Data-driven event trigger control method for linear variable-parameter nonlinear system

Abstract

The invention discloses a data-driven event trigger control method for a linear variable-parameter nonlinear system, which comprises the following steps: for a discrete-time nonlinear system with an unknown model, expressing the nonlinear system as a parameter-dependent linear form by using a linear variable-parameter embedding method; constructing a convex polyhedron-based noise matrix set for unknown bounded noise in the measurement data, and proposing polyhedral data-driven LPV system representation by using offline collected state, input and scheduling variable data; designing a bounded dynamic event trigger transmission mechanism, and optimizing the use of communication resources by adjusting a trigger threshold in real time and setting the upper and lower bounds of a transmission interval; based on a discrete time cycle functional analysis method, controller gain and trigger parameters are jointly designed through a linear matrix inequality tool. The method does not depend on an accurate system model, stable control over a nonlinear system is achieved only through historical data, the communication frequency is remarkably reduced, and meanwhile the system performance and robustness are guaranteed.

Description

Technical Field

[0001] This invention generally relates to the field of automatic control technology, and more specifically, to a data-driven event-triggered control method for linear variable parameter nonlinear systems. Background Technology

[0002] With the increasing complexity of modern industrial systems, control system design faces multiple challenges, including nonlinear dynamics, model uncertainty, and resource constraints. Among these, the control problem of nonlinear systems is particularly prominent. In robotic systems, their dynamics typically exhibit strong nonlinear characteristics, and due to practical factors such as load variations, sensor measurement noise, and communication bandwidth limitations, traditional model-based control methods struggle to achieve accurate closed-loop control. Linear Parameter Variation (LPV) embedding technology, as an effective means of handling nonlinear systems, transforms nonlinear systems into parameter-dependent linear forms by introducing measurable scheduling parameters, thus allowing the application of mature linear system theory for controller design. Although the LPV method possesses theoretical advantages, its practical application still has limitations. For example, the control performance of LPV nonlinear systems largely depends on accurate system matrix information, while the state matrix in real-world systems is often difficult to obtain accurately through mechanistic analysis or system identification. This is especially true when the system contains unmodeled dynamics and strongly nonlinear elements, posing a significant challenge to model-based LPV controller design. Furthermore, traditional LPV methods have limited robustness to measurement noise and parameter disturbances, and struggle to provide strict stability guarantees in the presence of bounded noise interference. Furthermore, the selection of scheduling parameters and the parameterization dependency of the system matrix require sufficient prior knowledge, which to some extent limits the applicability of this method in complex robot systems with scarce model information, such as flexible joint robots and multi-legged walking platforms.

[0003] Currently, research on data-driven event-triggered control for LPV nonlinear systems in noisy environments is still in its early stages. Existing model-based event-triggered control methods and model-free adaptive control methods based on tight-form dynamic linearization have significant shortcomings when simultaneously handling unknown models, noise interference, and communication constraints. Furthermore, in the presence of both offline and online noise, it is difficult to directly construct robust data-driven system representations based on Willems' lemma. Simultaneously, the nonlinear conditions in the event-triggered mechanism lead to nonconvex controller design problems, increasing the complexity of synthesis. Summary of the Invention

[0004] To address the above technical problems, this invention provides a data-driven event-triggered control method for linear variable parameter nonlinear systems.

[0005] A data-driven event-triggered control method for a linear variable-parameter nonlinear system, provided by the present invention, includes the following steps: S100: For the LPV discrete-time nonlinear system of the robot, an event-triggered control strategy is constructed, which includes a state feedback controller and a bounded dynamic event-triggered transmission mechanism. S200: Runs the LPV discrete-time nonlinear system, while collecting data reflecting unknown bounded noise, and constructs a noise matrix set based on convex polyhedra through the data of unknown bounded noise; S300: Collect robot state, input, and scheduling variable data offline, and construct a polyhedron data-driven LPV system representation based on the noise matrix set based on the convex polyhedron and the offline collected robot state, input, and scheduling variable data; S400: Based on the LPV system representation driven by the polyhedron data, establish a closed-loop system data-driven stability criterion under the event-triggered transmission strategy to optimize the gain matrix of the state feedback controller and the trigger matrix of the bounded dynamic event-triggered transmission mechanism, thereby achieving stable control and communication optimization of the robot system.

