Consistency control method and system for second-order nonlinear multi-agent system

Abstract

The invention relates to the field of multi-agent system control, and particularly provides a second-order nonlinear multi-agent system consistency control method and system, and the method comprises the steps: building a second-order nonlinear multi-agent dynamic system model with a plurality of same agents; establishing a leader following finite time consistency sufficient condition; establishing a distributed sliding mode surface based on a second-order nonlinear multi-agent dynamic system model; obtaining a control protocol by combining a preset dynamic event triggering condition, a preset adaptive law and a distributed sliding mode surface, and introducing the control protocol into a distributed time triggering controller to obtain a novel controller; and verifying the novel controller by utilizing a condition that the leader follows the finite time consistency is sufficient, obtaining a stable expected trajectory of the multi-agent, and completing the control of the consistency of the second-order nonlinear multi-agent system. According to the invention, trajectory tracking and consistency control of the leader following intelligent agent system are realized, and external disturbance can be effectively inhibited.

Description

Technical Field

[0001] The present invention belongs to the technical field of multi-agent control, and specifically relates to a second-order nonlinear multi-agent system consistency control method and system. Background Art

[0002] With the widespread application of multi-agent systems (MAS) in the fields of autonomous driving, intelligent transportation, drone group collaboration, robot group control, etc., how to achieve effective collaboration and consistency control among multiple agents has become a hot research issue. Especially in complex dynamic environments, the impact of system disturbances, external interference and uncertainty factors on system performance has become one of the difficulties in current multi-agent control research. The consistency problem of multi-agent systems, that is, the consistency of the states of multiple agents, is the basis for ensuring that these agents can complete the predetermined tasks in collaboration. At present, the research on the consistency problem of multi-agent systems mainly focuses on two types of control methods: leader-follower control and distributed control. In leader-follower control, one or more leader agents guide the remaining follower agents to move by setting reference trajectories. The goal of the follower agent is to follow the behavior of the leader agent and maintain consistency in the case of system disturbances. Finite-time consensus means that the states of all agents can converge to a consistent state within a finite time. This control method has significant advantages in many practical applications, especially when the task must be completed in a short time, such as disaster relief and military missions.

[0003] In the current research, the existing technologies for the consistency control of second-order nonlinear multi-agent systems have the following deficiencies: 1) Limitation of linearization assumptions: In the existing technologies, many control methods assume that multi-agent systems are linear systems. However, multi-agent systems in practical applications usually have complex nonlinear characteristics. This assumption is obviously inconsistent with the actual situation, resulting in reduced effectiveness and applicability of the control algorithm. 2) Insufficient processing capabilities for unknown disturbances: The existing control algorithms have limited processing capabilities for external unknown disturbances and internal uncertainties of the system. Most methods require known disturbances or use preset parameter models for compensation, which is difficult to meet the requirements in complex dynamic environments, resulting in reduced control accuracy. 3) Low time response efficiency: When achieving multi-agent consistency, existing methods usually focus on asymptotic stability rather than fast convergence in a finite time. This approach is not efficient enough in some practical scenarios with high time requirements (such as disaster emergency response and military cluster control). 4) Insufficient robustness: The existing methods are not robust enough for dynamic changes in the system and uncertainties in the external environment. For example, when there is a delay in the communication network or some link failures, the system performance is prone to a significant decline or even failure. Summary of the invention

[0004] In order to solve the problems existing in the prior art, the present invention provides a second-order nonlinear multi-agent system consistency control method and system, which solves the shortcomings of traditional methods in dealing with nonlinear dynamics and unknown disturbances by modeling the second-order nonlinear system and adopting a strategy combining adaptive control and robust control. The finite-time consistency control algorithm is used to ensure that the agents can reach consistency within a specified finite time while ensuring the stability of the system, thereby meeting the high requirements of practical applications for time response.

