Security cooperative control method and device for nonlinear cluster unmanned system under data driving

Abstract

The invention belongs to the technical field of nonlinear cooperative control, and particularly relates to a data-driven nonlinear cluster unmanned system security cooperative control method and device. The method comprises the following steps: S100, aiming at a nonlinear cluster unmanned system, designing a distributed state feedback controller based on a feedback gain matrix, and constructing an equivalent closed-loop system based on the controller; s200, acquiring input data and state data of the nonlinear cluster unmanned system through an offline experiment, and realizing non-parametric representation of the equivalent closed-loop system by using the input data and the state data; and S300, state constraint is converted into limitation on an attraction domain of a closed-loop system, a distributed feedback gain matrix is calculated based on parameterized representation of the closed-loop system, then a state feedback controller is obtained, data-driven cooperative control over the nonlinear cluster unmanned system is achieved, and the situation that the state of a single body in the system enters a dangerous area is avoided.

Description

Technical Field

[0001] The present invention belongs to the technical field of nonlinear collaborative control, and specifically relates to a data-driven nonlinear cluster unmanned system safety collaborative control method and device. Background Art

[0002] As an important research direction of the "New Generation Artificial Intelligence Development Plan", distributed swarm intelligence based on bionics has attracted great attention from the academic community. Multi-agent systems (MASs) are composed of multiple simple-structured monomers with certain perception, communication, computing, decision-making and execution capabilities. Agents work together to complete complex tasks through simple information interaction, which not only reduces the functional and structural complexity of the monomers, but also effectively improves the reliability, robustness and flexibility of the system. The "2023 China Artificial Intelligence Series White Paper" points out that intelligent collaborative control is an important application direction of artificial intelligence technology. Cluster unmanned systems represented by multiple unmanned vehicles, drones, and unmanned ships are typical multi-agent systems with a wide range of application scenarios. Nowadays, the goal of collaborative control in practical applications includes not only making all unmanned systems reach a common state, but also ensuring that each unmanned monomer avoids entering a dangerous area where it cannot work normally, which is called safe collaborative control. Specifically, the state of the unmanned monomer needs to meet certain constraints, including the amplitude and rate limits of the actuator, the process variable boundaries for safe and efficient operation of the system, and the conditions for avoiding collisions and obstacles. Therefore, achieving high-precision, fast-response safe collaborative control of distributed, nonlinear, and strongly coupled clustered unmanned systems in complex environments has important contemporary value.

[0003] However, existing modeling methods such as physical mechanism and system identification require sufficient physical knowledge, engineering experience and massive data, and cannot accurately model highly dynamic and nonlinear unmanned systems. This leads to insufficient control accuracy and slow response speed in complex application environments, limiting the application of advanced control methods in military and engineering fields. Therefore, how to integrate mechanisms and data, characterize accurate models of nonlinear unmanned systems, and achieve high-precision, ultra-fast safe collaborative control has become an urgent problem to be solved.

[0004] In recent years, the development of computer technology has made direct data-driven control methods a reality. This method uses only data to control and analyze unknown systems, providing a new end-to-end control paradigm. Once proposed, the direct data-driven control method has attracted widespread attention from scholars. From linear to nonlinear, from state feedback control to model predictive control, in-depth research has been carried out. However, current research on nonlinear systems is still mainly focused on monomer systems. How to design and analyze distributed control strategies while considering the connectivity between monomers in the system to achieve safe collaborative control of unknown nonlinear cluster unmanned systems is still an open problem. Therefore, it is urgent to fill the gap in this field. Summary of the invention

[0005] In response to the above problems, the present invention considers a nonlinear cluster unmanned system with an unknown system model under an undirected connected graph, and proposes a data-driven safe collaborative control method for a nonlinear cluster unmanned system, which realizes asymptotic consistency control of the system and avoids its state from entering a dangerous area.

[0006] The technical solution for implementing the present invention is as follows:

[0007] In a first aspect, an embodiment of the present application provides a data-driven method for safe collaborative control of a nonlinear cluster unmanned system, comprising the steps of:

[0008] S100, for nonlinear cluster unmanned systems, a distributed state feedback controller based on feedback gain matrix is ​​designed, and an equivalent closed-loop system is constructed based on the controller;

[0009] S200, obtaining input data and state data of the nonlinear cluster unmanned system through an offline experiment, and using the input data and state data to implement a non-parametric representation of the equivalent closed-loop system;

[0010] S300, converting the state constraints into restrictions on the attraction domain of the closed-loop system, calculating the distributed feedback gain matrix based on the parameterized representation of the closed-loop system, and then obtaining the state feedback controller to realize data-driven collaborative control of the nonlinear cluster unmanned system to prevent the state of the monomers in the system from entering the dangerous area.

