefficients, and the function [·] α represents the αth element of the vector; Combined with Theorem 2, the system and the designed controller meet the state and control input constraints and have anti-shake performance: Theorem 2. Consider the variable mode system shown in equation (1). If there exists a positive scalar γ2>0, the positive definite matrix Z, G, S σ(k) >0 and the matrix W σ(k) =K σ(k) G, so that equation (9) in Theorem 1 and the following linear matrix inequality hold: trace(Z)≤γ2 (14) Where Ω is the system constraint matrix and satisfies [Ω] αα =([ω] α ) 2 ,function[·] αα represents the element in the αth row and αth column of the matrix; Then the system satisfies the constraint shown in equation (11), and the upper limit of the anti-shake control performance cost of the system is γ2.

5. The anti-shake model predictive control method for a variable mode system according to claim 4, characterized in that: In step S300, it includes: establishing a rolling horizon optimization problem based on linear matrix inequality, selecting a solver to solve the optimization problem, and obtaining the system state feedback control gain K σ(k) and control input u(k), acting on the variable mode control system, The optimization problem for controller design is formulated as: The Yalmip toolbox and Sdpt3 solver are selected to solve the linear matrix inequality. At each sampling time, the optimization problem shown in equation (15) is solved to obtain the state feedback control gain K σ(k) =W σ(k) G -1 And control input u(k) = K σ(k) x(k), acts on the control system (1) to achieve rolling optimization control.

6. The anti-shake model predictive control method for a variable mode system according to claim 5, characterized in that: The anti-shake model predictive control method is used for control system modeling of actual physical objects, including the flight control system of unmanned aerial vehicles, the motion control system of mobile robots and the collaborative control system of multi-agent platforms.

7. An anti-shake model predictive control system for a 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 in the anti-shake model predictive control method of the variable mode system 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 anti-shake model predictive control method for a variable mode system according to any one of claims 1 to 6 when called by a processor.

Images