[0005] To achieve the above object, the present invention provides the following solutions:

[0006] A second-order nonlinear multi-agent system consistency control method comprises the following steps:

[0007] Based on the position and velocity of the follower agent, the position and velocity of the leader agent, and the distributed time-triggered controller, a second-order nonlinear multi-agent dynamic system model with several identical agents is established.

[0008] Based on the distributed time-triggered controller, a sufficient condition for leader-follower finite-time consistency is established;

[0009] Based on the second-order nonlinear multi-agent dynamic system model, a distributed sliding surface is established;

[0010] Combining the preset dynamic event triggering condition, the preset adaptive law and the distributed sliding surface, a control protocol is obtained, and the control protocol is introduced into the distributed time-triggered controller to obtain a new controller;

[0011] Based on Lyapunov stability theory, the parameters of the second-order nonlinear multi-agent system and the new controller that meet the preset judgment conditions are obtained. The new controller is verified using the sufficient conditions for the leader-follower finite-time consistency, and the expected trajectory for the multi-agent to achieve stability is obtained, thus completing the control of the consistency of the second-order nonlinear multi-agent system.

[0012] Preferably, the method for establishing a second-order nonlinear multi-agent dynamic system model having a plurality of identical agents comprises:

[0013] The agents in the multi-agent system are abstracted as nodes. Based on the position and velocity of the follower agent, a dynamic system model of the follower agent is established. The modeling formula is as follows:

[0014]

[0015] Where N is the number of multi-agent nodes, and denote the position and velocity of the ith follower, respectively. represents the nonlinear function of the ith follower, represents the controller of the ith agent, d i Indicates external interference;

[0016] Based on the position and speed of the leader agent, a dynamic system model of the leader agent is established. The modeling formula is as follows:

[0017]

[0018] Among them, f(x0(t),v0(t),t) represents the nonlinear function of the leader, and denote the position and speed of the leader, respectively. and They represent n-dimensional Euclidean space and n×m-dimensional real matrix respectively.

[0019] Preferably, sufficient conditions for leader-follower finite-time consistency include:

[0020]

[0021] Among them, ||*|| represents the Euclidean norm of the matrix, T is the stable time, and when the distributed time-triggered controller satisfies the sufficient condition of leader-follower finite-time consistency, the multi-agent system is said to reach a stable desired trajectory in a finite time;

[0022] The calculation formula of the stabilization time T is as follows:

[0023] consider where f(0) = 0 and Suppose there is a continuous function V(ξ) such that In the case of υ>0, 0<x<1 and 0<φ<∞, the trajectory of the system is finite-time stable, and the stable time in is a given constant, V(ξ0) is the initial value of V(ξ); υ represents the convergence rate parameter of the system, x represents the exponential decay factor, and φ represents the decay factor of the Lyapunov function; represents the stabilization time control constant;

[0024] Based on the function whose derivative is σ′(x)=σ(x)(1-σ(x)) For any scalar ξ, the following relationship holds:

[0025]

[0026] Wherein, v>0 and q=0.368, v represents the convergence rate of the system, and q represents the error constraint constant.

[0027] Preferably, the calculation formula of the distributed sliding surface is as follows:

[0028]

[0029] Where m, k1, k2, k3 are positive constants, a ij Represents the elements of the adjacency matrix, e xi represents the position error of the ith agent, e vi represents the speed error of the ith agent, e xj Represents the position error of the j-th agent.

[0030] Preferably, the preset dynamic event triggering conditions are as follows:

[0031] t k+1 = inf{t>t k :h i1 >0||h i2 >0},

[0032] where h i1 and h i2 There are two sub-conditions of the dynamic event trigger condition. The first sub-condition is expressed as:

[0033]

[0034] in, κ1, is a normal number, represents the latest update time of the ith agent, ε1 and ε2 are both positive numbers; χ i1 represents the state error term of the i-th agent;

[0035] θ i represents the dynamic adaptive parameters of the ith agent;

[0036] The second sub-condition is expressed as:

[0037]

[0038] in, Among them, κ3, is a normal number, ε3 and ε4 are both normal numbers, χ i2 Represents the dynamic error compensation term of the ith agent.