[0011] Furthermore, the state feedback controller based on the distributed feedback gain matrix in step S100 of the present invention is specifically designed as follows:

[0012] u i (t) = KZ i (t)

[0013]

[0014] in, is the feedback gain matrix to be designed; and Represent the state and control input of monomer i respectively; a ij is the adjacency matrix The element in the i-th row and j-th column of i is a constant scalar, satisfying i=1,2,…,q when l i >0, i=q+1,2,...,N i =0, is the basis function.

[0015] Furthermore, the equivalent closed-loop system of the present invention is specifically designed as follows:

[0016]

[0017] Among them, the state variable and The matrices are The smallest and largest eigenvalues ​​of the matrix Δ=diag(l1,…,l N ), diag represents a diagonal matrix,, matrix A connectivity graph consisting of the connectivity relationships between monomers The Laplace matrix of , matrices A and B are unknown;

[0018] The nonlinear function H(ε(t)) is divided into linear ε(t) and nonlinear Two parts, namely

[0019]

[0020] Furthermore, in step S200 of the present invention, at the sampling time A set of control input, state and state derivative measurements are collected, and a data matrix is ​​obtained based on the measurements:

[0021] U i =[u i (τ1)u i (τ2)…u i (τ L )]

[0022] X i =[x i (τ1)x i (τ2)…x i (τ L )]

[0023]

[0024] The above data matrix satisfies the relationship

[0025] Furthermore, the non-parametric representation of the equivalent closed-loop system of the present invention is constructed as:

[0026]

[0027] in, Matrix G i satisfy and

[0028] Furthermore, the present invention converts the state constraint into a restriction on the attraction domain of the closed-loop system as follows:

[0029] The attraction domain of the closed-loop system is defined as:

[0030]

[0031] Among them, V(x) is the Lyapunov function, and α is a positive constant;

[0032] The danger zone is defined as a set of constraints on the states of individual cells in the system, namely:

[0033]

[0034] in, represents the safety constraint parameter;

[0035] make Get Ω α and The distance between i >0, the following inequality holds:

[0036]

[0037] Further, step S300 of the present invention solves a semi-positive definite programming problem based on the parameterized representation of the closed-loop system and the safety constraints to obtain a data-based distributed feedback gain matrix K. The semi-positive definite programming problem is:

[0038] For a given constant α>0, if And there exists a matrix and Satisfies the following semi-positive programming problem:

[0039]

[0040] in, and represents the safety constraint parameter,

[0041] If the above planning problem has a feasible solution, the feedback gain matrix is ​​designed as

[0042] In a second aspect, an embodiment of the present application provides a data-driven nonlinear cluster unmanned system safety collaborative control device, comprising:

[0043] A data acquisition module, which acquires input data and state data of the nonlinear cluster unmanned system through offline experiments, and uses the input data and state data to realize a non-parametric representation of the equivalent closed-loop system;

[0044] A calculation module converts the state constraints into restrictions on the attraction domain of the closed-loop system and calculates a feedback gain matrix based on a parameterized representation of the closed-loop system;

[0045] The state feedback controller calculates a distributed state feedback controller based on the feedback gain matrix according to the feedback gain matrix, realizes data-driven collaborative control of the nonlinear cluster unmanned system, and prevents the state of a single unit in the system from entering a dangerous area.

[0046] Beneficial Effects

[0047] First, the distributed data-driven controller design method proposed in the present invention transforms the state constraints into restrictions on the attraction domain of the closed-loop system, ensuring that the monomer does not enter the dangerous area and ensuring the stability of the closed-loop system.

[0048] Second, the equivalent closed-loop system constructed by the present invention does not require the connectivity between monomers in the known system, thus avoiding the use of global information, and is more suitable for high-dimensional, real-time operating systems and has a wide range of application scenarios.

[0049] Third, the data-driven safe collaborative control method for nonlinear cluster unmanned systems proposed in the present invention does not require a known system model, eliminates the dependence of traditional control methods on system models, and for the first time realizes safe collaborative control of the system using only data. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0051] Figure 1 It is a flow chart of a data-driven nonlinear cluster unmanned system safety collaborative control method provided by the present invention;

[0052] Figure 2It is a diagram of the displacement trajectory and speed trajectory of a vehicle row system under the action of a data-driven distributed state feedback controller in one embodiment of the present invention. DETAILED DESCRIPTION

[0053] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0054] It should be noted that the following embodiments and features in the embodiments may be combined with each other in the absence of conflict; and, based on the embodiments in the present disclosure, all other embodiments obtained by ordinary technicians in the field without making any creative work are within the scope of protection of the present disclosure.

