A data-driven event-triggered control method for linear parameter-varying nonlinear systems

Abstract

The application discloses a data-driven event-triggered control method for a linear parameter-varying nonlinear system, comprising the following steps: for a discrete-time nonlinear system with an unknown model, a linear parameter-varying embedding method is used to represent the nonlinear system in a linear form dependent on parameters; for unknown bounded noise in measurement data, a noise matrix set based on a convex polyhedron is constructed, and a polyhedron data-driven LPV system representation is proposed by using offline collected state, input and scheduling variable data; a bounded type dynamic event-triggered transmission mechanism is designed, the communication resource usage is optimized by adjusting a trigger threshold in real time and setting upper and lower bounds of a transmission interval; and based on a discrete-time cyclic functional analysis method, a controller gain and a trigger parameter are jointly designed by using a linear matrix inequality tool. The method does not depend on an accurate system model, realizes stable control of the nonlinear system only by using historical data, significantly reduces a communication frequency, and guarantees system performance and robustness.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of automatic control, and particularly relates to a data-driven event-triggered control method for a linear parameter varying nonlinear system. BACKGROUND

[0002] With the increasing complexity of modern industrial systems, control system design faces multiple challenges such as nonlinear dynamics, model uncertainty and resource constraints. Among them, the control problem of nonlinear systems is particularly prominent. In robot systems, the dynamics usually exhibit strong nonlinear characteristics. Due to actual factors such as load changes, sensor measurement noise and communication bandwidth limitations, it is difficult for traditional model-based control methods to achieve accurate closed-loop control. Linear parameter varying (LPV) embedding technology is an effective means for processing nonlinear systems. By introducing measurable scheduling parameters, nonlinear systems are converted into parameter-dependent linear forms, allowing the use of mature linear system theory for controller design. Although the LPV method has systematic advantages in theory, its practical application still has limitations. For example, the control performance of the LPV nonlinear system depends largely on accurate system matrix information, which is often difficult to obtain accurately through mechanism analysis or system identification, especially when the system contains unmodeled dynamics and strong nonlinear elements. Model-based LPV controller design faces serious challenges. At the same time, the traditional LPV method has limited robustness to measurement noise and parameter disturbances, and it is difficult to provide strict stability guarantees in the presence of bounded noise disturbances. In addition, the selection of scheduling parameters and the parameterization dependence of system matrices require sufficient prior knowledge, which to some extent limits the applicability of this method in complex robotic systems with limited model information such as flexible joint robots and multi-legged walking platforms.

[0003] Currently, the data-driven event-triggered control of 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 format dynamic linearization have obvious shortcomings in simultaneously handling model uncertainty, noise disturbance and communication constraints. In the presence of offline and online noise, it is difficult to directly construct a data-driven system representation with robustness based on Willems' lemma. At the same time, the nonlinear conditions in the event-triggering mechanism make the controller design problem non-convex, increasing the difficulty of synthesis. SUMMARY

[0004] To solve the above technical problems, the present application provides a data-driven event-triggered control method for a linear parameter varying nonlinear system.

[0005] The application provides a data-driven event-triggered control method for a linear parameter-varying (LPV) nonlinear system, comprising the following steps:

[0006] S100: constructing an event-triggered control strategy for an LPV discrete-time nonlinear system of a robot, wherein the control strategy comprises a state feedback controller and a bounded-type dynamic event-triggered transmission mechanism;

[0007] S200: running the LPV discrete-time nonlinear system, collecting data reflecting unknown bounded noise, and constructing a convex polyhedron-based noise matrix set based on the unknown bounded noise data;

[0008] S300: collecting robot state, input and scheduling variable data offline, and constructing a polyhedron data-driven LPV system representation based on the convex polyhedron-based noise matrix set and the offline collected robot state, input and scheduling variable data;

[0009] S400: establishing a data-driven stability criterion for a closed-loop system under an event-triggered transmission strategy based on the polyhedron data-driven LPV system representation, so as to optimize a gain matrix of the state feedback controller and a trigger matrix of the bounded-type dynamic event-triggered transmission mechanism, and realize stable control and communication optimization of the robot system.