[0039] Preferably, the preset adaptive law calculation formula is as follows:

[0040]

[0041] Among them, k4, k5, and is a positive constant, is η i The estimated value of i Representing the upper bound of the unknown external disturbance of the i-th agent, ε1, ε2, ε3, κ2 and κ4 are also positive constants.

[0042] Preferably, the novel controller is a distributed finite-time consensus controller triggered by dynamic events, and the expression is as follows:

[0043]

[0044] in,

[0045] The present invention also provides a second-order nonlinear multi-agent system consistency control system for implementing the method, comprising:

[0046] A dynamic system model building module, which is used to build a second-order nonlinear multi-agent dynamic system model with several identical agents based on the position and velocity of the follower agent, the position and velocity of the leader agent, and a distributed time-triggered controller;

[0047] A sufficient condition establishment module, used for establishing a sufficient condition for leader-follower finite time consistency based on the distributed time-triggered controller;

[0048] Sliding surface establishment module, used to establish distributed sliding surface based on second-order nonlinear multi-agent dynamic system model;

[0049] A novel controller construction module is used to obtain a control protocol by combining a preset dynamic event trigger condition, a preset adaptive law and the distributed sliding surface, and introduce the control protocol into the distributed time-triggered controller to obtain a novel controller;

[0050] The new controller verification module is used to obtain the second-order nonlinear multi-agent system parameters and new controller parameters that meet the preset judgment conditions based on Lyapunov stability theory, and verify the new controller using the sufficient conditions for the leader-follower finite-time consistency, obtain the expected trajectory for the multi-agent to achieve stability, and complete the control of the consistency of the second-order nonlinear multi-agent system.

[0051] Compared with the prior art, the present invention has the following beneficial effects:

[0052] 1) Fast consistency convergence. Based on the finite time control theory, this paper designs a control law that enables the multi-agent system to quickly achieve state consistency within a finite time. Compared with the traditional asymptotic consistency method, it greatly improves the time response efficiency of the system and is particularly suitable for time-sensitive application scenarios (such as disaster emergency response, drone formation, and industrial automation).

[0053] 2) Strong robustness and anti-interference ability By introducing adaptive control and robust control strategies, the present invention achieves the robustness and stability of the system through anti-disturbance control terms and adaptive parameter estimation, which can effectively deal with unknown disturbances and external uncertainties in the system, and ensure the stability and reliability of the system. Even in complex dynamic environments, such as communication delays, incomplete information transmission or partial node failures, the system can still maintain high control performance.

[0054] 3) Improve the adaptability of nonlinear systems. Aiming at the nonlinear characteristics of multi-agent systems, the control method of the present invention breaks through the limitations of traditional linearization assumptions and directly models and controls nonlinear dynamics, significantly improving the applicability and accuracy of the control algorithm.

[0055] 4) Communication efficiency and system fault tolerance. The present invention optimizes the communication mechanism between intelligent agents, reduces the communication load and improves the energy efficiency of the system while ensuring the reliability of information transmission. When there is partial failure or noise interference in the communication network, the system can still maintain stable operation through robust design.

[0056] 5) Wide range of practical application value The method of the present invention has strong versatility and is applicable to multiple fields such as drone cluster control, robot team collaboration, intelligent transportation systems, etc., especially in complex environments and unknown disturbance conditions, showing significant technical advantages. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] In order to more clearly illustrate the technical solution of the present invention, the following briefly introduces the drawings required for use in the embodiments. 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 labor.

[0058] Figure 1 This is a flow chart of a method for consistency control of a second-order nonlinear multi-agent system according to an embodiment of the present invention.

[0059] Figure 2 This is a communication topology diagram consisting of a leader and four follower agents according to an embodiment of the present invention.