[0055] It should be noted that various aspects of the embodiments within the scope of the appended claims are described below. It should be apparent that the aspects described herein may be embodied in a wide variety of forms, and any specific structure and / or function described herein is merely illustrative. Based on the present disclosure, it should be understood by those skilled in the art that an aspect described herein may be implemented independently of any other aspect, and two or more of these aspects may be combined in various ways. For example, any number of aspects described herein may be used to implement the device and / or practice the method. In addition, other structures and / or functionalities other than one or more of the aspects described herein may be used to implement this device and / or practice this method.

[0056] The design concept of the present invention is: first, based on the local information between monomers, a distributed state feedback controller is designed to construct an equivalent closed-loop system; second, the trajectory data of the system during open-loop operation is collected to construct a non-parametric representation of the equivalent closed-loop system; finally, the state constraints are converted into restrictions on the attraction domain of the closed-loop system, and a data-based distributed feedback gain matrix design method is proposed to achieve progressive collaborative control of the unknown nonlinear cluster unmanned system and avoid the state of the monomers in the system from entering the dangerous area. The present invention solves the problem of safe collaborative control of nonlinear cluster unmanned systems with unknown system models under undirected communication topology.

[0057] like Figure 1 The flowchart of the present invention is a data-driven nonlinear cluster unmanned system safety collaborative control method, comprising the following steps:

[0058] S100, for a nonlinear cluster unmanned system with an unknown dynamic model, a distributed state feedback controller based on a distributed feedback gain matrix is ​​designed, and an equivalent closed-loop system is constructed based on the controller.

[0059] In one embodiment, a nonlinear swarm unmanned system containing N units is considered, and the dynamic model of each unit is:

[0060]

[0061] Where, at time t>0, i=1,2,…,N, and Respectively represent the state and control input of monomer i, and the nonlinear function f: and matrix B are unknown. Assume there is a known basis function So that for some unknown matrix There is f(x i (t)) = AF(x i (t)). represents the set of real numbers, represents an n-dimensional real vector, Represents n×n f Dimensional real matrix.

[0062] Based on this, the dynamic equation of the above cluster unmanned system can be rewritten as:

[0063]

[0064] Among them, the matrices A and B are unknown, and the function F(x i (t)) contains two parts, linear and nonlinear, namely Q(x i (t)): is a nonlinear basis function, n f represents a positive constant. And, F(x i (t)) linear x i (t) and nonlinear Q(x i (t)) part satisfies the following relationship:

[0065]

[0066] In addition, the connectivity between the monomers in the system can be represented by an undirected connectivity graph to describe, and each monomer in the system can only obtain the connectivity graph The Laplace matrix of The maximum eigenvalue of .

[0067] Furthermore, based on the dynamic equation of the above-mentioned cluster unmanned system, the distributed state feedback controller based on the feedback gain matrix is ​​designed in step S100, and the specific design is:

[0068] u i (t) = KZ i (t)

[0069]

[0070] in, is the feedback gain matrix to be designed; a ij It is a connected graph The adjacency matrix of The element in the i-th row and j-th column of i is a constant scalar, satisfying i=1,2,...,q when l i >0, i=q+1,2,…,N i =0, q represents a normal number.

[0071] Furthermore, based on the above-mentioned distributed state feedback controller, the equivalent closed-loop system in step S100 is specifically designed as follows:

[0072]

[0073] Among them, the state variable and The matrices are The smallest and largest eigenvalues ​​of the matrix A connectivity graph consisting of the connectivity relationships between monomers The Laplace matrix of Δ=diag(l1,…,l N ), diag represents a diagonal matrix, A is n×n f dimension unknown real matrix and B is an n×m dimension unknown real matrix, the matrix The nonlinear function H(ε(t)) can be divided into linear ε(t) and nonlinear Two parts, namely

[0074]

[0075] S200, obtaining input data and state data of the nonlinear cluster unmanned system through offline experiments, and using the input data and state data to implement a non-parametric representation of the equivalent closed-loop system.

