A method and system for online data-driven event-triggered control of nonlinear unmanned systems under polytopic noise

Abstract

The application discloses a kind of polyhedral noise under nonlinear unmanned system online data-driven event trigger control method and system, method includes: for unknown nonlinear function dynamic discrete time nonlinear system equation, discrete time nonlinear system equation is changed into linear time-varying system equation;For unknown bounded noise in measurement data, construct noise polyhedron set, construct data-driven system set in combination with linear time-varying system equation;Dynamic event trigger transmission strategy of data-driven is constructed;Stability criterion and new trigger condition are established, optimization problem is constructed and is solved, new event trigger transmission mechanism weight matrix and state feedback controller gain matrix are obtained, in combination with stability criterion, state feedback controller gain matrix, new event trigger transmission mechanism weight matrix is controlled to nonlinear unmanned system.This application can make nonlinear unmanned system meet performance index and reach the goal of minimizing feedback controller transmission frequency.

Description

Technical Field

[0001] This invention relates to the field of automatic control technology for nonlinear unmanned systems, and in particular to an online data-driven event-triggered control method and system for nonlinear unmanned systems under polyhedral noise. Background Technology

[0002] Against the backdrop of current technological development and industrial upgrading, unmanned systems, as intelligent equipment capable of operating autonomously without direct human control or requiring only minimal human intervention, are increasingly becoming a key force driving transformation in various fields such as industry, agriculture, and scientific research. They demonstrate enormous potential in improving operational efficiency, reducing labor costs, and coping with high-risk environments.

[0003] The dynamics of unmanned systems generally exhibit strong nonlinearity, leading to complex phenomena such as limit cycles, chaotic states, and multiple equilibrium points during their motion and control processes. This presents significant challenges for system modeling and controller design. Traditional mechanism-based modeling methods often have limitations when dealing with strong nonlinearity, parameter uncertainties, and unmodeled dynamics, making it difficult to meet the requirements of high-precision control. Therefore, researchers are increasingly turning to data-driven control strategies, extracting system dynamic characteristics from actual operational data and constructing effective control laws to overcome the shortcomings of traditional methods and enhance the adaptability and robustness of unmanned systems in unknown or dynamic environments.

[0004] Traditional nonlinear unmanned systems typically exhibit complex and unpredictable behavior, but their dynamics are state-dependent. State-dependent modeling methods can transform their nonlinear models into equivalent linear time-varying models, laying the foundation for system design and stability analysis. However, establishing precise nonlinear mathematical models for nonlinear unmanned systems is difficult. Model-based control schemes often require mechanistic modeling or system identification, and inaccurate modeling can lead to poor control performance. In contrast, data-driven control does not rely on precise mathematical models but designs controllers directly based on measurement data, avoiding the step of establishing mathematical models. For nonlinear unmanned systems, data-driven control methods based on Willems' fundamental lemma can effectively solve the above problems, starting directly from system behavior data and completing controller design through data satisfying the rank condition.

[0005] Online real-time control demands high response speeds, but with limited wireless communication bandwidth, frequent transmissions and calculations can become a heavy burden. To balance these two aspects, event-triggered control methods dynamically determine when to perform data sampling and control updates, reducing computational burden and sensor data sampling frequency, decreasing energy consumption, and improving the system's dynamic adaptability and stability.

[0006] Although data-driven control methods have made some progress in the analysis and control of unknown nonlinear unmanned systems, such as trajectory tracking and cooperative control, systematic research is still lacking, especially under conditions of noise interference and limited communication resources. Therefore, how to achieve data-driven event-triggered control of nonlinear systems under unknown model conditions has become a pressing technical challenge in this field. Summary of the Invention

[0007] This invention provides an online data-driven event-triggered control method and system for nonlinear unmanned systems under polyhedral noise, in order to solve the technical problems in the prior art.

[0008] To achieve the above objectives, the technical solution of the present invention is implemented as follows:

[0009] This invention provides an online data-driven event-triggered control method for a nonlinear unmanned system under polyhedral noise, comprising the following steps:

[0010] S1. For the discrete-time nonlinear system equations with unknown nonlinear function dynamics, the known nonlinear basis functions are used to transform the discrete-time nonlinear system equations into a linear time-varying system equation.

[0011] S2. For unknown bounded noise in the measurement data, construct a set of noise polyhedra, and then construct a set of data-driven systems based on polyhedral perturbations based on the set of noise polyhedra and the linear time-varying system equations; then construct a description matrix based on the set of data-driven systems.