[0010] According to some embodiments of the application, the LPV discrete-time nonlinear system model in S100 is:

[0011] ;

[0012] wherein, , represents a discrete-time sequence, represents a non-negative integer set, represents a control input vector of the system at time t, and represents joint driving instructions or motion control quantities in a robot system, , represents a system state, and comprises joint motion states and body attitude variables in a robot system, represents a real number set, n represents the dimension of the system state, the nonlinear function f is continuous and satisfies , and the system is represented as:

[0013] ;

[0014] wherein, represents a measured state, and represents real-time measurable motion parameters and dynamic characteristics in a robot system, is a value set of a scheduling variable , and is a tight convex set, which is usually defined by the upper and lower bounds of the scheduling variable, dimension of scheduling variable , represents dimensional real vector space, represents unknown bounded noise, which comes from robot sensor measurement error or external environment disturbance, , and there exists a nonnegative constant for all , satisfying , represents the infinity norm of vector , represents the upper bound of the infinity norm of noise, and is a system matrix with affine parameter dependence:

[0015] ;

[0016] ;

[0017] wherein, and are real matrices with appropriate dimensions, represents the i-th component of scheduling variable .

[0018] According to some embodiments of the present application, the state feedback controller in S100 is specifically:

[0019] ;

[0020] wherein, is the transmission interval, represents the set of all natural numbers starting from 1, is the transmission time sequence, is the next trigger time sequence, represents the controller gain matrix, represents the state of the system at time; the state feedback controller is used for motion control and trajectory tracking tasks in a robot system.

[0021] According to some embodiments of the present application, the bounded-type dynamic event-triggered transmission mechanism in S100 is specifically:

[0022] ;

[0023] wherein, and are the lower bound and the upper bound of the trigger interval, which are used in a robot system to ensure control real-time performance and reduce communication load, is a state error, representing a deviation of an actual state from a state at a triggering time in a robot system, , is a controller triggering matrix, , , is a triggering parameter;

[0024] dynamic variable satisfies: ;

[0025] wherein, , is a dynamic variable related parameter, and an initial value when the parameter satisfies , for all , there is .

[0026] According to some embodiments of the present application, the set of noise matrices based on convex polyhedron in S200 is:

[0027] ;

[0028] wherein, is a noise matrix based on a convex polyhedron, represents a vertex of the noise matrix, is a number of collected data samples, is a number of vertices, is a weight coefficient, non-negative and summing to 1; and there is a non-negative constant for all , so that the noise vector satisfies , and belongs to the set of convex polyhedrons ;

[0029] the set is represented as:

[0030] ;

[0031] wherein, is a vertex of the noise vector, represents the i-th vertex of the set . is a weight coefficient of the convex combination.

[0032] According to some embodiments of the present application, the polyhedral data-driven LPV system in S300 is represented as:

[0033] ;

[0034] wherein, , , denotes a set of noise matrices associated with the collected data samples offline, is a subsequent state data matrix, the data matrix is constructed by collecting the operation data of the robot joint control system and the robot state sensing system in the robot system, and the data matrix satisfies , and the row of the data matrix is full rank, denotes a unit matrix of appropriate dimension, is a current state data matrix, is a Kronecker product data matrix of the scheduling variable and the state, is an input data matrix, is a Kronecker product data matrix of the scheduling variable and the input.

[0035] According to some embodiments of the application, the data-driven stability criterion in S400 is based on a discrete-time cyclic functional method and is expressed in the form of a linear matrix inequality:

[0036] Given the trigger parameter satisfies , the lower and upper bounds of the trigger interval , the scheduling variable boundary , is the boundary of the i-th component of the scheduling variable, is the dimension of the scheduling variable ; and a set of noise vertices, if there is a symmetric matrix , the transformed trigger weight matrix , the transformed controller gain matrix , a non-singular real matrix , so that the following LMI condition is satisfied:

[0037] ;

[0038] ;

[0039] wherein denotes a symmetric term in the symmetric matrix, is a disturbance attenuation parameter, is the trigger interval, and the core matrix expression in the LMI: ;

[0040] Data-driven system dynamics expression:

[0041] ,

[0042] The matrix related to the trigger interval ,

[0043] , is a positive definite matrix, used to construct the vector combination of terms in the LMI:

[0044] ;

[0045] The selected matrix , n is the dimension of the system state; and are free matrices, used to sum the inequality and system dynamics constraints, and are positive definite matrices.

