Data-driven LPV system robust tracking control method based on event triggering

Abstract

The invention relates to the field of LPV system tracking control, in particular to a robust tracking control method for a data-driven LPV system under an event triggering strategy. The method comprises the following steps: 1, introducing an integral compensator, and popularizing a perturbation LPV system to an augmented perturbation LPV system; and 2, based on an LPV system-continuous excitation condition, collecting data such as a state variable and a scheduling variable of an unknown augmented perturbation LPV open-loop system, and establishing closed-loop representation of the LPV system based on the data. 3, based on the closed-loop data representation of the augmented perturbation LPV system, synthesizing data to drive a controller, and ensuring the closed-loop stability of the system; 4, on the basis of the whole-block S-process, infinite constraints in semi-definite programming for controlling gain calculation are converted into limited constraints calculated on vertexes of a polyhedron; 5, designing an event triggering strategy, and designing a controller for ensuring the closed-loop stability performance of the augmented perturbation LPV system; and 6, performing robust tracking control applied to the augmented perturbation LPV system.

Description

Technical Field

[0001] This invention relates to the field of tracking control for LPV systems, and more specifically to a robust tracking control method for LPV systems based on event-triggered data-driven approaches. Background Technology

[0002] Linear variable parameter (LPV) systems, as an important class of dynamic system models, have been widely used in dealing with complex systems exhibiting parameter variations. Their core principle lies in transforming a nonlinear system into a combination of several linear systems by introducing scheduling variables, thereby enabling the analysis and design of the system using mature linear control theory. In practice, LPV systems are frequently used for modeling and representing complex systems such as variable-wing aircraft, flexible robotic arms, and unmanned ground vehicles, and these applications often involve motion trajectory tracking control of these systems. To achieve robust tracking performance, accurate identification and design of robust controllers for LPV systems have become key technical means in this field.

[0003] However, acquiring model knowledge of LPV systems through first-principles analysis or system identification not only involves high computational costs but also lacks theoretical support related to control synthesis. This situation directly spurred the birth and development of data-driven control. Based on Willems' fundamental lemma of continuous excitation, this approach can parameterize linear feedback systems using offline acquired data. It eliminates the need for explicit system identification, directly synthesizing the controller from the data, thus significantly reducing the computational load in modeling and control processes, and possessing substantial technical advantages.

[0004] Building upon this foundation, event-triggered control, as an effective control strategy, further demonstrates its unique advantages. Traditional time-triggered control requires data sampling and control command updates at fixed intervals, often leading to redundant data transmission and wasted computational resources, especially in resource-constrained complex systems. In contrast, event-triggered control only initiates data transmission and control updates when preset trigger conditions are met. This reduces unnecessary communication and computational load while ensuring system control performance, lowering hardware resource requirements and providing a better option for real-time control of complex dynamic systems.

[0005] Against this backdrop, based on the above analysis, it is essential to study robust tracking control methods for data-driven LPV systems under event-triggered strategies. Summary of the Invention

[0006] The purpose of this invention is to provide a robust tracking control method for data-driven LPV systems based on event triggering, which can solve the problem that LPV systems are difficult to effectively implement robust tracking control due to unknown system equations, external disturbances, and limited communication resources.

[0007] The objective of this invention is achieved through the following technical solution:

[0008] A robust tracking control method for an event-triggered, data-driven LPV system, comprising the following steps:

[0009] Step 1: By introducing an integral compensator, the perturbation LPV system is extended to an augmented perturbation LPV system for output reference tracking scenarios;

[0010] Step 2: Based on LPV system - Under continuous excitation conditions, data on the state variables, system input variables, external disturbance variables, and scheduling variables of the unknown augmented perturbation LPV open-loop system are collected by the built-in sensors of the control system to establish a data-based closed-loop representation of the LPV system;

[0011] Step 3: Based on the closed-loop data representation of the unknown augmented perturbation LPV system, design a data-based controller to ensure the closed-loop stability of the output tracking system;

[0012] Step 4: Based on the full block S-process, the infinite constraints in the semidefinite programming of control gain calculation are transformed into finite constraints calculated on the vertices of the polyhedron, ensuring the feasibility of controller implementation;

[0013] Step 5: Design an event triggering strategy, and design a controller based on the strategy to ensure the closed-loop stability of the augmented perturbation LPV system;