[0012] S3. Construct a data-driven dynamic event-triggered transmission strategy and determine the data transmission time based on the dynamic event-triggered transmission strategy;

[0013] S4. Establish a data-driven stability criterion, optimize the dynamic event-triggered transmission strategy to obtain new triggering conditions, construct an optimization problem, solve the optimization problem, and obtain the online-updated weight matrix of the new event-triggered transmission mechanism and the online-updated gain matrix of the state feedback controller. Combine the stability criterion, the online-updated gain matrix of the state feedback controller, and the online-updated weight matrix of the new event-triggered transmission mechanism to control the nonlinear unmanned system so that the nonlinear unmanned system satisfies... The performance metrics and the goal of minimizing the feedback controller transmission frequency are achieved.

[0014] Furthermore, the discrete-time nonlinear system equations in S1 are as follows:

[0015] ;

[0016] in, Indicates the first A signal given at each time step; Represents a nonlinear function with two unknown dynamics; Represents the set of real numbers; represent 3D real matrix; n and m These represent the number of rows and columns, respectively. Indicates control input; Represents unknown bounded noise; Indicates the first t Each time step Represents a non-negative integer;

[0017] The expression for the state feedback controller is as follows:

[0018] ;

[0019] in, Represents the controller gain matrix; Indicates the first One time step; Indicates the first A signal given at each time step.

[0020] Furthermore, the linear time-varying system equations in S1 are as follows:

[0021] ;

[0022] in, , They are two unknown matrices; and These are two known nonlinear basis functions; and satisfy... and .

[0023] Furthermore, step S2 specifically includes the following steps:

[0024] S21. Unknown bounded noise in the measurement data satisfy Under the assumptions, construct a set of noisy polyhedra. Among them, the upper limit of noise noise vector ; Represents the infinite norm; set The specific expression is as follows:

[0025] ;

[0026] In the formula, and Representing sets The number of vertices and the first Vertex vectors; Indicates the first Convex combination coefficients, It is the vertex index;

[0027] S22. Construct a data-driven system set for a polyhedral nonlinear unmanned system by utilizing offline measured state and system input.

[0028] S23, in discrete time steps Inside, a nonlinear unmanned system offline collects system state, system input, and noise interference; and constructs a data matrix based on the system state, system input, and noise interference. ;in, Indicates the first Each time step The matrix represents the set of system states; This indicates the use of nonlinear basis functions. The transformed state matrix; This indicates that the system input passes through a nonlinear basis function. Modulated input matrix; Represents the noise set matrix;

[0029] S24, combine the data matrix and the set of noise polyhedra in S21. By combining linear time-varying system equations, a system set that matches the collected dataset is constructed. ;

[0030] S25. Using the data matrix, and based on the linear time-varying system equations and system set... Construct data equations;

[0031] S26. Then, based on the data equations and the data-driven system set of polyhedral nonlinear unmanned systems, a data-driven system set based on polyhedral perturbation is constructed. Then, a description matrix is ​​constructed based on the data-driven system set based on polyhedral perturbation. .

[0032] Furthermore, the set of noise polyhedra in S21 The specific expression is as follows:

[0033] ;

[0034] In the formula, Indicates the first l The vertices of the basis noise matrix; Indicates the first l Convex combination coefficients of a noise matrix Represents the noise matrix;

[0035] The system set in S24 The specific expression is as follows:

[0036] ;

[0037] The specific expression of the data equation in S25 is as follows:

[0038] ;

[0039] The specific data-driven system set based on polyhedral perturbation in S26 is as follows:

[0040] ;

[0041] Wherein, the description matrix satisfy And matrix Complete the order and simultaneously satisfy , Indicates any, Represents the identity matrix; T This indicates transpose.

[0042] Furthermore, step S3 specifically includes the following steps:

[0043] S31. To dynamically adjust the trigger threshold, a dynamic variable is introduced. and dynamic variables The update law, where dynamic variables The update law is as follows:

[0044] ;

[0045] in, This indicates a dynamic variable controlled by a difference equation; Represents a scalar; This indicates a dynamically triggered function, and the dynamically triggered function... The formula for calculation is:

[0046] ;

[0047] in, as well as This indicates that two steps need to be taken at time step. t The design of the event-triggered transmission mechanism weight matrix; and 0, 0, symbol Indicates positive determination; Represents the state vector acquired by the sensor With the latest transmission status The cumulative deviation between them, and In the formula, Indicates the first k A signal given at each time step; k Indicates the first k Each time step Represents the 2-norm;

[0048] S32, Combining dynamic variables and proportional parameters The data-driven dynamic event-triggered transmission strategy is obtained, and the data transmission time is determined based on the dynamic event-triggered transmission strategy.

[0049] Furthermore, the data-driven dynamic event-triggered transmission strategy in S3 is as follows:

[0050] ;

[0051] in, Indicates the first One time step; This indicates an event-triggered system.