[0046] According to some embodiments of the application, the controller gain matrix is ; and the controller trigger matrix is .

[0047] From the above technical solutions, the advantages and positive effects of the data-driven event-triggered control method for a linear parameter-varying nonlinear system of the application are that: by constructing an event-triggered control strategy for the LPV discrete-time nonlinear system of the robot, the nonlinear system is represented in a parameter-dependent linear form; the unknown bounded noise in the measurement data is constructed into a noise matrix set based on a convex polyhedron, thereby enhancing the robustness of the system; the robot state, input and scheduling variable data collected offline are used to avoid continuous detection, and a polyhedron data-driven LPV system representation is proposed to design a bounded type dynamic event-triggered transmission mechanism, thereby significantly reducing the communication frequency while ensuring the stability and performance of the system; by adjusting the trigger threshold and setting the upper and lower bounds of the transmission interval in real time, the performance deterioration caused by long-term non-triggering is prevented, and the use of communication resources is optimized; based on the discrete-time cyclic functional analysis method, the controller gain and trigger parameters are designed together through linear matrix inequality tools, thereby providing strict asymptotic stability and disturbance attenuation performance guarantees for the closed-loop system. The method does not rely on the accurate model of the system, but only uses historical data to achieve stable control of the nonlinear system, significantly reduces the communication frequency while ensuring the system performance and robustness. It is particularly suitable for high-performance comprehensive control of the robot system in the scene where the model is unknown, there is sensor noise and the communication bandwidth is limited. While dealing with unknown system models and noise interference, the method effectively optimizes the communication resources, and has universality and scalability. BRIEF DESCRIPTION OF DRAWINGS

[0048] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed in the embodiments or prior art description will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application, and those skilled in the art can also obtain other drawings according to these drawings without creative labor.

[0049] Figure 1 is a flow chart of a data-driven event-triggered control method for a linear parameter-varying nonlinear system in an embodiment of the present application;

[0050] Figure 2 is a schematic diagram of a data-driven event-triggered control structure for a LPV nonlinear system provided by the present application;

[0051] Figure 3 is a state and dynamic variable response graph for a LPV nonlinear system in an embodiment of the present application, in which subgraph (a) shows the change of the angular position signal x1(t) of a disc with time step, and subgraph (b) corresponds to the evolution process of the angular velocity signal x2(t);

[0052] Figure 4 is a graph of event-triggered transmission time in an embodiment of the present application, in which subgraph (a) shows the evolution trajectory of the dynamic variable , and subgraph (b) presents the time interval distribution between adjacent trigger times in the form of discrete sequence. DETAILED DESCRIPTION

[0053] The embodiments of the present application will be further described in detail with reference to the accompanying drawings and examples. The detailed description and the accompanying drawings of the following examples are used to exemplarily illustrate the principles of the present application, but cannot be used to limit the scope of the present application, and the present 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.

[0054] The techniques, methods, and devices known to those of ordinary skill in the relevant art can not be discussed in detail, but should be considered as part of the specification where appropriate.

[0055] As shown in the figure, according to the data-driven event-triggered control method for a linear parameter-varying nonlinear system provided by the present application, the following steps are included: Figure 1

[0056] S100: For a robot's LPV discrete-time nonlinear system, an event-triggered control strategy is constructed, which includes a state feedback controller and a bounded-type dynamic event-triggered transmission mechanism;

[0057] S200: Run the LPV discrete-time nonlinear system, collect data reflecting unknown bounded noise at the same time, and construct a noise matrix set based on convex polyhedron through the data of unknown bounded noise;

[0058] ​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;

[0059] 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.