[0006] According to some embodiments of the present invention, the LPV discrete-time nonlinear system model in S100 is as follows: ; in, , Let N represent a discrete-time series, and N represent the set of non-negative integers. This represents the control input vector of the system at time t, and in a robot system, it represents joint drive commands or motion control quantities. , This represents the system state, which in a robot system includes joint motion states and body posture variables. Let n represent the set of real numbers, n represent the dimension of the system state, and the nonlinear function f be continuous and satisfy... Through LPV embedding, the system is represented as: ; in, Indicates the measurement state; in a robot system, it represents the motion parameters and dynamic characteristics that can be measured in real time. It is a scheduling variable The set of values ​​for is a compact convex set, typically defined by the upper and lower bounds of the scheduling variable. For scheduling variables dimensionality express 3D real vector space, This represents unknown bounded noise, originating from measurement errors of robot sensors or external environmental disturbances. And there exists a nonnegative constant. For all ,satisfy , Representing vectors The infinite norm, The upper bound of the infinity norm of noise. and For a system matrix with affine parameter dependence: ; ; in, and It is a real matrix with appropriate dimensions. Represents scheduling variables The i-th component.

[0007] According to some embodiments of the present invention, the state feedback controller in S100 is specifically: ; in, It is a transmission range. Represents the set of all natural numbers starting from 1. To transmit time sequences, For the next trigger time sequence, Represents the controller gain matrix. Indicates that the system is in The state at any given moment; the state feedback controller is used for motion control and trajectory tracking tasks in the robot system.

[0008] According to some embodiments of the present invention, the bounded dynamic event triggering transmission mechanism in S100 is specifically as follows: ; in, and The lower and upper bounds of the trigger interval are used in robot systems to ensure real-time control and reduce communication load. State error, in a robot system, represents the deviation between the actual state and the state at the trigger moment. , Represents the controller trigger matrix. , , For trigger parameters; Dynamic variables satisfy: ; in, , These are parameters related to dynamic variables, and their initial values ​​are... It can be proven that when the parameters satisfy At that time, for all ,have .

[0009] According to some embodiments of the present invention, the set of noise matrices based on convex polyhedra in S200 is as follows: ; in, It is a noise matrix based on convex polyhedra. Represents the vertices of the noise matrix. The number of data samples collected. The number of vertices. The weights are non-negative and sum to 1; and there exists a non-negative constant. For all This makes the noise vector satisfy And it belongs to the set of convex polyhedra. ; gather Represented as: ; in, It is the vertex of the noise vector. Represents a set The i-th vertex; These are the weighting coefficients of the convex combination.

[0010] According to some embodiments of the present invention, the polyhedral data-driven LPV system in S300 is represented as follows: ; in, , , This represents the set of noise matrices associated with offline collected data samples. To form the subsequent state data matrix, a data matrix is ​​constructed within the robot system by collecting operational data from the robot's joint control system and state perception system. satisfy And the data matrix has full row rank. Represents an identity matrix of appropriate dimension. This is the current state data matrix. The Kronecker product data matrix of the scheduling variables and the state. For the input data matrix, The Kronecker product of the scheduling variable and the input is a data matrix.

[0011] According to some embodiments of the present invention, the data-driven stability criterion in S400 is based on the discrete-time cyclic functional method and is expressed as a linear matrix inequality: Given trigger parameters ,satisfy upper and lower bounds of trigger interval Scheduling variable boundaries , It is the boundary of the i-th component of the scheduling variable. It is a scheduling variable The dimension of the matrix; and the set of noise vertices, if a symmetric matrix exists. Transformed trigger weight matrix Transformed controller gain matrix Non-singular real matrix This makes the following LMI conditions true: ; ; in, To represent the symmetric terms in a symmetric matrix, It is the disturbance attenuation parameter. It refers to the trigger interval, the core matrix expression in LMI: ; Data-driven system dynamics expressions: , Matrix related to trigger interval , , It is a positive definite matrix used to construct vector combinations of terms in the LMI: ; Select matrix , where n is the dimension of the system state; and It is a free matrix used for solving summation inequalities and system dynamic constraints. and It is a positive definite matrix.

[0012] According to some embodiments of the present invention, the controller gain matrix is: The controller trigger matrix is: .