[0052] Furthermore, step S4 specifically includes the following steps:

[0053] S41, Based on non-singular matrices Define state vector And define unknown bounded noise ;

[0054] in, Represents the transformed state variable. Indicates the changed disturbance;

[0055] S42, via state vector and unknown bounded noise Control input exist Performing an algebraic transformation within the interval yields the transformed nonlinear unmanned system; where, Represents non-integer AND The intersection;

[0056] S43, for the transformed nonlinear unmanned system in S42 and the data-driven dynamic event-triggered transmission strategy, and based on dynamic variables The update law is chosen to be a Lyapunov function for stability analysis to verify the stability of the transformed nonlinear unmanned system.

[0057] S44. Combining the system state and the data equations in S25, the forward difference is derived. The expression;

[0058] S45. Under the condition that the initial conditions are zero, i.e. , Indicates the initial time step. This indicates that the Lyapunov function is at time step The state-related part, Indicates time step The dynamic variables, and satisfy Under the condition of forward difference Summing the expressions yields the summation result. Based on this summation result, a nonlinear unmanned system under perturbation conditions is constructed. Performance indicators, this Performance metrics serve as data-driven stability criteria; The performance indicators are robust control performance indicators; among them, This indicates that the Lyapunov function is at time step The state-related part; Indicates time step Dynamic variables;

[0059] S46. A new event-triggered transport mechanism weight matrix updated online in a given optimization problem. , and proportional parameters Furthermore, the weight matrix of the new event-triggered transmission mechanism is updated online in the optimization problem. , and proportional parameters Under the condition that all are positive definite and symmetric, and simultaneously satisfying Under the conditions, based on the original triggering conditions Construct new triggering conditions;

[0060] S47. The new triggering conditions indicate how to adjust parameters to reduce the transmission frequency of the feedback controller. Based on the new triggering conditions, an optimization problem is constructed. Solving the optimization problem yields the online-updated weight matrix of the new event-triggered transmission mechanism. , Combined with the online-updated state feedback controller gain matrix, the stability criterion, the online-updated state feedback controller gain matrix, and the online-updated new event-triggered transmission mechanism weight matrix. , Controlling a nonlinear unmanned system to minimize the transmission frequency of the feedback controller and achieve the desired performance of the nonlinear unmanned system. Performance metrics targets.

[0061] Furthermore, the transformed nonlinear unmanned system in S42 is specifically as follows:

[0062] ；

[0063] in, Let the linearization function represent the state dependency, and the linearization function... State-related expressions Export, This indicates the state change at the last trigger moment. Represents the transformed controller gain, and satisfies ;

[0064] The Lyapunov function in S43 is as follows:

[0065] ；

[0066] in, Represents the Lyapunov function. This indicates that the Lyapunov function is at time step t The state-related part, and ; Indicates time step t Time-varying location;

[0067] The forward difference in S44 The specific expression is as follows:

[0068] ;

[0069] in, express The level of performance degradation, and >0, express ; Represents a composite matrix inequality;

[0070] In S45 The specific expressions for the performance metrics are as follows:

[0071] ;

[0072] in, , These represent the minimum and maximum eigenvalues, respectively.

[0073] The expression for the new triggering condition in S46 is as follows:

[0074] ;

[0075] in, Represents state error; dynamic variable and dynamic variables The following relationship must be satisfied:

[0076] ;

[0077] The optimization problem in S47 is expressed as a linear matrix inequality, as follows:

[0078] ;

[0079] ;

[0080] in, Indicates an adjustable parameter; Indicates trace, Represents a scalar. Represents the selection matrix, and subscript , The dimension is The zero matrix; The dimension is The zero matrix; symbol Indicates negative definiteness; This represents a data-driven dynamic constraint matrix, and ; This represents the stability-dynamic event-triggered transmission strategy matrix, and , Elements that represent symmetrical positions.

[0081] The online-updated state feedback controller gain matrix obtained in S47 is as follows:

[0082] ;

[0083] The weight matrix of the new online-updated event-triggered transmission mechanism obtained in S47 is as follows:

[0084] ;

[0085] .

[0086] In another aspect, the present invention provides an online data-driven event-triggered control system, including a nonlinear unmanned system, wherein the nonlinear unmanned system is configured to execute the above-described online data-driven event-triggered control method.

[0087] The beneficial effects of this invention are:

[0088] This invention proposes an online data-driven event-triggered control method for nonlinear unmanned systems under polyhedral noise. It does not rely on any system model information and has certain universality and scalability.

[0089] Furthermore, this invention uses only offline collected states and system inputs to determine the transmission time, avoiding continuous detection of the nonlinear unmanned system; at the same time, this invention effectively saves transmission resources while ensuring the asymptotic stability of the nonlinear unmanned system.