[0060] Figure 3 A schematic diagram of the position status of a multi-agent system according to an embodiment of the present invention;

[0061] Figure 4 A schematic diagram of the speed state of a multi-agent system according to an embodiment of the present invention;

[0062] Figure 5 A relative position error diagram of a multi-agent system according to an embodiment of the present invention;

[0063] Figure 6 A relative speed error diagram of a multi-agent system according to an embodiment of the present invention;

[0064] Figure 7 This is a schematic diagram of event triggering time interval information according to an embodiment of the present invention. DETAILED DESCRIPTION

[0065] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0066] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0067] In the field of automatic control, Lyapunov stability can be used to describe the stability of a dynamic system. If the trajectory of any initial condition near the equilibrium state can be maintained near the equilibrium state, then the system is called Lyapunov stable at . If the trajectory of any initial condition near the equilibrium state eventually approaches , then the system is called asymptotically stable at . Exponential stability can be used to ensure the minimum decay rate of the system, and can also estimate the speed of trajectory convergence. Lyapunov stability can be used in linear and nonlinear systems. However, the stability of linear systems can be obtained by other methods, so Lyapunov stability is mostly used to analyze the stability of nonlinear systems. The concept of Lyapunov stability can be extended to infinite-dimensional manifolds, that is, structural stability, which considers the behavior of a group of different but "close" solutions to differential equations. Input-state stability (ISS) applies Lyapunov stability to systems with input.

[0068] Embodiment 1

[0069] like Figure 1 As shown, a second-order nonlinear multi-agent system consistency control method includes the following steps:

[0070] S1: Based on the position and speed of the follower agent, the position and speed of the leader agent and the distributed time-triggered controller, a second-order nonlinear multi-agent dynamic system model with a plurality of identical agents is established; a further implementation method is that the method for establishing the second-order nonlinear multi-agent dynamic system model with a plurality of identical agents includes:

[0071] The agents in the multi-agent system are abstracted as nodes. Based on the position and velocity of the follower agent, a dynamic system model of the follower agent is established. The modeling formula is as follows:

[0072]

[0073] Where N is the number of multi-agent nodes, and denote the position and velocity of the ith follower, respectively. represents the nonlinear function of the ith follower, represents the controller of the ith agent, d i Indicates external interference.

[0074] Based on the position and speed of the leader agent, a dynamic system model of the leader agent is established. The modeling formula is as follows:

[0075]

[0076] Among them, f(x0(t),v0(t),t) represents the nonlinear function of the leader, and denote the position and speed of the leader, respectively. and They represent n-dimensional Euclidean space and n×m-dimensional real matrix respectively.

[0077] S2: Based on the distributed time-triggered controller, a sufficient condition for leader-follower finite-time consistency is established; a further implementation method is that the sufficient condition for leader-follower finite-time consistency includes:

[0078]

[0079] Among them, ||*|| represents the Euclidean norm of the matrix, T is the stable time, and when the distributed time-triggered controller satisfies the sufficient condition of leader-follower finite-time consistency, the multi-agent system is said to reach a stable desired trajectory in a finite time;

[0080] The calculation formula of the stabilization time T is as follows:

[0081] consider where f(0) = 0 and Suppose there is a continuous function V(ξ) such that In the case of υ>0, 0<x<1 and 0<φ<∞, the trajectory of the system is finite-time stable, and the stable time in is a given constant and is the initial value of V(ξ)V(ξ0); υ represents the convergence rate parameter of the system, x represents the exponential decay factor, and φ represents the decay factor of the Lyapunov function; represents the stable time control constant;

[0082] Based on the function whose derivative is σ′(x)=σ(x)(1-σ(x)) For any scalar ξ, the following relationship holds:

[0083]

[0084] Wherein, v>0 and q=0.368, v represents the convergence rate of the system, and q represents the error constraint constant.