[0013] As can be seen from the above technical solution, the advantages and positive effects of the data-driven event-triggered control method for a linear variable-parameter nonlinear system of the present invention are as follows: An event-triggered control strategy is constructed for the LPV discrete-time nonlinear system of the robot, representing the nonlinear system as a parameter-dependent linear form; for unknown bounded noise in the measurement data, a noise matrix set based on convex polyhedra is constructed to enhance the robustness of the system; offline collected robot state, input, and scheduling variable data are used to avoid continuous detection, and a polyhedral data-driven LPV system representation is proposed, designing a bounded dynamic event-triggered transmission mechanism to significantly reduce communication frequency while ensuring system stability and performance; by adjusting the trigger threshold in real time and setting the upper and lower bounds of the transmission interval, performance degradation caused by long-term non-triggering is prevented, optimizing the use of communication resources; based on the discrete-time cyclic functional analysis method, the controller gain and trigger parameters are jointly designed using linear matrix inequalities, providing a strict guarantee of asymptotic stability and disturbance attenuation performance for the closed-loop system. This method does not rely on an accurate system model, but only uses historical data to achieve stable control of the nonlinear system, significantly reducing communication frequency while ensuring system performance and robustness. It is particularly suitable for high-performance integrated control of robot systems in scenarios where the model is unknown, sensor noise exists, and communication bandwidth is limited. While dealing with unknown system models and noise interference, it can effectively optimize communication resources and has universality and scalability. Attached Figure Description

[0014] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0015] Figure 1 This is a flowchart of a data-driven event-triggered control method for a linear variable-parameter nonlinear system according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the data-driven event-triggered control structure of the LPV nonlinear system provided by the present invention; Figure 3 This is a state and dynamic variable response diagram of an LPV nonlinear system in one embodiment of the present invention, wherein sub-graph (a) shows the change of the disk's angular position signal x1(t) with the time step, and sub-graph (b) shows the evolution of the angular velocity signal x2(t). Figure 4 This is an event-triggered transmission timeline diagram in one embodiment of the present invention, wherein sub-graph (a) shows dynamic variables. The evolutionary trajectory, subgraph (b) presents the time interval between adjacent triggering moments in the form of a discrete sequence. distributed. Detailed Implementation

[0016] The embodiments of this application will be further described in detail below with reference to the accompanying drawings and examples. The detailed description of the following embodiments and the accompanying drawings are used to illustrate the principles of this application by way of example, but should not be used to limit the scope of this application. This application can be implemented in many different forms and is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.

[0017] Techniques, methods, and equipment known to those skilled in the art may not be discussed in detail, but where appropriate, they should be considered part of the specification.

[0018] like Figure 1 As shown, a data-driven event-triggered control method for a linear variable-parameter nonlinear system according to the present invention includes the following steps: S100: For the LPV discrete-time nonlinear system of the robot, an event-triggered control strategy is constructed, which includes a state feedback controller and a bounded dynamic event-triggered transmission mechanism. S200: Runs the LPV discrete-time nonlinear system, while collecting data reflecting unknown bounded noise, and constructs a noise matrix set based on convex polyhedra through the data of unknown bounded noise; S300: Collect robot state, input, and scheduling variable data offline, and construct a polyhedron data-driven LPV system representation based on the noise matrix set based on the convex polyhedron and the offline collected robot state, input, and scheduling variable data; S400: Based on the LPV system representation driven by the polyhedron data, establish a closed-loop system data-driven stability criterion under the event-triggered transmission strategy to optimize the gain matrix of the state feedback controller and the trigger matrix of the bounded dynamic event-triggered transmission mechanism, thereby achieving stable control and communication optimization of the robot system.

[0019] like Figure 2 The diagram shows a data-driven event-triggered control structure for an LPV nonlinear system, including a nonlinear robot controlled object, an LPV embedded module, sensors, an event-triggered decision-maker, a controller, and a hold-and-hold mechanism. The event-triggered decision-maker dynamically determines the transmission timing based on the system state to save communication resources. By collecting robot system state, input, and scheduling variable data offline in an open-loop manner, a data-driven controller and event-triggered decision-maker are designed to achieve robust and stable control of an unknown LPV robot nonlinear system.

