Multi-agent system bidirectional formation control method based on dynamic event triggering

Abstract

The invention provides a multi-agent system bidirectional formation control method based on dynamic event triggering, and relates to the technical field of cooperative control and formation of a multi-agent system, and the method comprises the steps: building a second-order nonlinear multi-agent system model containing a competition relation; designing a distributed adaptive controller; constructing a dynamic event triggering mechanism containing dynamic parameters; and constructing a controlled error system, and analyzing the controlled error system to obtain a sufficient condition and an index convergence rate of the multi-agent system for realizing adaptive bidirectional formation control. In addition, it is proved that the multi-agent system does not have the sesame effect through inequality derivation, and a numerical simulation case is designed to verify the effectiveness of the control strategy and the correctness of the two-way formation criterion. According to the invention, by introducing a dynamic event triggering mechanism, the triggering frequency is reduced, the control resources are saved, and the bidirectional formation analysis process of the second-order nonlinear multi-agent system is simplified.

Description

Technical Field

[0001] The present invention relates to the field of cooperative control and formation technology of multi-agent systems, and in particular to a bidirectional formation control method of a multi-agent system based on dynamic event triggering. Background Art

[0002] Multi-Agent System (MAS) consists of multiple independent agent nodes that complete complex tasks through information exchange and coordination. Due to its wide application prospects, MAS has attracted the attention of many researchers from the fields of biology, electronic information and engineering. Among them, the formation problem, as an important research direction of multi-agent system, has shown great application potential in the fields of microgrid, robot collaborative control, and drone collaboration.

[0003] Traditionally, research on multi-agent formations is based on the assumption of continuity of information exchange between agent nodes. However, in real applications, long-term stable and continuous communication is often difficult to achieve due to practical factors such as energy limitations, communication bandwidth limitations, and external interference. To meet this challenge, event-triggered control strategies have been introduced into the research of multi-agent control.

[0004] Under the event trigger mechanism, the intelligent agent node only exchanges information with adjacent nodes when specific conditions (i.e. event trigger conditions) are met, and the controller only updates the control strength at this time. This strategy can effectively reduce unnecessary communication and control updates, thereby saving control resources.

[0005] The dynamic event trigger mechanism is a further improvement on the static event trigger strategy. By introducing internal dynamic parameters to adjust the trigger threshold, the dynamic event trigger mechanism can more flexibly respond to changes in system status, further reduce control frequency, and optimize resource utilization. It is worth noting that the static event trigger mechanism can be regarded as a special case of the dynamic event trigger mechanism.

[0006] Although remarkable achievements have been made in the field of multi-agent cooperative formation control, in some real-world situations, there may be both cooperative and competitive relationships between system nodes. For the problem of multi-agent bidirectional formation with competitive relationships, current research is still insufficient. In addition, the application of dynamic event triggering mechanism in the analysis of multi-agent system formation is relatively rare. Summary of the invention

[0007] To this end, an embodiment of the present invention provides a bidirectional formation control method for a multi-agent system based on dynamic event triggering, which is used to solve the problem in the prior art that it is difficult to effectively balance communication frequency and control performance under complex relationships between nodes (such as coexistence of cooperation and competition), resulting in low resource utilization and limited system stability.

[0008] In order to solve the above problems, an embodiment of the present invention provides a bidirectional formation control method for a multi-agent system based on dynamic event triggering, the method comprising:

[0009] Establish a second-order nonlinear multi-agent system model including competitive relationships;

[0010] Based on the established second-order nonlinear multi-agent system model with competitive relations, a distributed adaptive controller is designed by introducing an adaptive control gain mechanism into the controller.

[0011] Based on the designed distributed adaptive controller, a dynamic event triggering mechanism with dynamic parameters is constructed;

[0012] Based on the distributed adaptive controller and dynamic event triggering mechanism, a controlled error system is constructed and analyzed to obtain the sufficient conditions and exponential convergence speed for the multi-agent system to realize adaptive bidirectional formation control.

[0013] Preferably, the method further comprises: proving through inequality derivation that under the action of a dynamic event triggering mechanism and a distributed adaptive controller, the Zeno effect will not occur in the process of a multi-agent system realizing a bidirectional formation.

