Anti-shake model prediction control method and system of variable-mode system

Abstract

The invention provides an anti-shake model prediction control method and system of a variable-mode system, and belongs to the field of hybrid system control. The invention aims to solve the problems that the convergence speed of a control system is remarkably reduced and the overshoot is greatly increased in the stabilization control performance due to the fact that the traditional anti-shake variable mode control algorithm is difficult to balance the anti-shake control performance and the stabilization control performance. The method comprises the steps of establishing a variable modal control system model and designing a cost function, designing a linear inequality condition about stability based on an average residence time variable modal system stability criterion and a multi-Lyapunov function method, and calculating a cost upper limit; designing a linear inequality condition meeting system constraints and calculating a system control performance cost upper limit; and finally, obtaining a multi-mode state feedback control gain according to a designed rolling time domain optimization algorithm and acting on a control system. According to the method, the comprehensive performance of the system is improved, the application object and the application range of the method are widened, and the method has good engineering application value.

Description

Technical Field

[0001] The present invention relates to the technical field of control of hybrid systems, and in particular 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, variable modal system consists of multiple sub-modes and modal switching signals that control the change behavior of these modes. This type of system is widely used in the control system modeling of actual physical objects such as drones, mobile robots, and multi-agent platforms. According to the type of modal switching signal, variable modal systems can be divided into time-dependent and state-dependent types. Among them, the average dwell time switching signal is a typical time-dependent modal switching signal, that is, the number of modal changes within a certain period of time has an upper limit, and the average time required for multiple consecutive modal changes needs to exceed a fixed value. This type of signal allows the system mode to switch quickly when necessary, and then compensates for the energy increase caused by the rapid switching process by slowing down the frequency of modal changes.

[0003] However, in order to achieve system stability under frequent modal changes, the designed controller parameters usually jump at the moment of modal change, which will cause severe "jitter" phenomenon of control input and lead to problems such as reduced actuator life. In order to overcome this defect, anti-shake variable mode control methods have been proposed in existing studies. They extend the time required for control gain change and impose maximum control jitter constraints to reduce the impact of controller parameter jumps. Nevertheless, better anti-shake control performance usually leads to a decrease in system stabilization control performance indicators (such as convergence speed and overshoot). With the diversification of system control objectives, the pursuit of different types of control performance limits the applicability of traditional anti-shake control algorithms on specific systems. Therefore, developing an optimization method that weighs multiple types of control objectives to achieve optimal control performance under comprehensive multi-objectives has become the main research direction of anti-shake control.

[0004] As a powerful tool for dealing with 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 studies have 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 results have been applied to economic systems and wind energy conversion systems, and achieved good results. For example, the existing patent is an active fault-tolerant control method for unmanned aerial vehicles with jitter suppression performance (application number: CN202211579411.1), which involves the field of unmanned aerial vehicle control technology. A UAV model in the form of a linearized discrete-time state-space expression is established; the hidden semi-Markov switching system theory is used to model the FDI process with inaccurate observation information, and an anti-shake controller that depends on the observation mode is constructed; the UAV system state anti-shake constraints are constructed; sufficient conditions are proposed to ensure the mean square stability of the UAV system under the condition of inaccurate FDI information; sufficient conditions are proposed for the existence of a fault-tolerant controller with anti-shake performance for discrete-time UAV systems; matrix inequalities are solved to obtain the gains of the UAV system fault-tolerant controller; and the gains of the UAV system fault-tolerant controller are used to realize active fault-tolerant control of the quadrotor UAV.

[0005] However, within the variable mode model predictive control framework, it is an effective but less studied idea to consider imposing constraints on the control jitter performance or integrating it into the cost function, and obtaining the best comprehensive performance through a multi-objective optimization scheme of anti-shake / stabilization performance. Therefore, the present invention proposes an anti-shake variable mode model predictive control algorithm that introduces a multi-objective function of stabilization performance and anti-shake performance into the cost function for the average residence time variable mode system, and simultaneously optimizes the comprehensive control performance of the system in a weighted sense. The relevant research results are of great significance in promoting the development of variable mode system control theory and promoting 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] In order to solve the problem that the traditional anti-shake variable mode control algorithm is difficult to balance the anti-shake performance and the stabilization performance, although the control system has good jitter suppression, there are problems in the stabilization performance such as significantly reduced convergence speed and drastic increase in overshoot.

[0008] The present invention adopts the following technical solutions to solve the above technical problems:

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

[0010] 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;

[0011] 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;

[0012] 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;

[0013] 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.

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

[0015] Establish variable mode control system model:

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

[0017] 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;

[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] Among them, x k+n|k and u k+n|kare the system state and control input predicted by the variable mode control system at time k+n, respectively. σ(k) To control the 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] in, is the system stabilization performance, Q and R are weight coefficients;

[0024] For system anti-shake performance, It represents the maximum value of the square of the second norm of the system control input change.