[0085] S3: Based on the second-order nonlinear multi-agent dynamic system model, a distributed sliding surface is established; a further implementation method is that the calculation formula of the distributed sliding surface is as follows:

[0086]

[0087] Where m, k1, k2, k3 are positive constants, a ij Represents the elements of the adjacency matrix, e xi represents the position error of the ith agent, e vi represents the speed error of the ith agent, e xj represents the position error of the jth agent. The adjacency matrix is ​​used to represent the communication relationship between agents. If there is a communication connection a between agents i and j ij =1, if there is no communication, then a ij =0, which means it is used to describe the communication topology, analyze the connectivity and consistency convergence of the system, and help design the controller and weight distribution.

[0088] S4: Combining the preset dynamic event triggering condition, the preset adaptive law and the distributed sliding surface, a control protocol is obtained, and the control protocol is introduced into a distributed time-triggered controller to obtain a new controller;

[0089] A further implementation method is that the dynamic event triggering conditions are preset as follows:

[0090] t k+1 = inf{t>t k :h i1 >0||h i2 >0},

[0091] where hi1 and h i2 There are two sub-conditions of the dynamic event trigger condition. The first sub-condition is expressed as:

[0092]

[0093] in, κ1, is a normal number, represents the latest update time of the ith agent, ε1 and ε2 are both positive numbers; χ i1 represents the state error term of the i-th agent; specifically, ε1 is a constant used to adjust the dynamic event triggering threshold; ε2 is an adjustment constant related to the sliding surface error term; κ1 is a constant that controls the decay rate of the dynamic error term; is the offset compensation in the event trigger mechanism.

[0094] θ i represents the estimated parameters in the adaptive control of the ith agent;

[0095] The second sub-condition is expressed as:

[0096]

[0097] in, e i represents the sliding mode error term of the ith agent,

[0098] Among them, κ3, is a normal number, ε3 and ε4 are both normal numbers, χ i2 Represents the dynamic error compensation term of the ith agent.

[0099] A further implementation method is that the preset adaptive law calculation formula is as follows:

[0100]

[0101] Among them, k4, k5, and is a positive constant, is η i The estimated value of i Representing the upper bound of the unknown external disturbance of the i-th agent, ε1, ε2, ε3, κ2 and κ4 are also positive constants.

[0102] A further implementation method is that the new controller is a distributed finite-time consensus controller triggered by dynamic events, and the expression is as follows:

[0103]

[0104] in,

[0105] S5: Based on Lyapunov stability theory, the parameters of the second-order nonlinear multi-agent system and the new controller that meet the preset judgment conditions are obtained, and the new controller is verified using the sufficient conditions for the leader-follower finite-time consistency, and the expected trajectory for the multi-agent to achieve stability is obtained, completing the control of the consistency of the second-order nonlinear multi-agent system.

[0106] In this embodiment, the new controller u designed by the present invention is verified. i (t) Make the multi-agent system reach leader-follow finite-time consensus. Definition Using Lyapunov stability theory, construct the Lyapunov function, the function is as follows:

[0107]

[0108] By defining M = diag{m, ...m} and setting Z = L + M, where L is the Laplace matrix, Z1 is the inverse matrix of Z, and Z represents the weight matrix of the system, which is the sum of the Laplace matrix L and the diagonal matrix M. The above equation is derived and the Lyapunov stability of the system is analyzed, thereby proving the stability and error convergence of the closed-loop system:

[0109]

[0110] Assume that the system state always remains Within the defined region, we then obtain:

[0111]

[0112] Based on the following facts:

[0113]

[0114] Can be rewritten as:

[0115]

[0116] In the above steps, the goal is to ensure that the time derivative of the Lyapunov function is The convergence conditions are met, thus proving the stability and boundedness of the system. Represents the constraint between the sliding surface error term and the state error term. It means that by introducing the quadratic term, the system state error is constrained within a specific range to ensure that the Lyapunov function decreases. It is an intermediate constraint condition. Its purpose is to ensure that the system state error and dynamic error terms satisfy the Lyapunov function framework by constructing inequalities: This ensures that the system is ultimately stable and the error converges to a small range.