[0090] Furthermore, this invention proposes a data-driven system set based on polyhedral perturbation, which effectively solves the controller design problem when offline data is subjected to unknown bounded noise interference, and has good robustness. Attached Figure Description

[0091] Figure 1 This is a flowchart of an online data-driven event-triggered control method for a nonlinear unmanned system under polyhedral noise according to the present invention.

[0092] Figure 2 This is a schematic diagram illustrating the operating principle of the present invention;

[0093] Figure 3 This is a state response diagram of a nonlinear unmanned system in an embodiment of the present invention;

[0094] Figure 4 This is a timeline of transmission for a nonlinear unmanned system in an embodiment of the present invention. Detailed Implementation

[0095] To facilitate understanding of the present invention, a more complete description will be given below with reference to the accompanying drawings. Preferred embodiments of the invention are shown in the drawings. However, the invention can be implemented in many other different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided to provide a thorough and complete understanding of the disclosure of the invention.

[0096] Reference Figure 1 and Figure 2 An online data-driven event-triggered control method for a nonlinear unmanned system under polyhedral noise includes the following steps:

[0097] S1. For the discrete-time nonlinear system equations with unknown nonlinear function dynamics, the known nonlinear basis functions are used to transform the discrete-time nonlinear system equations into a linear time-varying system equation.

[0098] S2. For unknown bounded noise in the measurement data, construct a set of noise polyhedra, and then construct a set of data-driven systems based on polyhedral perturbations based on the set of noise polyhedra and the linear time-varying system equations; then construct a description matrix based on the set of data-driven systems.

[0099] S3. Construct a data-driven dynamic event-triggered transmission strategy and determine the data transmission time based on the dynamic event-triggered transmission strategy;

[0100] S4. Establish a data-driven stability criterion, optimize the dynamic event-triggered transmission strategy to obtain new triggering conditions, construct an optimization problem, solve the optimization problem, and obtain the online-updated weight matrix of the new event-triggered transmission mechanism and the online-updated gain matrix of the state feedback controller. Combine the stability criterion, the online-updated gain matrix of the state feedback controller, and the online-updated weight matrix of the new event-triggered transmission mechanism to control the nonlinear unmanned system so that the nonlinear unmanned system satisfies... The performance metrics and the goal of minimizing the feedback controller transmission frequency are achieved.

[0101] In some embodiments, the discrete-time nonlinear system equations in S1 are specifically as follows:

[0102] ;

[0103] in, Indicates the first A signal given at each time step; Represents a nonlinear function with two unknown dynamics; Represents the set of real numbers; represent 3D real matrix; n and m These represent the number of rows and columns, respectively. Indicates control input; Represents unknown bounded noise; Indicates the first t Each time step Represents a non-negative integer;

[0104] The expression for the state feedback controller is as follows:

[0105] ;

[0106] in, Represents the controller gain matrix; Indicates the first One time step; Indicates the first A signal given at each time step.

[0107] In some embodiments, the linear time-varying system equations in S1 are specifically as follows:

[0108] ;

[0109] in, , They are two unknown matrices; and These are two known nonlinear basis functions; and satisfy... and .

[0110] In some embodiments, S2 specifically includes the following steps:

[0111] S21. Unknown bounded noise in the measurement data satisfy Under the assumptions, construct a set of noisy polyhedra. Among them, the upper limit of noise noise vector ; Represents the infinite norm; set The specific expression is as follows:

[0112] ;

[0113] In the formula, and Representing sets The number of vertices and the first Vertex vectors; Indicates the first Convex combination coefficients, It is the vertex index;

[0114] S22. Construct a data-driven system set for a polyhedral nonlinear unmanned system by utilizing offline measured state and system input.

[0115] S23, in discrete time steps Inside, a nonlinear unmanned system offline collects system state, system input, and noise interference; and constructs a data matrix based on the system state, system input, and noise interference. ;in, Indicates the first Each time step The matrix represents the set of system states; This indicates the use of nonlinear basis functions. The transformed state matrix; This indicates that the system input passes through a nonlinear basis function. Modulated input matrix; Represents the noise set matrix; data The definition is:

[0116] ;

[0117] ；

[0118] ；

[0119] ;

[0120] in, Indicates at time step The measured system state, Indicates at time step The measured system input, Indicates at time step The noise measured in the system; Indicates at time step The measured state matrix;

[0121] S24, combine the data matrix and the set of noise polyhedra in S21. By combining linear time-varying system equations, a system set that matches the collected dataset is constructed. ;

[0122] S25. Using the data matrix, and based on the linear time-varying system equations and system set... Construct data equations;

[0123] S26. Then, based on the data equations and the data-driven system set of polyhedral nonlinear unmanned systems, a data-driven system set based on polyhedral perturbation is constructed. Then, a description matrix is ​​constructed based on the data-driven system set based on polyhedral perturbation. .