[0014] Step Six: Robust tracking control applied to augmented perturbation LPV systems;

[0015] In step one, the state-space equation of the perturbation LPV system, which the scheduling parameters depend on, is:

[0016]

[0017] (1)

[0018] in, The sampling interval is... , , , , These represent system state, control input, reference output, scheduling signal, and external disturbance, respectively. Mapping , , , Affine-dependent Specifically, it is expressed as:

[0019]

[0020]

[0021] Among them, for ,matrix , , , All have appropriate dimensions and superscripts. Indicates scheduling signal The Elements. An augmented vector is defined by introducing an integral compensator. ,satisfy:

[0022] ,in Represents the reference signal. Define augmented state variables. , Combining equation (1), we obtain the augmented perturbation LPV system:

[0023] (2)

[0024] in , , , . , and , They have the same structure and are all affine dependent on Therefore, formula (2) can be reformulated as:

[0025] (3)

[0026] in , .

[0027] In step two, data on the state variables, system input variables, external disturbance variables, and scheduling variables of the unknown augmented perturbation LPV open-loop system are collected:

[0028]

[0029] (4)

[0030]

[0031] Therefore, the augmented LPV system (3) can be characterized by data as follows:

[0032]

[0033] The LPV system - The continuous excitation condition is: assuming the LPV system (3) is controllable and the disturbance is Satisfying Assumption 1, the control input sequence The order is of -Continuous incentives, i.e. It must be true and satisfy the following conditions. Based on this, we can obtain ,in , .

[0034] Assumption 1: For external disturbances When there is Its satisfaction It can also be expressed as ,in .

[0035] When the collected data (4) meets the requirements of the LPV system - Given continuous excitation conditions, the above data can be considered to contain the key dynamics of the augmented LPV system and can be used for synthetic controllers. Therefore, a control law is introduced. ,in and They have the same structure and affine depend on . use Representing the matrix of an unknown system , ,in ,Will Substituting into formula (2), the data-based closed-loop representation of the reference tracking LPV system can be obtained as follows:

[0036] (5)

[0037] in satisfy:

[0038]

[0039] in, The above results lay a solid foundation for designing a data-driven controller for a stable reference tracking LPV system.

[0040] In step three, the controller design process based on the collected data synthesis is as follows:

[0041] For the data matrix shown in Equation (4), to design a controller to ensure that the closed-loop LPV system shown in Equation (5) has exponential input-state stability, the following operations are required: Assuming there exists a matrix scalar , as well as Under known external disturbance boundaries When, the following matrix inequality condition holds:

[0042]

[0043] in When the above conditions are met, the closed-loop LPV system as shown in formula (5) under the action of the designed controller can achieve exponential input-state stability. This is the core criterion for controller design and stability verification, which is used to ensure that the controller enables the system to achieve the expected stability performance.

[0044] In step four, the operation of transforming the infinite constraints in the semidefinite programming of control gain calculation into finite constraints calculated on the vertices of the polyhedron is as follows:

[0045] When designing the controller in step three, For scheduling signals The quadratic dependency relationship presents a significant challenge to the design process. Semidefinite programming solvers are typically suited for linear problems or problems that can be transformed into linear constraints through convex relaxation. However, quadratic dependency results in an infinite number of constraints in semidefinite programming, making convex optimization extremely difficult and becoming a fundamental obstacle to the controller design process.

[0046] To overcome this obstacle, a polyhedral framework is used to model the parameter space. The polyhedron is characterized as a geometric set composed of vertices. A convex relaxation strategy is defined based on the vertices of the polyhedron using a full-block S-process. Specifically, this is achieved by constructing two key matrices. , ,Will Rephrased as:

[0047]

[0048] Then, for the data matrix as shown in formula (4), assume that there exists a matrix , , , , , It meets the following conditions:

[0049] Condition 1:

[0050] Condition 2:

[0051] Condition 3:

[0052] Condition 4:

[0053] Condition 5:

[0054] in,

[0055] (6)

[0056]

[0057] In the above formula (6) , , , , .

[0058] Therefore, the state feedback controller can be obtained. This controller ensures the exponential input-state stability of the closed-loop system (5). The calculated controller gain is: Step four transforms the infinite constraints in the semidefinite programming problem of control gain calculation into finite constraints calculated at the vertices of the polyhedron. Specifically, in condition 3, the solution is performed at each vertex of the polygon.