[0117] Using the inequality to derive the system state error e i and the dynamic error compensation term χ i2 The constraint relationship ensures that the time derivative of the Lyapunov function is negative, thus proving the stability of the system and the boundedness of all error terms. The specific implementation process is based on the following facts:

[0118]

[0119] Where b is a constant.

[0120] can be rewritten as:

[0121]

[0122] k5 represents the proportional gain parameter of the sliding mode controller, which is used to adjust the state error S i The feedback strength ensures the stability of the system and the speed of error convergence.

[0123] Based on the following facts:

[0124]

[0125] You can get:

[0126]

[0127] in

[0128]

[0129] 1 represents the bounded term in the derivative of the Lyapunov function, which is composed of dynamic error, parameter term and compensation term, ensuring that the system still has bounded stability in the presence of disturbances.

[0130] According to the relevant theorem, we can get:

[0131]

[0132] Therefore, this means that S i , χ i1 , and χ i2 They are all bounded.

[0133] Based on Lyapunov V2:

[0134] You can get:

[0135]

[0136] Considering the following facts

[0137]

[0138] Can become:

[0139]

[0140] Also available:

[0141]

[0142] According to the relevant lemma, the proof is complete.

[0143] Definition S i The attraction area is o1, and the following Lyapunov function is selected to verify e x and e v Convergence of:

[0144]

[0145] The time derivative of V3 is:

[0146]

[0147] According to the relevant theorem, we can get:

[0148]

[0149] Therefore, we can get:

[0150]

[0151] at the same time,

[0152]

[0153] According to the relevant lemma, e x and e v It can converge to a small region containing the origin in a finite time, and then e xi and e vi It can also converge to a small region containing the origin in a finite time. This proves that the Zeno behavior can be excluded under the proposed control scheme.

[0154] For the secondary dynamic trigger condition (the second sub-condition), the function is designed as follows:

[0155]

[0156] Based on the above analysis, it can be concluded that all signals in the closed-loop system are uniformly bounded.

[0157] consider:

[0158] Describe the system state error e i Constraints that decay over time:

[0159] pass It shows that the event triggering time interval and the error convergence rate k c Related, ensure that the system trigger mechanism is time-limited;

[0160] pass It shows that the upper bound of the trigger condition is determined by the sliding surface error, dynamic error compensation term and compensation offset, ensuring that the system remains stable and bounded under the trigger mechanism.

[0161] You can get:

[0162]

[0163] where k c yes upper limit.

[0164] According to the above similar analysis, we can get:

[0165]

[0166] where k a and k b They are and upper limit.

[0167] Therefore, it is guaranteed that Zeno behavior is avoided. The present invention can obtain:

[0168]

[0169] Among them, for t>T, x i (t) = x0(t), v i (t) = v0(t), which is consistent with S2 and satisfies the sufficient conditions for the finite-time consistency of the leader-follower of the second-order nonlinear multi-agent system. This shows that under the controller designed by the present invention, the finite-time consistency control problem of the leader-follower of the second-order nonlinear multi-agent system has been solved.

[0170] Embodiment 2

[0171] The present invention also provides a second-order nonlinear multi-agent system consistency control system, which is used to implement a method, including:

[0172] A dynamic system model building module, which is used to build a second-order nonlinear multi-agent dynamic system model with several identical agents based on the position and velocity of the follower agent, the position and velocity of the leader agent, and a distributed time-triggered controller;

[0173] A sufficient condition establishment module is used to establish sufficient conditions for leader-follower finite-time consistency based on a distributed time-triggered controller;

[0174] Sliding surface establishment module, used to establish distributed sliding surface based on second-order nonlinear multi-agent dynamic system model;

[0175] A new controller building module is used to combine preset dynamic event trigger conditions, preset adaptive laws and distributed sliding surfaces to obtain a control protocol, and introduce the control protocol into a distributed time-triggered controller to obtain a new controller;

[0176] The new controller verification module is used to obtain the second-order nonlinear multi-agent system parameters and new controller parameters that meet the preset judgment conditions based on Lyapunov stability theory, and to verify the new controller using the sufficient conditions for the leader-follower finite-time consistency, to obtain the expected trajectory for the multi-agent to achieve stability, and to complete the control of the consistency of the second-order nonlinear multi-agent system.