[0020] In some embodiments of the present invention, the LPV discrete-time nonlinear system model in S100 is as follows: ; in, , Represents a discrete time series. Represents the set of non-negative integers. Indicates the system at time... In a robot system, the control input vector represents joint drive commands or motion control quantities. , This represents the system state, which in a robot system includes joint motion states and body posture variables. Let n represent the set of real numbers, n represent the dimension of the system state, and the nonlinear function f be continuous and satisfy... Through LPV embedding, the system is represented as: ; in, Indicates the measurement state; in a robot system, it represents the motion parameters and dynamic characteristics that can be measured in real time. It is a scheduling variable The set of values ​​for is a compact convex set, typically defined by the upper and lower bounds of the scheduling variable. For scheduling variables dimensionality express 3D real vector space, This represents unknown bounded noise, originating from measurement errors of robot sensors or external environmental disturbances. And there exists a nonnegative constant. For all ,satisfy , Representing vectors The infinite norm, The upper bound of the infinity norm of noise. and For a system matrix with affine parameter dependence: ; ; in, and It is a real matrix with appropriate dimensions. Represents scheduling variables The i-th component.

[0021] In some embodiments of the present invention, the state feedback controller in S100 is specifically: ; in, It is a transmission range. Represents the set of all natural numbers starting from 1. To transmit time sequences, For the next trigger time sequence, Represents the controller gain matrix. Indicates that the system is in The state at any given moment.

[0022] The state feedback controller is used for motion control and trajectory tracking tasks in the robot system.

[0023] In some embodiments of the present invention, the bounded dynamic event triggering transmission mechanism in S100 is specifically as follows: ; in, and The lower and upper bounds of the trigger interval are used in robot systems to ensure real-time control and reduce communication load. State error, in a robot system, represents the deviation between the actual state and the state at the trigger moment. , Represents the controller trigger matrix. , , For trigger parameters; Dynamic variables satisfy: ; in, , These are parameters related to dynamic variables, and their initial values ​​are... It can be proven that when the parameters satisfy At that time, for all ,have .

[0024] In some embodiments of the present invention, the noise matrix set based on the convex polyhedron in S200 is as follows: ; in, It is a noise matrix based on convex polyhedra. Represents the vertices of the noise matrix. The number of data samples collected. The number of vertices. The weights are non-negative and sum to 1; and there exists a non-negative constant. For all This makes the noise vector satisfy And it belongs to the set of convex polyhedra. ; gather Represented as: ; in, It is the vertex of the noise vector. Represents a set The i-th vertex; These are the weighting coefficients of the convex combination.

[0025] In some embodiments of the present invention, the polyhedral data-driven LPV system in S300 is represented as follows: ; in, , , This represents the set of noise matrices associated with offline collected data samples. To form the subsequent state data matrix, a data matrix is ​​constructed within the robot system by collecting operational data from the robot's joint control system and state perception system. satisfy And the data matrix has full row rank. Represents an identity matrix of appropriate dimension. This is the current state data matrix. The Kronecker product data matrix of the scheduling variables and the state. For the input data matrix, The Kronecker product of the scheduling variable and the input is a data matrix.

[0026] Specifically, the steps for constructing the representation of a data-driven LPV system based on convex polyhedra are as follows: In the time interval Inside, Collect datasets And construct the following data matrix: ; ; ; ; .

[0027] Based on the LPV system equations in step S100, the following data equations can be obtained: ; in, , .

[0028] Assuming a data matrix Full rank (continuous incentive condition), i.e. ,in It is the sample size. Let n be the dimension of the scheduling variable, and m be the dimensions of the state and input, respectively. Then, the system set consistent with the data and noise sets is defined as follows: ; Based on the system set in the above steps, the polyhedral data-driven LPV system can be represented as follows: ; Among them, matrix satisfy The data matrix has full row rank.

[0029] In some embodiments of the present invention, the data-driven stability criterion, the state feedback controller gain matrix, and the trigger matrix of the event-triggered transmission mechanism mentioned in step S400 are specifically as follows: S411: By definition The dynamic equations of the state feedback control system described in step S100 are rewritten as follows: ; in, It is a non-singular matrix and These are the transformed state variables. The transformed controller gain. transformed noise = .

[0030] Based on the above dynamic equations, the following equality conditions are constructed: ; Based on the data-driven system expression described in step S300 and the above equality conditions, the following data-based equality conditions are obtained: ; in, For subsequent state data matrix, For the noise matrix, The selection matrix is ​​used to extract the corresponding part from the state vector.