[0059]

[0060] in, It is a set of scheduling signals The vertices of the polygon.

[0061] In step five, an event-triggered communication transmission scheme is deployed, and a controller is designed to ensure the closed-loop stability of the LPV system. The design process is as follows:

[0062] The event-triggered control input is: ,in This is represented as the transmission time. Substituting this control input into formula (2), we obtain the closed-loop LPV system under the event-triggered strategy as follows:

[0063] (7)

[0064] in, Represented as:

[0065]

[0066] make This describes the error between the most recently transmitted system state and the currently sampled system state. Therefore, an event-triggered LPV system characterized by data can be re-represented as:

[0067]

[0068] The event triggering strategy is designed as follows:

[0069]

[0070] in It is any variable. and It is a positive definite matrix. The following section designs a controller to ensure the closed-loop stability of the system based on an event-triggered strategy.

[0071] Based on the event-triggered LPV system (7) and the data matrix set (4), after all the aforementioned steps have been completed, if it is possible to find as well as If the matrix inequality condition 1 is satisfied, then a state feedback controller can be designed to ensure that the system (7) achieves practical exponential input-state stability.

[0072] Condition 1:

[0073] in, , , ,

[0074] , ,

[0075] In the above formula And matrix The solution has already been obtained in step four. Similar to step four, since... For scheduling signals The quadratic dependency relationship leads to an infinite number of constraints in the semidefinite programming problem, making convex optimization extremely difficult. Therefore, a polyhedral framework is used to address the parameter space. The polyhedron is characterized as a geometric set consisting of several vertices. A convex relaxation strategy is defined based on the vertices of the polyhedron using a full-block S-process. Specifically, based on the data matrix set (4), it is assumed that there exists... , as well as This allows conditions 1, 2, and 3 to be met. The feasible solution provides a data-based event triggering scheme and a feedback controller. This enables event-triggered LPV systems to have practical exponential input-state stability.

[0076] Condition 1:

[0077] Condition 2:

[0078] Condition 3:

[0079] in,

[0080] (8)

[0081] In the above formula (8), , ,

[0082] , , ,

[0083] In step six, the event-triggered LPV system data-driven robust tracking controller obtained in the above steps is applied to the circular trajectory tracking of the augmented perturbation LPV system, proving the feasibility of the controller.

[0084] The beneficial effects of this invention are as follows:

[0085] To address the challenges of unknown system equations, external disturbances, and limited communication resources in LPV systems, this invention introduces an integral compensator to construct an augmented perturbation LPV system and designs the controller directly from the data using a data-driven approach. Existing methods primarily model LPV systems through system identification; in contrast, the method described in this invention eliminates the need for explicit system model identification, significantly reducing the computational burden of modeling and control. Furthermore, by utilizing a total S-process to transform infinite constraints into finite constraints, the feasibility of the controller design is ensured, effectively achieving robust tracking control of the LPV system.

[0086] Furthermore, in terms of communication efficiency, existing methods transmit control signals at every moment, which places high demands on the real-time performance of the computing platform. This invention incorporates an event-triggered control strategy, which transmits data and updates control only when preset conditions are met. While ensuring the closed-loop stability and tracking performance of the system, it significantly reduces redundant data transmission and waste of computing resources, and lowers the demand for hardware resources. It is especially suitable for complex scenarios with limited resources, and provides an efficient and practical solution for real-time robust tracking control of complex LPV systems such as variable-wing aircraft and flexible robotic arms. Attached Figure Description

[0087] The present invention will now be described in further detail with reference to the accompanying drawings and specific implementation methods.

[0088] Figure 1This is a schematic diagram of the event-triggered data-driven robust tracking control method for LPV systems according to the present invention;

[0089] Figure 2 This is a robust tracking response diagram (0-10s) of the LPV system of the present invention for tracking a circular trajectory.

[0090] Figure 3 This is a robust tracking response diagram (10-20s) of the LPV system of the present invention for tracking a circular trajectory.

[0091] Figure 4 This is a robust tracking response diagram (20-30s) of the LPV system of the present invention for tracking a circular trajectory.

[0092] Figure 5 This is a timeline of event triggering for the LPV system of this invention to track a circular trajectory. Detailed Implementation

[0093] The present invention will now be described in further detail with reference to the accompanying drawings.