[0124] In some embodiments, the set of noise polyhedra in S21 The specific expression is as follows:

[0125] ;

[0126] In the formula, Indicates the first l The vertices of the basis noise matrix; Indicates the first l Convex combination coefficients of a noise matrix Represents the noise matrix; and the vertices The definition of is:

[0127] ;

[0128] ;

[0129] ;

[0130] in, Indicates the column position index of the matrix , Indicates the number of time steps , Represents non-negative integers and The intersection; These represent the first vertex, the middle vertex, and the last vertex, respectively. The dimension is The zero matrix; The dimension is The zero matrix; The dimension is The zero matrix;

[0131] The system set in S24 The specific expression is as follows:

[0132] ;

[0133] The specific expression of the data equation in S25 is as follows:

[0134] ;

[0135] The specific data-driven system set based on polyhedral perturbation in S26 is as follows:

[0136] ;

[0137] Wherein, the description matrix satisfy And matrix Complete the order and simultaneously satisfy , Indicates any; Represents the identity matrix; T This indicates transpose.

[0138] In some embodiments, S3 specifically includes the following steps:

[0139] S31. To dynamically adjust the trigger threshold, a dynamic variable is introduced. and dynamic variables The update law, where dynamic variables The update law is as follows:

[0140] ;

[0141] in, This indicates a dynamic variable controlled by a difference equation; Represents a scalar; This indicates a dynamically triggered function, and the dynamically triggered function... The formula for calculation is:

[0142] ;

[0143] in, as well as This indicates that two steps need to be taken at time step. t The design of the event-triggered transmission mechanism weight matrix; and 0, 0, symbol Indicates positive determination; Represents the state vector acquired by the sensor With the latest transmission status The cumulative deviation between them, and In the formula, Indicates the first A signal given at each time step; Indicates the first Each time step Represents the 2-norm;

[0144] S32, Combining dynamic variables and proportional parameters The data-driven dynamic event-triggered transmission strategy is obtained, and the data transmission time is determined based on the dynamic event-triggered transmission strategy.

[0145] In some embodiments, the data-driven dynamic event-triggered transmission strategy in S3 is specifically as follows:

[0146] ;

[0147] in, Indicates the first One time step; This indicates an event-triggered system.

[0148] In some embodiments, S4 specifically includes the following steps:

[0149] S41, Based on non-singular matrices Define state vector And define unknown bounded noise ;

[0150] in, Represents the transformed state variable. Indicates the changed disturbance;

[0151] S42, via state vector and unknown bounded noise Control input exist Performing an algebraic transformation within the interval yields the transformed nonlinear unmanned system; where, Represents non-integer AND The intersection;

[0152] S43, for the transformed nonlinear unmanned system in S42 and the data-driven dynamic event-triggered transmission strategy, and based on dynamic variables The update law is chosen to be a Lyapunov function for stability analysis to verify the stability of the optimized nonlinear unmanned system.

[0153] S44. Combining the system state and the data equations in S25, the forward difference is derived. The expression;

[0154] S45. Under the condition that the initial conditions are zero, i.e. , Indicates the initial time step. This indicates that the Lyapunov function is at time step The state-related part, Indicates time step The dynamic variables, and satisfy Under the condition of forward difference Summing the expressions yields the summation result. Based on this summation result, a nonlinear unmanned system under perturbation conditions is constructed. Performance indicators, this Performance metrics serve as data-driven stability criteria; The performance metric is a robust control performance metric; its objective is to withstand disturbances of all frequencies. Nonlinear unmanned systems require disturbances to affect the state error. The norm is constrained, thus ensuring that the worst-case gain from the disturbance energy to the error energy is bounded; where, This indicates that the Lyapunov function is at time step The state-related part; Indicates time step Dynamic variables;

[0155] S46. A new event-triggered transport mechanism weight matrix updated online in a given optimization problem. , and proportional parameters Furthermore, the weight matrix of the new event-triggered transmission mechanism is updated online in the optimization problem. , and proportional parameters Under the condition that all are positive definite and symmetric, and simultaneously satisfying Under the conditions, based on the original triggering conditions Construct new triggering conditions;

[0156] S47. The new triggering conditions indicate how to adjust parameters to reduce the transmission frequency of the feedback controller. Based on the new triggering conditions, an optimization problem is constructed. Solving the optimization problem yields the online-updated weight matrix of the new event-triggered transmission mechanism. , Combined with the online-updated state feedback controller gain matrix, the stability criterion, the online-updated state feedback controller gain matrix, and the online-updated new event-triggered transmission mechanism weight matrix. , Controlling a nonlinear unmanned system to minimize the transmission frequency of the feedback controller and achieve the desired performance of the nonlinear unmanned system. Performance metrics targets.