[0014] Preferably, the establishing of a second-order nonlinear multi-agent system model including a competitive relationship specifically includes:

[0015] The dynamic equations of the second-order nonlinear multi-agent system model are defined, including the position and velocity variables of the agents, as well as nonlinear continuous functions. The mathematical expression is:

[0016]

[0017] In the formula, t represents the time; Represents x i The derivative of (t), x i (t) represents the position of the i-th agent at time t; Indicates v i The derivative of (t), v i (t)∈R n represents the speed of the i-th agent at time t, where i = 1, 2, ..., N, R n represents n-dimensional Euclidean space, N represents the number of agents; u i (t)∈R n Represents the control effect exerted on the i-th node; It is a nonlinear continuous function;

[0018] Define the dynamic behavior of the leader agent, and its mathematical expression is:

[0019]

[0020] In the formula, represents the derivative of x0(t), x0(t)∈R n represents the position of the leader agent; represents the derivative of v0(t), v0(t)∈R n represents the speed of the leader agent;

[0021] A signed directed graph is introduced to represent the communication topology of a multi-agent system, including:

[0022] Signed directed graph: A signed directed graph G = (V, E, A) is used to represent the communication topology of a multi-agent system, where V = {1, 2, ..., N} is a set of nodes representing each agent; is a set of edges, representing the communication connections between agents; A = [a ij ]∈R N×N is the adjacency matrix of graph G;

[0023] Adjacency matrix A: element a in the matrix ij The relationship between node i and node j is defined as:

[0024] a ij >0 indicates that there is a cooperative relationship between nodes i and j; a ij <0 means that there is a competition relationship between node i and node j; a ij =0 means there is no communication connection between node i and node j;

[0025] Laplace matrix L:

[0026] In a multi-agent system, all agent nodes are divided into two clusters and The adjacent nodes within each cluster are in a cooperative relationship, while the nodes between two clusters are in a competitive relationship; define the matrix i=1,2,…,N, if the node Then q i =1, if the node Then q i = -1;

[0027] Determine the conditions for the multi-agent system to achieve bidirectional formation, which is expressed as:

[0028]

[0029] In the formula, Indicates the preset formation. T stands for transpose.

[0030] Preferably, a distributed adaptive controller is designed by introducing an adaptive control gain mechanism in the controller, specifically including:

[0031] By introducing the adaptive control gain mechanism into the controller, the mathematical expression of the designed distributed adaptive controller is:

[0032]

[0033] In the formula, α represents the free weight parameter, α>0; represents the kth triggering time of the ith agent, k∈{1,2,...}; express The position of the jth agent at the moment; Indicates the preset formation; δ 1i represents the feedback control gain, δ 1i ≥0; δ 2i represents the adaptive control gain;

[0034] By defining the error vector, we get the adaptive control gain δ 2i The update formula of (t) is:

[0035] i=1,2,…,N

[0036] in

[0037]

[0038] φ vi (t) = q i v i (t)-v0(t)

[0039] In the formula, Denotes δ 2i The derivative of (t); p represents a constant, p>0; φ xi (t),φ vi (t) represents the error vector.

[0040] Preferably, a dynamic event triggering mechanism containing dynamic parameters is constructed, specifically including: defining the measurement error γ xi (t), γ vi (t) are as follows:

[0041] Define the measurement error γ xi (t), γ vi (t) are as follows:

[0042]

[0043] Based on the defined measurement error γ xi(t), γ vi (t), construct a dynamic event triggering mechanism with dynamic parameters, which is expressed as follows:

[0044]

[0045] In the formula, inf{} represents the lower bound; g i (t) represents the trigger function; Indicates S i The derivative of (t), S i (t) represents a dynamic variable and satisfies the initial value S0(t)>0; β i represents the event update parameter, β i >0; c represents the weight coefficient, c>0; λ min represents the minimum eigenvalue; is a positive definite matrix, ψ2=||L+diag{δ 21 (t),...,δ 2N (t)}|| 2 .

[0046] Preferably, based on the distributed adaptive controller and the dynamic event triggering mechanism, a controlled error system is constructed and analyzed to obtain sufficient conditions and exponential convergence speed for the multi-agent system to realize adaptive bidirectional formation control, specifically including:

[0047] Construct a controlled error system based on distributed adaptive controller and dynamic event triggering mechanism;

[0048] Using Lyapunov stability theory, we analyze the stability and convergence of multi-agent systems by constructing and deriving Lyapunov functions.

[0049] According to the derivation results of the Lyapunov function, sufficient conditions and exponential convergence speed for the multi-agent system to achieve adaptive bidirectional formation control are obtained.