[0094] like Figures 1 to 5 As shown, in order to solve the technical problem that "LPV systems are difficult to effectively implement robust tracking control due to unknown system equations, external disturbances, and limited communication resources", the steps and functions of a data-driven robust tracking control method for LPV systems based on event triggering are described in detail below.

[0095] A robust tracking control method for an event-triggered, data-driven LPV system, comprising the following steps:

[0096] Step 1: By introducing an integral compensator, the perturbation LPV system is extended to an augmented perturbation LPV system for output reference tracking scenarios;

[0097] The state-space equations of the perturbation LPV system, which depend on scheduling parameters, are as follows:

[0098]

[0099] (1)

[0100] in, The sampling interval is... , , , , These represent system state, control input, reference output, scheduling signal, and external disturbance, respectively. Mapping , , , Affine-dependent Specifically, it is expressed as:

[0101]

[0102]

[0103] Among them, for ,matrix , , , All have appropriate dimensions and superscripts. Indicates scheduling signal The Elements. An augmented vector is defined by introducing an integral compensator. ,satisfy:

[0104] ,in Represents the reference signal. Define augmented state variables. , Combining equation (1), we obtain the augmented perturbation LPV system:

[0105] (2)

[0106] in , , , . , and , They have the same structure and are all affine dependent. Therefore, formula (2) can be reformulated as:

[0107] (3)

[0108] in , .

[0109] Step 2: Based on LPV system - Under continuous excitation conditions, collect data on the state variables, system input variables, external disturbance variables, and scheduling variables of the unknown augmented perturbation LPV open-loop system, and establish a data-based closed-loop representation of the LPV system.

[0110] Data collection is performed on the state variables, system input variables, external disturbance variables, and scheduling variables of the unknown augmented perturbation LPV open-loop system:

[0111]

[0112] (4)

[0113]

[0114] Therefore, the augmented LPV system (3) can be characterized by data as follows:

[0115]

[0116] The LPV system - The continuous excitation condition is: assuming the LPV system (3) is controllable and the disturbance is Satisfying Assumption 1, the control input sequence Is the order of of -Continuous incentives, i.e. It must be true and satisfy the following conditions. Based on this, we can obtain ,in , .

[0117] Assumption 1: For external disturbances When there is Its satisfaction It can also be expressed as ,in .

[0118] When the collected data (4) meets the requirements of the LPV system - Given continuous excitation conditions, the above data can be considered to contain the key dynamics of the augmented LPV system and can be used for synthetic controllers. Therefore, a control law is introduced. ,in and They have the same structure and affine depend on . use Representing the matrix of an unknown system , ,in ,Will Substituting into formula (2), the data-based closed-loop representation of the reference tracking LPV system can be obtained as follows:

[0119] (5)

[0120] in satisfy:

[0121]

[0122] in, The above results lay a solid foundation for designing a data-driven controller for a stable reference tracking LPV system.

[0123] Step 3: Based on the closed-loop data representation of the unknown augmented perturbation LPV system, design a data-based controller to ensure the closed-loop stability of the output tracking system;

[0124] The controller design process based on the collected data synthesis is as follows:

[0125] For the data matrix shown in Equation (4), to design a controller to ensure that the closed-loop LPV system shown in Equation (5) has exponential input-state stability, the following operations are required: Assuming there exists a matrix scalar , as well as Under known external disturbance boundaries When, the following matrix inequality condition holds:

[0126]

[0127] in When the above conditions are met, the closed-loop LPV system as shown in formula (5) under the action of the designed controller can achieve exponential input-state stability. This is the core criterion for controller design and stability verification, and is used to ensure that the controller enables the system to achieve the expected stability performance.

[0128] Step 4: Based on the full block S-process, the infinite constraints in the semidefinite programming of control gain calculation are transformed into finite constraints calculated on the vertices of the polyhedron, ensuring the feasibility of controller implementation;

[0129] The operation to transform the infinite constraints in the semidefinite programming problem of control gain calculation into finite constraints calculated on the vertices of the polyhedron is as follows:

[0130] When designing the controller in step three, For scheduling signals The quadratic dependency relationship presents a significant challenge to the design process. Semidefinite programming solvers are typically suited for linear problems or problems that can be transformed into linear constraints through convex relaxation. However, quadratic dependency results in an infinite number of constraints in semidefinite programming, making convex optimization extremely difficult and becoming a fundamental obstacle to the controller design process.