[0031] S412: For the algebraic equivalent system described in step S411, construct the Lyapunov function as follows: ; Among them, matrix , It is a discrete-time cyclic functional. These are dynamic variables. The forward difference of the above function is divided into: ; S413: By definition According to the dynamic variables in step S112 From the equation, we obtain the following conditions: ; in, To expand the state vector, This is the transformed trigger weight matrix.

[0032] S414: Combining S411, S412, and S413, we obtain the data-driven stability criterion, the state feedback controller gain matrix, and the trigger matrix of the event-triggered transmission mechanism, specifically: Given trigger parameters ,satisfy upper and lower bounds of trigger interval Scheduling variable boundaries , It is the boundary of the i-th component of the scheduling variable. It is a scheduling variable The dimension of the matrix; and the set of noise vertices, if a symmetric matrix exists. Transformed trigger weight matrix Transformed controller gain matrix Non-singular real matrix This makes the following LMI conditions true: ; ; in, To represent the symmetric terms in a symmetric matrix, It is the disturbance attenuation parameter. It refers to the trigger interval, the core matrix expression in LMI: ; Data-driven system dynamics expressions: ; Matrix related to trigger interval ; , It is a positive definite matrix used to construct vector combinations of terms in the LMI: ; Select matrix , where n is the dimension of the system state; and It is a free matrix used for solving summation inequalities and system dynamic constraints. and It is a positive definite matrix.

[0033] The system is asymptotically stable and exhibits disturbance attenuation performance. The controller gain and trigger weight matrix are designed as follows: and This design methodology is applicable to the design of motion controllers and the optimization of communication resources in robot systems.

[0034] In one embodiment, simulation experiments are used to verify the effectiveness and superiority of the data-driven event-triggered control method for LPV nonlinear systems in this invention.

[0035] Consider a common nonlinear unbalanced disk system in robotics, whose discrete-time model is: ; in, Indicates the angular position and angular velocity of the disk; The system input voltage; The discretization interval is [value missing]; the physical parameters are: m = 0.0735 kg, g = 9.81 m / s², l = 0.041 m, J = 1.14. kg·m² , The scheduling variable is selected as... The scheduling set is .noise satisfy It belongs to the set of polyhedra. The vertex is , , , .

[0036] Furthermore, the open-loop system input is Uniformly distributed signal, collection status and input data , ,in And construct a full-rank data matrix. Select parameters. trigger interval lower bound By solving the linear matrix inequality described in step S400, the gain matrix of the state feedback controller and the weight matrix of the event-triggered transmission mechanism are obtained as follows: ; Set the system initial state To obtain the system in time The system state and dynamic variable response trajectory diagram within, such as Figure 3 As shown, both states of the system eventually converged successfully to the origin, demonstrating the effectiveness of the method proposed in this application.

[0037] like Figure 4As shown, the transmission timeline of the system under the data-driven event triggering control is given. Only 346 points out of 2000 discrete time points were transmitted, which significantly reduces the number of transmissions compared to the traditional continuous transmission strategy, demonstrating the superiority of the method in this application.

[0038] The embodiments of this application have now been described in detail. To avoid obscuring the concept of this application, some details known in the art have not been described. Those skilled in the art can fully understand how to implement the technical solutions disclosed herein based on the above description.

[0039] While specific embodiments of this application have been described in detail by way of examples, those skilled in the art should understand that the above examples are for illustrative purposes only and are not intended to limit the scope of this application. Those skilled in the art should understand that modifications can be made to the above embodiments or equivalent substitutions can be made to some technical features without departing from the scope and spirit of this application. In particular, as long as there is no structural conflict, the various technical features mentioned in the embodiments can be combined in any manner.

Claims

1. A data-driven event-triggered control method for a linear variable parameter nonlinear system, characterized in that, The method includes the following steps: S100: For the LPV discrete-time nonlinear system of the robot, an event-triggered control strategy is constructed, which includes a state feedback controller and a bounded dynamic event-triggered transmission mechanism. S200: Runs the LPV discrete-time nonlinear system, while collecting data reflecting unknown bounded noise, and constructs a noise matrix set based on convex polyhedra through the data of unknown bounded noise; S300: Collect robot state, input, and scheduling variable data offline, and construct a polyhedron data-driven LPV system representation based on the noise matrix set based on the convex polyhedron and the offline collected robot state, input, and scheduling variable data; S400: Based on the LPV system representation driven by the polyhedron data, establish a closed-loop system data-driven stability criterion under the event-triggered transmission strategy to optimize the gain matrix of the state feedback controller and the trigger matrix of the bounded dynamic event-triggered transmission mechanism, thereby achieving stable control and communication optimization of the robot system.