[0050] Preferably, the controlled error system is:

[0051]

[0052] In the formula, Respectively represent φ x (t),φ v The derivative of (t), represents convolution, I n is the n-dimensional identity matrix,

[0053] Preferably, the Lyapunov function is:

[0054]

[0055] Where V(t) represents the Lyapunov function.

[0056] Preferably, according to the derivation result of the Lyapunov function, the sufficient condition for the multi-agent system to realize adaptive bidirectional formation control is obtained as follows:

[0057]

[0058] Where f represents the convergence coefficient; θ = 2 + h 2 +(c-2α)λ min B-αλ min (L + +L +T )+α 2 , h represents the Lipschitz coefficient, L +T Indicates L + The transpose of

[0059] Preferably, according to the derivation result of the Lyapunov function, the exponential convergence speed of the multi-agent system to achieve adaptive bidirectional formation control is obtained as -f.

[0060] It can be seen from the above technical solutions that the present invention has the following beneficial effects:

[0061] (1) Focusing on the second-order multi-agent system under the dynamic event triggering framework, the paper is committed to realizing adaptive two-way formation control with an isolated leader agent. Through a carefully designed distributed adaptive controller, the multi-agent system is ensured to follow and maintain the two-way formation mode with the leader. The paper uses the dynamic event triggering strategy and Lyapunov stability theory to strictly derive the sufficient conditions for realizing two-way formation and its exponential convergence rate. At the same time, it uses technical means such as inequality analysis to effectively avoid the potential Zeno phenomenon in the control process.

[0062] (2) Compared with the traditional continuous action control strategy, the event-triggered control strategy adopted by the present invention shows its unique advantage, that is, the control input is activated only when the preset dynamic trigger conditions are met, which significantly improves the adaptability and resource efficiency of the system in complex and changeable engineering environments. To further optimize the performance, the present invention innovatively introduces a dynamic event trigger mechanism, which effectively reduces the trigger frequency by dynamically adjusting the trigger threshold, thereby reducing the computational burden and maximizing the use of control resources.

[0063] (3) In view of the coexistence of cooperation and competition in the real system environment, the present invention takes into account the existence of competition factors when constructing the communication topology model of the multi-agent system. In the controller design stage, the adaptive control gain is creatively integrated, which can not only automatically adjust to the optimal control parameters, but also significantly enhance the control flexibility and robustness of the system, providing an effective solution for dealing with the formation control problem of multi-agent systems with competition relationships. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] In order to more clearly illustrate the implementation cases of the present invention or the technical solutions in the prior art, the following is a brief description of the drawings required for use in the embodiments. By referring to the drawings, the features and advantages of the present invention will be more clearly understood. The drawings are schematic and should not be understood as limiting the present invention in any way. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work. Among them:

[0065] Figure 1 A flowchart of a bidirectional formation control method for a multi-agent system based on dynamic event triggering provided in an embodiment;

[0066] Figure 2 A schematic diagram of the communication topology of a multi-agent system in an embodiment;

[0067] Figure 3 Schematic diagram of error vector trajectory in the embodiment, where (a) is a position error vector curve of the multi-agent system, and (b) is a velocity error vector curve of the multi-agent system; the abscissa of (a) and (b) represents time, and the ordinate represents formation error;

[0068] Figure 4 is a speed curve of a multi-agent system in an embodiment, wherein the horizontal axis in the figure represents time and the vertical axis represents the speed of the agent;

[0069] Figure 5 Schematic diagram of the position trajectory of the multi-agent system and the leader agent in the embodiment; the three coordinates in the figure are three-dimensional space coordinates;

[0070] Figure 6 : is a time slice diagram of the multi-agent system formation in the embodiment, wherein (a) is the formation of the multi-agent system at 0 seconds, (b) is the formation of the multi-agent system at 2 seconds, (c) is the formation of the multi-agent system at 7 seconds, and (d) is the formation of the multi-agent system at 8 seconds; the three coordinates of (a), (b), (c), and (d) are three-dimensional space coordinates;

[0071] Figure 7 Schematic diagram of adaptive control gain evolution curve in the embodiment; wherein the abscissa in the figure represents time, and the ordinate represents control gain;

[0072] Figure 8 It is a comparison chart of triggering moments under different triggering mechanisms in the embodiments; (a) is a triggering moment chart under a static event triggering mechanism, and (b) is a triggering moment chart under a dynamic event triggering mechanism; the horizontal axis of (a) and (b) represents time, and the vertical axis represents the agent number. DETAILED DESCRIPTION

[0073] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are 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.