[0076] In one embodiment, the non-parametric representation design steps of the equivalent closed-loop system described in step S200 are:

[0077] S211, in offline experiments, at sampling time A set of input, state, and state derivative measurements are collected within And based on these measurements the following data matrix is ​​constructed:

[0078] U i =[u i (τ1)u i (τ2)…u i (τ L )]

[0079] X i =[x i (τ1)x i (τ2)…x i (τ L )]

[0080]

[0081] The above data matrix satisfies the relationship

[0082] S212, based on the above data, the non-parametric representation of the equivalent closed-loop system is constructed as:

[0083]

[0084] in, Matrix G i satisfy and Indicates n f dimensional identity matrix.

[0085] S300, converting the state constraints into restrictions on the attraction domain of the closed-loop system, calculating the distributed feedback gain matrix based on the parameterized representation of the closed-loop system, and then obtaining the state feedback controller to realize data-driven collaborative control of the nonlinear cluster unmanned system to prevent the state of the monomers in the system from entering the dangerous area.

[0086] In one embodiment, the data-based distributed feedback gain matrix design method in step S300 is specifically:

[0087] Consider the undirected connected graph formed by the connection relationship between each monomer in the system and nonlinear swarm unmanned system with unknown system model. For a given constant α>0, if And there exists a matrix and Satisfies the following semi-positive programming problem:

[0088]

[0089] in, Represents a given safety constraint parameter, which is assigned different values ​​according to different actual scenarios.

[0090] If the above planning problem has a feasible solution, the feedback gain matrix is ​​designed as For any initial state, under the action of the above-mentioned distributed state feedback controller, the nonlinear cluster unmanned system can achieve asymptotic collaborative control and effectively prevent the state of a single unit in the system from entering the dangerous area.

[0091] The following are the design steps of the distributed feedback gain matrix design method based on data in step S300:

[0092] S311, the attraction domain of the closed-loop system is defined as:

[0093]

[0094] Among them, V(x) is the Lyapunov function and α is a positive constant.

[0095] The danger zone is defined as a set of constraints on the states of individual cells in the system, namely:

[0096]

[0097] Among them, the parameters

[0098] By converting the safety constraints into restrictions on the closed-loop system's attraction domain, the monomer is ensured not to enter the dangerous area. Need to make Ω α and The distance between i >0, the following inequality holds:

[0099]

[0100] Where P is a positive definite symmetric matrix. Specifically, d i >0, that is make Can get Where i=1,2,...,N.

[0101] S312, non-parametric representation of the equivalent closed-loop system according to S200 The nonlinear cancellation method is used to realize the asymptotic cooperative control of cluster unmanned systems, that is, to ensure the linear part It is stable while minimizing the nonlinear part Specifically, Establishment and minimization

[0102] S313, based on S311 and S312, design a data-based semi-positive definite programming problem, including the data-based distributed feedback gain matrix design method, specifically:

[0103] Consider a connected graph and nonlinear swarm unmanned system with unknown system model. For a given constant α>0, if And there exists a matrix and Satisfies the following semi-positive programming:

[0104]

[0105] If the above planning problem has a feasible solution, the feedback gain matrix is ​​designed as Then, for any initial state, under the action of the distributed state feedback controller, the nonlinear cluster unmanned system can achieve asymptotic collaborative control and effectively prevent the state of a single unit in the system from entering the dangerous area.

[0106] In one embodiment, a simulation experiment is performed to verify the feasibility and effectiveness of the online design method of the data-driven controller in the present invention.

[0107] Consider a platoon system consisting of six vehicles, and the dynamic model of each vehicle is:

[0108]

[0109] Where i = 1, 2, ..., 6, m represents the mass of each vehicle, v i (t) represents its speed, s i (t) is the distance between vehicle i+1 and vehicle i, F r (v i (t)) represents the resistance and is expressed as:

[0110]

[0111] Among them, k1>0 and k2>0 are given scalars.

[0112] Given a virtual reference trajectory, the control goal is to design a distributed data-driven control strategy so that the connected vehicles can asymptotically track the virtual reference trajectory while maintaining a safe distance, that is, and here and v * They represent the required safe forward distance and reference speed respectively.

[0113] definition in and Knowable Corresponding to the distance s i (t) = 0, that is, vehicles i and i+1 have collided. Since we want to avoid this situation, we define the danger zone as:

[0114]

[0115] In step S100, the distributed state feedback controller is selected. i for li = 1, i = 1, ..., 4 and l5 = l6 = 0. Select the basis function Select parameters m = 1500kg, k1 = 150Ns / m, k2 = 300Ns 2 / m 2 , and v * =10m / s.