[0177] Embodiment 3

[0178] In order to demonstrate the effectiveness of the second-order nonlinear multi-agent system consistency control method and system proposed in the present invention, this embodiment provides a simulation experiment of distributed drone group control:

[0179] In this embodiment, a simulation experiment is conducted to demonstrate the effectiveness and practicality of the proposed distributed controller for a multi-UAV system. The simulation experiment involves five UAVs, including one leader UAV and four follower UAVs. The control task is to align the five UAVs horizontally and reach a consensus on position and speed. The communication topology of the UAVs is as follows: Figure 2 As shown. Among them, the dynamic model (dynamic system model) of the leader agent is as follows:

[0180]

[0181] The dynamic model of the follower agent is as follows:

[0182]

[0183] In addition, the adjacency matrix of the leader is as follows

[0184] The Laplacian matrix between followers is

[0185] Let k=2.0, k2=0.5, k3=1.0, m=3.0, k4=30.0, k5=3.5,

[0186] Choose the nonlinear function as f(x i (t),v i (t),t)=0.6(cos(0.01v0)-0.1sin(x0)-0.5x0) The external interference is d i (t)=0.05sin(2t), and the initial values ​​of other parameters are set to 1.

[0187] Through calculation, it is determined that the above parameter design meets the experimental requirements. The initial speed and position range of the drone are randomly set within [-10,30] and [-10,30]. The position state and speed state of the system under the action of Figure 3 and Figure 4 As shown. Figure 3 and Figure 4 In the example, it can be observed that the follower is about T s = Achieved consistency with the leader within 8s, which fully meets the defined stabilization time. Figure 5 and Figure 6 It clearly shows that the position error trajectory and velocity error trajectory between each follower and the leader gradually tend to 0. Figure 7 In the figure, the interval between event triggering between followers is shown.

[0188] The embodiments described above are only descriptions of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A second-order nonlinear multi-agent system consistency control method, characterized in that: The following steps are involved: Based on the position and velocity of the follower agent, the position and velocity of the leader agent, and the distributed time-triggered controller, a second-order nonlinear multi-agent dynamic system model with several identical agents is established. Based on the distributed time-triggered controller, a sufficient condition for leader-follower finite-time consistency is established; Based on the second-order nonlinear multi-agent dynamic system model, a distributed sliding surface is established; Combining the preset dynamic event triggering condition, the preset adaptive law and the distributed sliding surface, a control protocol is obtained, and the control protocol is introduced into the distributed time-triggered controller to obtain a new controller; Based on Lyapunov stability theory, the parameters of the second-order nonlinear multi-agent system and the new controller that meet the preset judgment conditions are obtained. The new controller is verified using the sufficient conditions for the leader-follower finite-time consistency, and the expected trajectory for the multi-agent to achieve stability is obtained, thus completing the control of the consistency of the second-order nonlinear multi-agent system.

2. The method according to claim 1, characterized in that Methods for building a second-order nonlinear multi-agent dynamic system model with several identical agents include: The agents in the multi-agent system are abstracted as nodes. Based on the position and velocity of the follower agent, a dynamic system model of the follower agent is established. The modeling formula is as follows: Where N is the number of multi-agent nodes, and denote the position and velocity of the ith follower, respectively. represents the nonlinear function of the ith follower, represents the controller of the ith agent, d i Indicates external interference; Based on the position and speed of the leader agent, a dynamic system model of the leader agent is established. The modeling formula is as follows: Among them, f(x0(t),v0(t),t) represents the nonlinear function of the leader, and denote the position and speed of the leader respectively, and They represent n-dimensional Euclidean space and n×m-dimensional real matrix respectively.