[0060] 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.

[0061] In some embodiments of the present invention, the LPV discrete-time nonlinear system model in S100 is as follows:

[0062] ;

[0063] 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:

[0064] ;

[0065] 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 dimension of the vector space, denotes a real vector space, denotes an unknown bounded noise, which is derived from the measurement error of robot sensors or external environmental disturbance, , and there exists a non-negative constant for all satisfying , denotes the infinity norm of vector , denotes the upper bound of the infinity norm of noise, and is the system matrix with affine parameter dependence:

[0066] ;

[0067] ;

[0068] wherein, and are real matrices with appropriate dimensions, denotes the i-th component of the scheduling variable .

[0069] In some embodiments of the present application, the state feedback controller in S100 is specifically:

[0070] ;

[0071] wherein, is the transmission interval, denotes the set of all natural numbers starting from 1, is the sequence of transmission time, is the sequence of next trigger time, denotes the controller gain matrix, denotes the state of the system at time.

[0072] The state feedback controller is used for motion control and trajectory tracking tasks in a robot system.

[0073] In some embodiments of the present application, the bounded-type dynamic event-triggered transmission mechanism in S100 is specifically:

[0074] ;

[0075] wherein, and are the lower bound and upper bound of the trigger interval, which are used in a robot system to ensure control real-time performance and reduce communication load, is a state error, representing the deviation of the actual state from the state at the triggering time in the robot system, , is a controller triggering matrix, , , is a triggering parameter;

[0076] dynamic variable satisfies: ;

[0077] wherein, , is a dynamic variable related parameter, and the initial value when the parameter satisfies , for all , .

[0078] In some embodiments of the present application, the set of noise matrices based on convex polyhedron in S200 is:

[0079] ;

[0080] wherein, is a noise matrix based on convex polyhedron, represents a vertex of the noise matrix, is the number of collected data samples, is the number of vertices, is a weight coefficient, non-negative and summing to 1; and there is a non-negative constant for all , so that the noise vector satisfies , and belongs to the set of convex polyhedron ;

[0081] the set is represented as:

[0082] ;

[0083] wherein, is a vertex of the noise vector, represents the i-th vertex of the set ; is a weight coefficient of convex combination.

[0084] In some embodiments of the present application, the polyhedral data-driven LPV system in S300 is represented as:

[0085] ;

[0086] wherein, , , denotes a set of noise matrices related to the offline collected data samples, is a data matrix for the subsequent state, which is constructed by collecting the operation data of the robot joint control system and the robot state sensing system in the robot system, the data matrix satisfies , and the row of the data matrix is full rank, denotes a unit matrix of appropriate dimension, is a current state data matrix, is a Kronecker product data matrix of the scheduling variable and the state, is an input data matrix, is a Kronecker product data matrix of the scheduling variable and the input.

[0087] Specifically, the data-driven LPV system representation construction step based on the convex polyhedron is:

[0088] In the time interval , , the data set is collected, and the following data matrix is constructed:

[0089] ;

[0090] ;

[0091] ;

[0092] ;

[0093] .

[0094] According to the LPV system equation in step S100, the following data equation can be obtained: ;

[0095] wherein , .

[0096] Assuming that the data matrix is full rank (continuous excitation condition), that is , wherein is the number of samples, is the dimension of the scheduling variable, and n and m are the dimensions of the state and the input. Then the system set consistent with the data and noise set is defined as:

[0097] ;

[0098] According to the system set in the above steps, a polyhedral data-driven LPV system representation is obtained as follows:

[0099] ;

[0100] wherein matrix satisfies , and the data matrix row is full rank.

[0101] In some embodiments of the present application, the data-driven stability criterion described in step S400, the state feedback controller gain matrix and the trigger matrix of the event-triggered transmission mechanism are specifically as follows:

[0102] S411: by defining , the dynamic equation of the state feedback control system described in step S100 is rewritten as:

[0103] ;

[0104] wherein is a non-singular matrix and is the transformed state variable. The transformed controller gain , the transformed noise = .