[0131] To overcome this obstacle, a polyhedral framework is used to model the parameter space. The polyhedron is characterized as a geometric set composed of vertices. A convex relaxation strategy is defined based on the vertices of the polyhedron using a full-block S-process. Specifically, this is achieved by constructing two key matrices. , ,Will Rephrased as:

[0132]

[0133] Then, for the data matrix as shown in formula (4), assume that there exists a matrix , , , , , It meets the following conditions:

[0134] Condition 1:

[0135] Condition 2:

[0136] Condition 3:

[0137] Condition 4:

[0138] Condition 5:

[0139] in,

[0140] (6)

[0141]

[0142] In the above formula (6) , , , , .

[0143] Therefore, the state feedback controller can be obtained. This controller ensures the exponential input-state stability of the closed-loop system (5). The calculated controller gain is: Step four transforms the infinite constraints in the semidefinite programming problem of control gain calculation into finite constraints calculated at the vertices of the polyhedron. Specifically, in condition 3, the solution is performed at each vertex of the polygon.

[0144]

[0145] in, It is a set of scheduling signals The vertices of the polygon.

[0146] Step 5: Design an event triggering strategy, and design a controller based on the strategy to ensure the closed-loop stability of the augmented perturbation LPV system;

[0147] Deploy an event-triggered communication transmission scheme and design a controller to ensure the closed-loop stability of the LPV system. The design process is as follows:

[0148] The event-triggered control input is: ,in This is represented as the transmission time. Substituting this control input into formula (2), we obtain the closed-loop LPV system under the event-triggered strategy as follows:

[0149] (7)

[0150] in, Represented as:

[0151]

[0152] make This describes the error between the most recently transmitted system state and the currently sampled system state. Therefore, an event-triggered LPV system characterized by data can be re-represented as:

[0153]

[0154] The event triggering strategy is designed as follows:

[0155]

[0156] in It is any variable. and It is a positive definite matrix. The following section designs a controller to ensure the closed-loop stability of the system based on an event-triggered strategy.

[0157] Based on the event-triggered LPV system (7) and the data matrix set (4), after all the aforementioned steps have been completed, if it is possible to find as well as If the matrix inequality condition 1 is satisfied, then a state feedback controller can be designed to ensure that the system (7) achieves practical exponential input-state stability.

[0158] Condition 1:

[0159] in, , , ,

[0160] , ,

[0161] In the above formula And matrix The solution has already been obtained in step four. Similar to step four, since... For scheduling signals The quadratic dependency relationship leads to an infinite number of constraints in the semidefinite programming problem, making convex optimization extremely difficult. Therefore, a polyhedral framework is used to address the parameter space. The polyhedron is characterized as a geometric set consisting of several vertices. A convex relaxation strategy is defined based on the vertices of the polyhedron using a full-block S-process. Specifically, based on the data matrix set (4), it is assumed that there exists... , as well as This allows conditions 1, 2, and 3 to be met. The feasible solution provides a data-based event triggering scheme and a feedback controller. This enables event-triggered LPV systems to have practical exponential input-state stability.

[0162] Condition 1:

[0163] Condition 2:

[0164] Condition 3:

[0165] in,

[0166] (8)

[0167] In the above formula (8), , ,

[0168] , , ,

[0169] Step 6: Robust tracking control applied to augmented perturbation LPV systems.

[0170] The robust tracking controller for an event-triggered data-driven LPV system, obtained from the above steps, was applied to circular trajectory tracking in an augmented perturbation LPV system, demonstrating the feasibility of the controller.