3. The method according to claim 2, characterized in that Sufficient conditions for leader-follower finite-time consistency include: Among them, ||*|| represents the Euclidean norm of the matrix, T is the stable time, and when the distributed time-triggered controller satisfies the sufficient condition of leader-follower finite-time consistency, the multi-agent system is said to reach a stable desired trajectory in a finite time; The calculation formula of the stabilization time T is as follows: consider where f(0) = 0 and Suppose there is a continuous function V(ξ) such that In the case of υ>0, 0<x<1 and 0<φ<∞, the trajectory of the system is finite-time stable, and the stable time in is a given constant, V(ξ0) is the initial value of V(ξ); υ represents the convergence rate parameter of the system, x represents the exponential decay factor, and φ represents the decay factor of the Lyapunov function; represents the stable time control constant; Based on the function whose derivative is σ′(x)=σ(x)(1-σ(x)) For any scalar ξ, the following relationship holds: Wherein, v>0 and q=0.368, v represents the convergence rate of the system, and q represents the error constraint constant.

4. The method according to claim 3, characterized in that The calculation formula of the distributed sliding surface is as follows: Where m, k1, k2, k3 are positive constants, a ij represents the elements of the adjacency matrix, e xi represents the position error of the ith agent, e vi represents the speed error of the ith agent, e xj Represents the position error of the j-th agent.

5. The method according to claim 4, characterized in that The preset dynamic event trigger conditions are as follows: t k+1 =inf{t>t k :h i1 >0||h i2 >0}, where h i1 and h i2 There are two sub-conditions of the dynamic event trigger condition. The first sub-condition is expressed as: in, κ1, is a normal number, represents the latest update time of the ith agent, ε1 and ε2 are both positive numbers; χ i1 represents the state error term of the i-th agent; θ i represents the adaptive parameters of the ith agent; The second sub-condition is expressed as: in, Among them, κ3, is a normal number, ε3 and ε4 are both normal numbers, χ i2 Represents the dynamic error compensation term of the ith agent.

6. The method according to claim 4, characterized in that The preset adaptive law calculation formula is as follows: Among them, k4, k5, and is a normal number, is η i The estimated value of i Representing the upper bound of the unknown external disturbance of the i-th agent, ε1, ε2, ε3, κ2 and κ4 are also positive constants.

7. The method according to claim 4, characterized in that The new controller is a distributed finite-time consensus controller based on dynamic event triggering, and the expression is as follows: in, 8. A second-order nonlinear multi-agent system consistency control system, used to implement the method described in any one of claims 1 to 7, characterized in that: include: A dynamic system model building module, which is used to build a second-order nonlinear multi-agent dynamic system model with several identical agents based on the position and velocity of the follower agent, the position and velocity of the leader agent, and a distributed time-triggered controller; A sufficient condition establishment module, used for establishing a sufficient condition for leader-follower finite time consistency based on the distributed time-triggered controller; Sliding surface establishment module, used to establish distributed sliding surface based on second-order nonlinear multi-agent dynamic system model; A novel controller construction module is used to obtain a control protocol by combining a preset dynamic event trigger condition, a preset adaptive law and the distributed sliding surface, and introduce the control protocol into the distributed time-triggered controller to obtain a novel controller; The new controller verification module is used to obtain the second-order nonlinear multi-agent system parameters and new controller parameters that meet the preset judgment conditions based on Lyapunov stability theory, and verify the new controller using the sufficient conditions for the leader-follower finite-time consistency, obtain the expected trajectory for the multi-agent to achieve stability, and complete the control of the consistency of the second-order nonlinear multi-agent system.

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