[0105] According to the above dynamic equation, the following equation condition is constructed:

[0106] ;

[0107] According to the data-driven system expression described in step S300 and the above equation condition, the following data-based equation condition is obtained:

[0108] ;

[0109] wherein is a subsequent state data matrix, is a noise matrix, is a selection matrix for extracting the corresponding part from the state vector.

[0110] S412: for the algebraically equivalent system described in step S411, the Lyapunov function is constructed as:

[0111] ;

[0112] wherein matrix , is a discrete-time cyclic functional, is a dynamic variable. The forward difference of the above function is:

[0113] ;

[0114] S413: According to the equation of the dynamic variable in step S112 , the following conditions are obtained:

[0115] ;

[0116] wherein, is an extended state vector, is a transformed trigger weight matrix.

[0117] S414: Obtain the data-driven stability criterion, state feedback controller gain matrix, and trigger matrix of the event-triggered transmission mechanism by combining S411, S412, and S413, specifically:

[0118] Given the trigger parameter , satisfying , the upper and lower bounds of the trigger interval , the scheduling variable boundary , is the boundary of the i-th component of the scheduling variable, is the dimension of the scheduling variable , and the noise vertex set, if the symmetric matrix , the transformed trigger weight matrix , the transformed controller gain matrix , the non-singular real matrix , make the following LMI conditions true:

[0119] ;

[0120] ;

[0121] wherein, denotes the symmetric term in the symmetric matrix, is the disturbance attenuation parameter, is the trigger interval, and the core matrix expression in the LMI: ;

[0122] Data-driven system dynamics expression:

[0123] ;

[0124] Matrix related to the trigger interval ;

[0125] , is a positive definite matrix used to construct the vector combination of terms in the LMI: ​

[0126] ;

[0127] selection matrix , n is the dimension of system state; and is a free matrix, used for sum inequality and system dynamics constraints, and are positive definite matrices.

[0128] Then the system is asymptotically stable and has disturbance attenuation performance. The controller gain and the triggering weight matrix are designed as and . The design method is suitable for the design of motion controller and the optimization of communication resources in robot systems.

[0129] In one embodiment, the effectiveness and superiority of the data-driven event-triggered control method for LPV nonlinear systems in the present application are verified by simulation experiments.

[0130] Consider a nonlinear unbalanced disc system commonly used in the field of robots, whose discrete-time model is:

[0131] ;

[0132] where, denotes the angular position and angular velocity of the disc; is the system input voltage; is the discretization interval; 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 chosen as , and the scheduling set is . The noise satisfies , belongs to the polyhedral set , and the vertices are , , , .

[0133] Further, the open-loop system input is a uniformly distributed signal with , and the state and input data , are collected, where , and a row full-rank data matrix is constructed. The parameters , and the lower bound of the triggering interval are selected.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:

[0134] ;

[0135] 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.

[0136] like Figure 4 As 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.

[0137] 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.