2. The method according to claim 1, characterized in that, The discrete-time nonlinear system model of LPV in S100 is as follows: ； in, , Represents a discrete time series. Represents the set of non-negative integers. Indicates the system at time 10:00 In a robot system, the control input vector represents joint drive commands or motion control quantities. , This represents the system state, which in a robot system includes joint motion states and body posture variables. Let n represent the set of real numbers, n represent the dimension of the system state, and the nonlinear function f be continuous and satisfy... Through LPV embedding, the system is represented as: ； in, Indicates the measurement state; in a robot system, it represents the motion parameters and dynamic characteristics that can be measured in real time. It is a scheduling variable The set of values ​​for is a compact convex set, usually defined by the upper and lower bounds of the scheduling variable. For scheduling variables dimensionality express 3D real vector space, This represents unknown bounded noise, originating from measurement errors of robot sensors or external environmental disturbances. And there exists a nonnegative constant. For all ,satisfy , Representing vectors The infinite norm, The upper bound of the infinity norm of noise. and For a system matrix with affine parameter dependence: ； ； in, and It is a real matrix with appropriate dimensions. Represents scheduling variables The i-th component.

3. The method according to claim 2, characterized in that, The state feedback controller in S100 is specifically as follows: ； in, It is a transmission range. Represents the set of all natural numbers starting from 1. To transmit time sequences, For the next trigger time sequence, Represents the controller gain matrix. Indicates that the system is in The state at any given moment; The state feedback controller is used for motion control and trajectory tracking tasks in the robot system.

4. The method according to claim 3, characterized in that, The bounded dynamic event triggering transmission mechanism in S100 is as follows: ； in, and The lower and upper bounds of the trigger interval are used in robot systems to ensure real-time control and reduce communication load. State error, in a robot system, represents the deviation between the actual state and the state at the trigger moment. , Represents the controller trigger matrix. , , For triggering parameters; Dynamic variables satisfy: ; in, , These are parameters related to dynamic variables, and their initial values ​​are... It can be proven that when the parameters satisfy At that time, for all ,have .

5. The method according to claim 4, characterized in that: The set of noise matrices based on convex polyhedra in S200 is as follows: ； in, It is a noise matrix based on convex polyhedra. Represents the vertices of the noise matrix. The number of data samples collected. The number of vertices. The weights are non-negative and sum to 1; and there exists a non-negative constant. For all This makes the noise vector satisfy And it belongs to the set of convex polyhedra. ; gather Represented as: ； in, It is the vertex of the noise vector. Represents a set The i-th vertex; These are the weighting coefficients of the convex combination.

6. The method according to claim 5, characterized in that: In S300, a polyhedral data-driven LPV system is represented as follows: ； in, , , This represents the set of noise matrices associated with offline collected data samples. To form the subsequent state data matrix, a data matrix is ​​constructed within the robot system by collecting operational data from the robot's joint control system and state perception system. satisfy And the data matrix has full row rank. Represents an identity matrix of appropriate dimension. This is the current state data matrix. The Kronecker product data matrix of the scheduling variables and the state. For the input data matrix, The Kronecker product of the scheduling variable and the input is a data matrix.

7. The method according to claim 6, characterized in that: The data-driven stability criterion in S400 is based on the discrete-time cyclic functional method and is expressed as a linear matrix inequality: Given trigger parameters ,satisfy upper and lower bounds of trigger interval Scheduling variable boundaries , It is the boundary of the i-th component of the scheduling variable. It is a scheduling variable dimensionality; And the set of noise vertices, if a symmetric matrix exists. Transformed trigger weight matrix Transformed controller gain matrix Non-singular real matrix This makes the following LMI conditions true: ； ； in, To represent the symmetric terms in a symmetric matrix, It is the disturbance attenuation parameter. It refers to the trigger interval, the core matrix expression in LMI: ; Data-driven system dynamics expressions: ， Matrix related to trigger interval , , It is a positive definite matrix used to construct vector combinations of terms in the LMI: ; Select Matrix , where n is the dimension of the system state; and It is a free matrix used for solving summation inequalities and system dynamic constraints. and It is a positive definite matrix.

8. The method according to claim 7, characterized in that: The controller gain matrix is The controller trigger matrix is: .

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