[0157] In some embodiments, the transformed nonlinear unmanned system in S42 is specifically as follows:

[0158] ;

[0159] in, Let the linearization function represent the state dependency, and the linearization function... State-related expressions Export, This indicates the state change at the last trigger moment. Represents the transformed controller gain, and satisfies ;

[0160] The Lyapunov function in S43 is as follows:

[0161] ;

[0162] in, Represents the Lyapunov function. This indicates that the Lyapunov function is at time step t The state-related part, and ; Indicates time step t Time-varying location;

[0163] The forward difference in S44 The specific expression is as follows:

[0164] ;

[0165] in, express The level of performance degradation, and >0, express ;when Due to disturbance It can be deduced that a positive scalar exists. Make forward difference ,for Represents non-negative integers and The intersection of the two. This condition is naturally satisfied when the disturbance is zero. Performance metrics, i.e., due to the matrix Non-singular properties, nonlinear unmanned systems for any All can gradually converge to the origin; Represents a composite matrix inequality;

[0166] In S45 The specific expressions for the performance metrics are as follows:

[0167] ；

[0168] in, 、 These represent the minimum and maximum eigenvalues, respectively.

[0169] The expression for the new triggering condition in S46 is as follows:

[0170] ;

[0171] in, Represents state error; dynamic variable and dynamic variables The following relationship must be satisfied:

[0172] ;

[0173] The optimization problem in S47 is expressed as a linear matrix inequality, as follows:

[0174] ;

[0175] ;

[0176] in, Indicates an adjustable parameter; Indicates trace, Represents a scalar. Represents the selection matrix, and subscript , The dimension is The zero matrix; The dimension is The zero matrix; symbol Indicates negative definiteness; The dimension isn The identity matrix; This represents a data-driven dynamic constraint matrix, and ; This represents the stability-dynamic event-triggered transmission strategy matrix, and , Elements that represent symmetrical positions.

[0177] At the same time, when hour, ;

[0178] ；

[0179] ；

[0180] ；

[0181] in, express A zero matrix of dimension; express Zero-dimensional matrix;

[0182] The online-updated state feedback controller gain matrix obtained in S47 is as follows:

[0183] ;

[0184] The weight matrix of the new online-updated event-triggered transmission mechanism obtained in S47 is as follows:

[0185] ;

[0186] .

[0187] This invention discloses an online data-driven event-triggered control method for nonlinear unmanned systems under polyhedral noise. It does not rely on any system model information and has certain universality and scalability.

[0188] Furthermore, this invention uses only offline collected status and system input to determine the transmission time, avoiding continuous detection of the system; at the same time, this invention effectively saves transmission resources while ensuring the asymptotic stability of the nonlinear unmanned system.

[0189] Furthermore, this invention proposes a data-driven system set based on polyhedral perturbation, which effectively solves the controller design problem when offline data is subjected to unknown bounded noise interference, and has good robustness.

[0190] The effectiveness and superiority of the data-driven event-triggered control method for nonlinear unmanned systems in this invention are verified through simulation experiments:

[0191] Consider a nonlinear unmanned system as follows:

[0192] ;

[0193] Where the state vector The origin is the nonlinear unmanned system in the unknown bounded noise. The equilibrium point at that time.

[0194] The aforementioned nonlinear unmanned system is an open-loop unstable system. Assume the system's dynamic characteristics are unknown, and there is unknown bounded noise. obey The uniform distribution, but the known dataset and The noise boundary is formed by... This is confirmed. Therefore, we apply a uniformly distributed control input to the aforementioned system. , conducted Secondary excitation. Selection of basis functions. and And construct the following data matrix:

[0195] ；

[0196] ；

[0197] ;

[0198] Setting parameters By solving the linear matrix inequalities described in the optimization problem S4, the state feedback controller gain matrix and the event-triggered transmission mechanism weight matrix corresponding to each online time step can be obtained. The initial system conditions are set as follows: The initial state is To obtain the system in time The state trajectory diagram within, such as Figure 3 As shown, the system state gradually approaches zero over time, demonstrating the effectiveness of the invention.

[0199] Figure 4 The transmission timeline of the system under the data-driven event triggering control is given, which significantly reduces the number of transmissions compared to the traditional continuous transmission strategy, demonstrating the superiority of the present invention.

[0200] In another aspect, the present invention provides an online data-driven event-triggered control system, including a nonlinear unmanned system (i.e., the controlled object), wherein the nonlinear unmanned system is configured to execute the above-described online data-driven event-triggered control method.