[0171] like Figures 2 to 5 As shown, to verify and demonstrate the efficiency of the event-triggered data-driven robust tracking method for LPV systems, experiments were conducted on a MATLAB simulation platform, and the semidefinite programming problem was solved using the YALMIP toolkit and the Mosek solver. The distance step length was set. Consider the augmented linear parameter variation system (3), whose corresponding dimension is , ,and At this point, the system parameters are specified as follows:

[0172]

[0173] Furthermore, the scheduling signal set is represented as During step 2, the data acquisition length Must meet In practice, the setting , making To meet the needs of LPV systems - Continuous incentive conditions. Selection. , , This is used to solve semidefinite programming problems in controller design. Using the YALMIP toolkit and the Mosek solver, the solution is obtained as follows:

[0174]

[0175] To eliminate the problem during the solution process Numerical problems arising from inversion can be addressed by adding constraints. .definition , , Time-triggered logic parameters Based on the solution obtained and Event triggering gain can be obtained:

[0176]

[0177] The simulation experiment time is set to 0-30s, and the external disturbance is... satisfy , =2.51. The design reference trajectory is a circle with a radius of 2.5, and its trajectory tracking diagram is as follows. Figures 2 to 4 As shown in the figure, the robust tracking control method for the data-driven LPV system based on event triggering can effectively track circular trajectories. The event trigger timing diagram is shown below. Figure 5 As shown, this method effectively reduces the communication burden.

Claims

1. A robust tracking control method for a data-driven LPV system based on event triggering, characterized in that: The method includes the following steps: Step 1: By introducing an integral compensator, the perturbation LPV system is extended to an augmented perturbation LPV system for output reference tracking scenarios; Step 2: Based on LPV system - Under continuous excitation conditions, data on the state variables, system input variables, external disturbance variables, and scheduling variables of the unknown augmented perturbation LPV open-loop system are collected by the built-in sensors of the control system to establish a data-based closed-loop representation of the LPV system; Step 3: Based on the closed-loop data representation of the unknown augmented perturbation LPV system, design a data-based controller to ensure the closed-loop stability of the output tracking system; Step 4: Based on the full block S-process, the infinite constraints in the semidefinite programming of control gain calculation are transformed into finite constraints calculated on the vertices of the polyhedron, ensuring the feasibility of controller implementation; Step 5: Design an event triggering strategy, and design a controller based on the strategy to ensure the closed-loop stability of the augmented perturbation LPV system; Step 6: Robust tracking control applied to augmented perturbation LPV systems.

2. The robust tracking control method for a data-driven LPV system based on event triggering according to claim 1, characterized in that: In step one, the state-space equation of the perturbation LPV system, which the scheduling parameters depend on, is: (1) in, The sampling interval is... , , , , These represent system state, control input, reference output, scheduling signal, and external disturbance, respectively; mapping , , , Affine-dependent Specifically, it is expressed as: Among them, for ,matrix , , , All have appropriate dimensions and superscripts. Indicates scheduling signal The Each element.

3. The robust tracking control method for a data-driven LPV system based on event triggering according to claim 2, characterized in that: By introducing an integral compensator, an augmented vector is defined. ,satisfy: ,in Represent the reference signal; define the augmented state variables. , Combining equation (1), we obtain the augmented perturbation LPV system: (2) in , , , ; , and , They have the same structure and are all affine dependent. Therefore, formula (2) can be reformulated as: (3) in , .

4. The robust tracking control method for a data-driven LPV system based on event triggering according to claim 3, characterized in that: In step two, data on the state variables, system input variables, external disturbance variables, and scheduling variables of the unknown augmented perturbation LPV open-loop system are collected: (4) Therefore, the augmented LPV system (3) can be characterized by data as follows: 。 5. A robust tracking control method for a data-driven LPV system based on event triggering according to claim 4, characterized in that: The LPV system - The continuous excitation condition is: assuming the LPV system (3) is controllable and the disturbance is Satisfying Assumption 1, the control input sequence Is the order of of -Continuous incentives, i.e. It must be true and satisfy the following conditions. Based on this, we can obtain ,in , ; Assumption 1: For external disturbances When there is Its satisfaction It can also be expressed as ,in ; When the collected data (4) meets the requirements of the LPV system - Given continuous excitation conditions, the above data can be considered to contain the key dynamics of the augmented LPV system and can be used for the synthetic controller; therefore, a control law is introduced. ,in and They have the same structure and affine depend on ; use Representing the matrix of an unknown system , ,in ,Will Substituting into formula (2), the data-based closed-loop representation of the reference tracking LPV system can be obtained as follows: (5) in satisfy: in, The above results lay a solid foundation for designing a data-driven controller for a stable reference tracking LPV system.