[0138] 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 linear parameter-varying nonlinear systems, characterized in that, The method comprises the following steps: S100: constructing an event-triggered control strategy for a robot LPV discrete-time nonlinear system, the control strategy comprising a state feedback controller and a bounded-type dynamic event-triggered transmission mechanism; S200: running the LPV discrete-time nonlinear system while collecting data reflecting unknown bounded noise, and constructing a convex polyhedron-based noise matrix set based on the data of unknown bounded noise; S300: offline collecting robot state, input and scheduling variable data, and constructing a polyhedron data-driven LPV system representation based on the convex polyhedron-based noise matrix set and the offline collected robot state, input and scheduling variable data; S400: establishing a data-driven stability criterion for a closed-loop system under an event-triggered transmission strategy based on the polyhedron data-driven LPV system representation, to optimize a gain matrix of the state feedback controller and a trigger matrix of the bounded-type dynamic event-triggered transmission mechanism, and realize stable control and communication optimization of the robot system; The bounded-type dynamic event-triggered transmission mechanism in S100 is specifically: ； wherein and are lower and upper bounds of the triggering interval, in a robot system for guaranteeing control real-time and reducing communication load, is a state error, in a robot system, representing the deviation of the actual state from the state at the triggering time, , denotes the controller triggering matrix, , , is a triggering parameter; Dynamic variable Satisfies: ; wherein, , is a dynamic variable dependent parameter, and the initial value is when the parameter satisfies for all ; The data-driven stability criterion in S400 is based on a discrete-time cyclic functional method and is expressed in the form of a linear matrix inequality: Given trigger parameters , satisfy , trigger interval lower and upper bounds , scheduling variable bounds , is the bound of the i-th component of the scheduling variable, is the dimension of the scheduling variable ; and a set of noise vertices, if the symmetric matrix is the transformed trigger weight matrix is the transformed controller gain matrix is a nonsingular real matrix such that the following LMI condition holds: ； ； wherein denotes the symmetric terms in the symmetric matrix, is a disturbance attenuation parameter, is a triggering interval, the core matrix expression in the LMI: ; The data-driven system dynamics expression is: ， Matrix related to trigger interval , , is a positive definite matrix, used to construct the vector combination of terms in the LMI: ; selection matrix n is the dimension of the system state; denotes the controller gain matrix, denotes the identity matrix of appropriate dimension, and is a free matrix used to sum inequality and system dynamics constraints, and are positive definite matrices.

2. The method of claim 1, wherein, The LPV discrete-time nonlinear system model in S100 is: ； wherein, , denotes a discrete-time sequence, denotes a set of non-negative integers, denotes the control input vector of the system at time , in a robotic system, denotes joint driving commands or motion control quantities, , denotes the system state, in a robotic system, includes joint motion states and body pose variables, denotes the set of real numbers, n denotes the dimension of the system state, the nonlinear function f is continuous and satisfies , through LPV embedding, the system is represented as: ； where denotes the measurement state, which represents the motion parameters and dynamics characteristics that can be measured in real-time in a robotic system, is a scheduling variable whose value set is a compact set, usually defined by the upper and lower bounds of the scheduling variable, is the dimension of the scheduling variable , denotes an n-dimensional real vector space, denotes an unknown bounded noise, which comes from the measurement error of the robot sensors or external environmental disturbances, , and there exists a non-negative constant such that for all , denotes the infinity norm of the vector , denotes the upper bound of the infinity norm of the noise, and is the system matrix with affine parameter dependence: ； ； wherein and are real matrices, of appropriate dimensions, denotes the i-th component of the scheduling variable x.

3. The method of claim 2, wherein, The state feedback controller in S100 is specifically: ； wherein, is a transmission interval, denotes the set of all natural numbers starting from 1, is a sequence of transmission instants, is a sequence of next trigger instants, denotes a controller gain matrix, denotes the state of the system at the instant The state feedback controller is used for motion control and trajectory tracking tasks in a robot system.

4. The method of claim 3, wherein: The convex polyhedron-based noise matrix set in S200 is: ； wherein, is a noise matrix based on a convex polyhedron, denotes a vertex of the noise matrix, is the number of collected data samples, is the number of vertices, is a weight coefficient, non-negative and summing to 1; and there is a non-negative constant for all such that the noise vector satisfies and belongs to the convex polyhedron set ; Collection is represented as: ； wherein is a vertex of the noise vector, denotes the set of the i-th vertex; is a weight coefficient of the convex combination.

5. The method of claim 4, wherein: The polyhedron data-driven LPV system representation in S300 is: ； wherein , , denotes a set of noise matrices related to the offline collected data samples, is a subsequent state data matrix, in a robot system, the data matrix is constructed by collecting the running data of the robot joint control system and the robot state sensing system, the data matrix satisfies , and the data matrix row is full rank, denotes a unit matrix of appropriate dimension, is a current state data matrix, is a Kronecker product data matrix of scheduling variables and state, is an input data matrix, is a Kronecker product data matrix of scheduling variables and input.

6. The method of claim 5, wherein: The controller gain matrix is ; and the controller trigger matrix is .

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