[0201] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Furthermore, the technical solutions of the various embodiments of the present invention can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. An online data-driven event-triggered control method for a nonlinear unmanned system under polyhedral noise, characterized in that, Includes the following steps: S1. For the discrete-time nonlinear system equations with unknown nonlinear function dynamics, the known nonlinear basis functions are used to transform the discrete-time nonlinear system equations into a linear time-varying system equation. S2. For unknown bounded noise in the measurement data, construct a set of noise polyhedra, and then construct a set of data-driven systems based on polyhedral perturbations based on the set of noise polyhedra and the linear time-varying system equations. Then, a description matrix is ​​constructed based on the data-driven system set; S3. Construct a data-driven dynamic event-triggered transmission strategy and determine the data transmission time based on the dynamic event-triggered transmission strategy; S4. Establish a data-driven stability criterion, optimize the dynamic event-triggered transmission strategy to obtain new triggering conditions, construct an optimization problem, solve the optimization problem, and obtain the online-updated weight matrix of the new event-triggered transmission mechanism and the online-updated gain matrix of the state feedback controller. Combine the stability criterion, the online-updated gain matrix of the state feedback controller, and the online-updated weight matrix of the new event-triggered transmission mechanism to control the nonlinear unmanned system so that the nonlinear unmanned system satisfies... The performance metrics and the goal of minimizing the feedback controller transmission frequency are achieved. S2 specifically includes the following steps: S21. Unknown bounded noise in the measurement data satisfy Under the assumptions, construct a set of noisy polyhedra. Among them, the upper limit of noise noise vector gather ; Represents the infinite norm; set The specific expression is as follows: ； In the formula, and Representing sets respectively The number of vertices and the first i Vertex vectors; Indicates the first Convex combination coefficients, It is the vertex index; S22. Construct a data-driven system set for a polyhedral nonlinear unmanned system by utilizing offline measured state and system input. S23, in discrete time steps Inside, a nonlinear unmanned system offline collects system state, system input, and noise interference; and constructs a data matrix based on the system state, system input, and noise interference. ;in, Indicates the first Each time step The matrix represents the set of system states; This indicates the use of nonlinear basis functions. The transformed state matrix; This indicates that the system input passes through a nonlinear basis function. Modulated input matrix; Represents the noise set matrix; S24, combine the data matrix and the set of noise polyhedra in S21. By combining linear time-varying system equations, a system set that matches the collected dataset is constructed. ; S25. Using the data matrix, and based on the linear time-varying system equations and system set... Construct data equations; S26. Then, based on the data equations and the data-driven system set of polyhedral nonlinear unmanned systems, a data-driven system set based on polyhedral perturbation is constructed. Then, a description matrix is ​​constructed based on the data-driven system set based on polyhedral perturbation. ; S4 specifically includes the following steps: S41, Based on non-singular matrices Define state vector And define unknown bounded noise ; in, Represents the transformed state variable. Indicates the changed disturbance; S42, via state vector and unknown bounded noise Control input exist Performing an algebraic transformation within the interval yields the transformed nonlinear unmanned system; where, Represents non-integer AND The intersection; S43, for the transformed nonlinear unmanned system in S42 and the data-driven dynamic event-triggered transmission strategy, and based on dynamic variables The update law is chosen to be a Lyapunov function for stability analysis to verify the stability of the optimized nonlinear unmanned system. S44. Combining the system state and the data equations in S25, the forward difference is derived. The expression; S45. Under the condition that the initial conditions are zero, i.e. , Indicates the initial time step. This indicates that the Lyapunov function is at time step The state-related part, Indicates time step The dynamic variables, and satisfy Under the condition of forward difference Summing the expressions yields the summation result. Based on this summation result, a nonlinear unmanned system under perturbation conditions is constructed. Performance indicators, this Performance metrics serve as data-driven stability criteria; The performance indicators are robust control performance indicators; among them, This indicates that the Lyapunov function is at time step The state-related part; Indicates time step Dynamic variables; S46. A new event-triggered transport mechanism weight matrix updated online in a given optimization problem. , and proportional parameters Furthermore, the weight matrix of the new event-triggered transmission mechanism is updated online in the optimization problem. , and proportional parameters Under the condition that all are positive definite and symmetric, and simultaneously satisfying Under the conditions, based on the original triggering conditions Construct new triggering conditions; S47. The new triggering conditions indicate how to adjust parameters to reduce the transmission frequency of the feedback controller. Based on the new triggering conditions, an optimization problem is constructed. Solving the optimization problem yields the online-updated weight matrix of the new event-triggered transmission mechanism. , Combined with the online-updated state feedback controller gain matrix, the stability criterion, the online-updated state feedback controller gain matrix, and the online-updated new event-triggered transmission mechanism weight matrix. , Controlling a nonlinear unmanned system to minimize the transmission frequency of the feedback controller and achieve the desired performance of the nonlinear unmanned system. Performance metrics targets.