6. A robust tracking control method for a data-driven LPV system based on event triggering, as described in claim 5, characterized in that: In step three, the controller design process based on the collected data synthesis is as follows: For the data matrix shown in Equation (4), to design a controller to ensure that the closed-loop LPV system shown in Equation (5) has exponential input-state stability, the following operations are required: Assuming there exists a matrix scalar , as well as Under known external disturbance boundaries When, the following matrix inequality condition holds: in When the above conditions are met, the closed-loop LPV system as shown in formula (5) under the action of the designed controller can achieve exponential input-state stability. This is the core judgment basis for controller design and stability verification, which is used to ensure that the controller enables the system to achieve the expected stability performance.

7. A robust tracking control method for a data-driven LPV system based on event triggering, as described in claim 6, characterized in that: In step four, the operation of transforming the infinite constraints in the semidefinite programming of control gain calculation into finite constraints calculated on the vertices of the polyhedron is as follows: When designing the controller in step three, For scheduling signals The quadratic dependency relationship presents a significant challenge to the design process. Semidefinite programming solvers are typically suited for dealing with linear problems or problems that can be transformed into linear constraints through convex relaxation. However, quadratic dependency leads to an infinite number of constraints in semidefinite programming, making convex optimization extremely difficult and becoming a fundamental obstacle to the controller design process. To overcome this obstacle, a polyhedral framework is used to model the parameter space. To depict it, we consider it as a geometric set composed of several vertices; Using a full-block S-process, a convex relaxation strategy is defined based on the vertices of a polyhedron; specifically, this is achieved by constructing two key matrices. , ,Will Rephrased as: Then, for the data matrix as shown in formula (4), assume that there exists a matrix , , , , , It meets the following conditions: Condition 1: Condition 2: Condition 3: Condition 4: Condition 5: in, (6) In the above formula (6) , , , , ; Therefore, the state feedback controller can be obtained. The controller ensures the exponential input-state stability of the closed-loop system (5); whereby the controller gain obtained by solving is: Step four transforms the infinite constraints in the semidefinite programming problem of control gain calculation into finite constraints calculated at the vertices of the polyhedron. Specifically, in condition 3, the solution is performed at each vertex of the polygon. in, It is a set of scheduling signals The vertices of the polygon.

8. A robust tracking control method for a data-driven LPV system based on event triggering, as described in claim 7, characterized in that: In step five, an event-triggered communication transmission scheme is deployed, and a controller is designed to ensure the closed-loop stability of the LPV system. The design process is as follows: The event-triggered control input is: ,in The transmission time is expressed as: Substituting this control input into formula (2), we can obtain the closed-loop LPV system under the event-triggered strategy as follows: (7) in, Represented as: make This describes the error between the most recently transmitted system state and the currently sampled system state; therefore, an event-triggered LPV system characterized by data can be re-represented as: The event triggering strategy is designed as follows: in It is any variable. and It is a positive definite matrix; the following design is based on an event-triggered strategy to ensure the closed-loop stability of the system.

9. A robust tracking control method for a data-driven LPV system based on event triggering, as described in claim 8, characterized in that: Based on the event-triggered LPV system (7) and the data matrix set (4), after all the aforementioned steps have been completed, if it is possible to find as well as If the matrix inequality condition 1 is satisfied, then a state feedback controller can be designed to ensure that the system (7) achieves practical exponential input-state stability. Condition 1: , in, , , , ， ， In the above formula And matrix The solution has already been obtained in step four; similar to step four, since For scheduling signals The quadratic dependency relationship leads to an infinite number of constraints in the semidefinite programming problem, making convex optimization extremely difficult. Therefore, a polyhedral framework is used to address the parameter space. The polyhedron is characterized as a geometric set consisting of several vertices; a convex relaxation strategy is defined based on the vertices of the polyhedron using the full block S-process; specifically, based on the data matrix set (4), it is assumed that there exists , as well as This allows conditions 1, 2, and 3 to be met. The feasible solution provides a data-based event triggering scheme and a feedback controller. This enables event-triggered LPV systems to possess practical exponential input-state stability; Condition 1: Condition 2: Condition 3: in, (8) In the above formula (8), , , ， ， 。 10. A robust tracking control method for a data-driven LPV system based on event triggering, as described in claim 9, characterized in that: In step six, the event-triggered LPV system data-driven robust tracking controller obtained in the above steps is applied to the circular trajectory tracking of the augmented perturbation LPV system, proving the feasibility of the controller.

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