[0025] Further, 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 ∞ Function κ 1 and κ 2 , 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:

[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 consistent asymptotically stable for switching signals that satisfy the average dwell time condition:

[0030]

[0031] Among them, τ a represents the average residence time of the system, is the minimum average residence time of the system;

[0032] Combined with Theorem 1, the linear matrix inequality condition that can ensure the stability of the system is designed:

[0033] 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 γ 1 >0, 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:

[0034]

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

[0036] The system satisfies the average residence time condition The variable modal system is globally consistent and asymptotically stable, and the upper limit of the stabilization cost of the system is γ 1 .

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

[0038] The constraints of the given system are in the form:

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

[0040] 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;

[0041] Combined with Theorem 2, the system and the designed controller meet the state and control input constraints and have anti-shake performance:

[0042] Theorem 2. Consider the variable mode system shown in equation (1). If there exists a positive scalar γ 2 >0, 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:

[0043]

[0044] trace(Z)≤γ 2 (14)

[0045] 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;

[0046] 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 .

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

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

[0049]

[0050] 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.

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

[0052] 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.

[0053] 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 an anti-shake model predictive control method for a variable mode system when called by a processor.

[0054] Compared with the prior art, the present invention has the following beneficial effects:

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

[0056] The present invention establishes a controller design method under the framework of rolling horizon optimization, in which the system stabilization performance and anti-shake control performance are considered separately in the cost function, and the two types of system performance are optimized simultaneously by solving the linear matrix inequality conditions to obtain the control gain that can ensure the optimal comprehensive performance of the system;

[0057] The present invention aims to address the defect in the existing anti-shake variable mode controller design method that it is unable to balance the anti-shake control performance and the stabilization control performance. An anti-shake variable mode model predictive control method that takes both types of control performance into account is proposed, which improves the comprehensive performance of the system, broadens the application objects and scope of application of such methods, and has good engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

[0060] Figure 3 It is a state response comparison curve diagram of the variable mode system under the action of the traditional controller and the controller proposed by the present invention in the embodiment of the present invention;

[0061] Figure 4 A control input comparison curve diagram of the variable mode system in an embodiment of the present invention under the action of a traditional controller and the controller proposed in the present invention;

[0062] Figure 5 It is a comparison curve diagram of the control change of the variable mode system under the action of the traditional controller and the controller proposed by the present invention in the embodiment of the present invention. DETAILED DESCRIPTION

[0063] 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.

[0064] Specific implementation plan 1: Combine Figure 1 As shown, the present invention provides an anti-shake model predictive control method for a variable mode system, comprising the following steps:

[0065] S100, establishing a variable mode control system model and designing a cost function, including describing the system as a variable mode 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 system, specifically including:

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

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

[0070] u k+n|k =K σ(k) x k+n|k (2)

[0071] Among them, x k+n|k and u k+n|k are the system state and control input predicted by the system at time k+n, respectively. σ(k) To control the 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] 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;

[0075] S200. Design linear matrix inequality conditions that can ensure system stability and calculate the upper limit of the system's stabilization control performance cost, including relying on the stability criterion of the average residence time variable mode system and based on the multi-Lyapunov function method, designing linear matrix inequality conditions that can ensure system stability and giving the upper limit of the system's stabilization control performance cost, including:

[0076] First, the stability condition of the mean residence time variable mode system is given: 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) (x) and two types of K ∞ Function κ 1 and κ 2 , 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 ) represent the state x j For the Lyapunov function in mode j and mode i, the following inequality holds:

[0077] κ 1 (|x k |)≤V σ(k) (x k )≤κ 2 (|x k |) (4)

[0078] V σ(k) (x k+1 )-V σ(k) (x k )≤-(1-λ)V σ(k) (x k ) (5)

[0079] V j (x j )≤μV i (x j ) (6)

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

[0081]

[0082] Among them, τ a represents the average residence time of the system, is the minimum average residence time of the system;

[0083] On this basis, relying on Theorem 1, a linear matrix inequality condition is designed to ensure the stability of the system:

[0084] 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 γ 1 >0, positive definite matrix G,S σ(k) >0 and the matrix W σ(k) =K σ(k) G, such that the following linear matrix inequality holds:

[0085]

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

[0087] The system satisfies the average residence time condition The variable modal system is globally consistent and asymptotically stable, and the upper limit of the stabilization cost of the system is γ 1 ;

[0088] 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 system, deriving a linear matrix inequality condition that can make the system state and controller input satisfy the constraints, and determining the upper limit of the anti-shake control performance cost, specifically including:

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

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

[0091] 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;

[0092] Theorem 2 is given below, which makes the system and the designed controller meet 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 exists a positive scalar γ 2 >0, 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:

[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 Figure 1. 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, such 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