2. The online data-driven event-triggered control method for a nonlinear unmanned system under polyhedral noise according to claim 1, characterized in that, The discrete-time nonlinear system equations in S1 are as follows: ； in, Indicates the first A signal given at each time step; and Represents a nonlinear function with two unknown dynamics; Represents the set of real numbers; represent 3D real matrix; n and m These represent the number of rows and columns, respectively. Indicates control input; Represents unknown bounded noise; Indicates the first Each time step Represents a non-negative integer; The expression for the state feedback controller is as follows: ； in, Represents the controller gain matrix; Indicates the first One time step; Indicates the first A signal given at each time step.

3. The online data-driven event-triggered control method for a nonlinear unmanned system under polyhedral noise as described in claim 2, characterized in that, The linear time-varying system equations in S1 are as follows: ； in, , They are two unknown matrices; and These are two known nonlinear basis functions; and satisfy... and .

4. The online data-driven event-triggered control method for a nonlinear unmanned system under polyhedral noise according to claim 3, characterized in that, The set of noise polyhedra in S21 The specific expression is as follows: ； In the formula, Indicates the first l The vertices of the basis noise matrix; Indicates the first l noise matrix coefficient, Represents the noise matrix; The system set in S24 The specific expression is as follows: ； The specific expression of the data equation in S25 is as follows: ； The specific data-driven system set based on polyhedral perturbation in S26 is as follows: ； Wherein, the description matrix satisfy And matrix Complete the order and simultaneously satisfy , Indicates any, Represents the identity matrix; T This indicates transpose.

5. The online data-driven event-triggered control method for a nonlinear unmanned system under polyhedral noise according to claim 4, characterized in that, S3 specifically includes the following steps: S31. To dynamically adjust the trigger threshold, a dynamic variable is introduced. and dynamic variables The update law, where dynamic variables The update law is as follows: ； in, This indicates a dynamic variable controlled by a difference equation; Represents a scalar; This indicates a dynamically triggered function, and the dynamically triggered function... The formula for calculation is: ； in, as well as This indicates that two steps need to be taken at time step. t The design of the event-triggered transmission mechanism weight matrix; and 0, 0, symbol Indicates positive determination; Represents the state vector acquired by the sensor With the latest transmission status The cumulative deviation between them, and In the formula, Indicates the first k A signal given at each time step; k Indicates the first k Each time step Represents the 2-norm; S32, Combining dynamic variables and proportional parameters The data-driven dynamic event-triggered transmission strategy is obtained, and the data transmission time is determined based on the dynamic event-triggered transmission strategy.

6. The online data-driven event-triggered control method for a nonlinear unmanned system under polyhedral noise according to claim 5, characterized in that, The data-driven dynamic event-triggered transmission strategy in S3 is as follows: ； in, Indicates the first One time step; This indicates an event-triggered system.

7. The online data-driven event-triggered control method for a nonlinear unmanned system under polyhedral noise according to claim 6, characterized in that, The transformed nonlinear unmanned system in S42 is as follows: ； in, Let the linearization function represent the state dependency, and the linearization function... State-related expressions Export, This indicates the state change at the last trigger moment. Represents the transformed controller gain, and satisfies ; The Lyapunov function in S43 is as follows: ； in, Represents the Lyapunov function. This indicates that the Lyapunov function is at time step t The state-related part, and ; Indicates time step t Time-varying location; The forward difference in S44 The specific expression is as follows: ； in, express The level of performance degradation, and >0, express ; Represents a composite matrix inequality; In S45 The specific expressions for the performance metrics are as follows: ； in, , These represent the minimum and maximum eigenvalues, respectively. The expression for the new triggering condition in S46 is as follows: ； in, Represents state error; dynamic variable and dynamic variables The following relationship must be satisfied: ； The optimization problem in S47 is expressed as a linear matrix inequality, as follows: ； ； in, Indicates an adjustable parameter; Indicates trace, Represents a scalar. Represents the selection matrix, and subscript , The dimension is The zero matrix; The dimension is The zero matrix; symbol Indicates negative definiteness; Represents a data-driven dynamic constraint matrix, and ; This represents the stability-dynamic event-triggered transmission strategy matrix, and , Elements indicating symmetrical positions; The online-updated state feedback controller gain matrix obtained in S47 is as follows: ； The newly updated event-triggered transmission mechanism weight matrix obtained in S47 is as follows: ； 。 8. An online data-driven event-triggered control system, characterized in that, Includes a nonlinear unmanned system, which is configured to perform the online data-driven event-triggered control method according to any one of claims 1 to 7.

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