[0116] Based on step S200, data is collected Set the sampling interval to τ k+1 -τ k = 0.1, length L = 10. Solve the semi-positive programming problem described in step S300 to obtain the safety controller gain, and act on the above vehicle platoon system. Thus, the simulation results are as follows: Figure 2 The horizontal axis in the simulation results represents the time step, and the velocity trajectory and displacement trajectory of each vehicle are shown as follows: Figure 2 (a) and Figure 2 (b) The simulation results show that the entire vehicle platoon system achieves safe coordinated control, that is, the front and rear connected vehicles maintain the same speed (10m / s) while maintaining a safe distance (15m). In addition, since the method proposed in the present invention does not require system model information during the implementation process, it has certain advantages.

[0117] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. A data-driven safe collaborative control method for nonlinear cluster unmanned systems, characterized in that: Includes steps: S100, for nonlinear cluster unmanned systems, a distributed state feedback controller based on feedback gain matrix is ​​designed, and an equivalent closed-loop system is constructed based on the controller; S200, obtaining input data and state data of the nonlinear cluster unmanned system through offline experiments, and using the input data and state data to implement a non-parametric representation of the equivalent closed-loop system; S300, converting the state constraints into restrictions on the attraction domain of the closed-loop system, calculating the distributed feedback gain matrix based on the parameterized representation of the closed-loop system, and then obtaining the state feedback controller to realize data-driven collaborative control of the nonlinear cluster unmanned system to prevent the state of the monomers in the system from entering the dangerous area.

2. According to the data-driven nonlinear cluster unmanned system safety collaborative control method of claim 1, it is characterized by: The state feedback controller based on the distributed feedback gain matrix in step S100 is specifically designed as follows: u i (t)=KZ i (t) in, is the feedback gain matrix to be designed; and Represent the state and control input of monomer i respectively; a ij is the adjacency matrix The element in the i-th row and j-th column of ; is a constant scalar, satisfying i=1,2,...,q When i=q+1,2,…,N is the basis function.

3. According to the data-driven nonlinear cluster unmanned system safety collaborative control method of claim 2, it is characterized by: The equivalent closed-loop system is specifically designed as follows: Among them, the state variable and The matrices are The smallest and largest eigenvalues ​​of the matrix diag represents a diagonal matrix, A connectivity graph consisting of the connectivity relationships between monomers The Laplace matrix of , matrices A and B are unknown; The nonlinear function H(ε(t)) is divided into linear ε(t) and nonlinear Two parts, namely 4. According to the data-driven nonlinear cluster unmanned system safety collaborative control method of claim 2, it is characterized by: Step S200 is at the sampling time A set of control input, state and state derivative measurements are collected, and a data matrix is ​​obtained based on the measurements: U i =[u i (τ1)u i (τ2)…u i (t L )] X i =[x i (τ1)x i (τ2)…x i (t L )] 5. According to the data-driven nonlinear cluster unmanned system safety collaborative control method of claim 4, it is characterized by: The non-parametric representation of the equivalent closed-loop system is constructed as: in, Matrix G i satisfy and 6. According to the data-driven safe collaborative control method of nonlinear cluster unmanned system in claim 2, it is characterized by: The transformation of the state constraint into a restriction on the attraction domain of the closed-loop system is specifically as follows: The attraction domain of the closed-loop system is defined as: Among them, V(x) is the Lyapunov function, and α is a positive constant; The danger zone is defined as a set of constraints on the states of individual cells in the system, namely: in, represents the safety constraint parameter; make Get Ω α The distance d between i >0, the following inequality holds:

7. The data-driven safe collaborative control method for nonlinear cluster unmanned systems according to claim 6 is characterized in that: Step S300 solves a semi-positive definite programming problem based on the parameterized representation of the closed-loop system and the safety constraints to obtain a data-based distributed feedback gain matrix K. The semi-positive definite programming problem is: For a given constant α>0, if And there exists a matrix and Satisfies the following semi-positive programming problem: in, and represents the safety constraint parameter, If the above planning problem has a feasible solution, the feedback gain matrix is ​​designed as 8. A data-driven nonlinear cluster unmanned system safety collaborative control device, characterized in that: include: A data acquisition module, which acquires input data and state data of the nonlinear cluster unmanned system through offline experiments, and uses the input data and state data to realize a non-parametric representation of the equivalent closed-loop system; A calculation module converts the state constraints into restrictions on the attraction domain of the closed-loop system and calculates a feedback gain matrix based on a parameterized representation of the closed-loop system; The state feedback controller calculates a distributed state feedback controller based on the feedback gain matrix according to the feedback gain matrix, realizes data-driven collaborative control of the nonlinear cluster unmanned system, and prevents the state of a single unit in the system from entering a dangerous area.

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