[0074] Embodiment 1

[0075] In the existing technology, it is difficult to effectively balance the communication frequency and control performance under the complex relationship between nodes (such as the coexistence of cooperation and competition), resulting in low resource utilization and limited system stability. Figure 1 As shown, an embodiment of the present invention proposes a bidirectional formation control method for a multi-agent system based on dynamic event triggering, the method comprising:

[0076] Step S1: Establish a second-order nonlinear multi-agent system model including competition relationship;

[0077] Step S2: Based on the established second-order nonlinear multi-agent system model including competition relationship, a distributed adaptive controller is designed by introducing an adaptive control gain mechanism in the controller;

[0078] Step S3: constructing a dynamic event triggering mechanism containing dynamic parameters based on the designed distributed adaptive controller;

[0079] Step S4: Based on the distributed adaptive controller and the dynamic event triggering mechanism, a controlled error system is constructed and analyzed to obtain the sufficient conditions and exponential convergence speed for the multi-agent system to realize adaptive bidirectional formation control.

[0080] It can be seen from the above technical scheme that the present invention provides a bidirectional formation control method for a multi-agent system based on dynamic event triggering. The present invention innovatively constructs a second-order nonlinear multi-agent system model, which incorporates the concept of signed directed communication topology and depicts the complex relationship between agents in a more precise way, where there is both cooperation and competition. In the design of the distributed controller, the present invention introduces an adaptive control gain mechanism, which not only improves the flexibility of control, but also significantly enhances the control performance. Further, in order to optimize the utilization of control resources and reduce unnecessary communication loads, the present invention designs a dynamic event triggering mechanism containing dynamic parameters. Compared with the traditional static threshold event triggering strategy, this mechanism can effectively reduce the triggering frequency by dynamically adjusting the triggering threshold, thereby saving precious control resources. In addition, the present invention also constructs a controlled error system and cleverly uses the Lyapunov stability theory. Through this theoretical framework, the present invention derives the sufficient conditions for the second-order nonlinear multi-agent system to achieve adaptive bidirectional formation control and the convergence speed of the system under the dynamic event triggering mechanism, providing a solid theoretical support for subsequent engineering applications.

[0081] In step S1, a second-order nonlinear multi-agent system model including competition relationship is established, which specifically includes:

[0082] The present invention first defines the dynamic equation of the second-order nonlinear multi-agent system model, including the position and velocity variables of the agent, and the nonlinear continuous function, and its mathematical expression is:

[0083]

[0084] In the formula, t represents the time; Represents x i The derivative of (t), x i (t) represents the position of the i-th agent at time t; Indicates v i The derivative of (t), v i (t)∈R n represents the speed of the i-th agent at time t, where i = 1, 2, ..., N, R n represents n-dimensional Euclidean space, N represents the number of agents; u i (t)∈R n Represents the control effect exerted on the i-th node; is a nonlinear continuous function.

[0085] Next, the dynamic behavior of the leader agent is defined, and its mathematical expression is:

[0086]

[0087] In the formula, represents the derivative of x0(t), x0(t)∈R n represents the position of the leader agent; represents the derivative of v0(t), v0(t)∈R n Represents the speed of the leader agent.

[0088] Secondly, the present invention introduces a signed directed graph to represent the communication topology of the multi-agent system, including:

[0089] Signed directed graph: A signed directed graph G = (V, E, A) is used to represent the communication topology of a multi-agent system, where V = {1, 2, ..., N} is a set of nodes representing each agent; is a set of edges, representing the communication connections between agents; A = [a ij ]∈R N×N is the adjacency matrix of graph G.

[0090] Adjacency matrix A: element a in the matrix ij The relationship between node i and node j is defined as:

[0091] a ij >0 indicates that there is a cooperative relationship between nodes i and j; a ij <0 means that there is a competition relationship between node i and node j; a ij =0 means there is no communication connection between node i and node j.

[0092] Laplace matrix L:

[0093] In a multi-agent system, all agent nodes are divided into two clusters and The adjacent nodes within each cluster are in a cooperative relationship, while the nodes between two clusters are in a competitive relationship; define the matrix i=1,2,…,N, if the node Then q i =1, if the node Then q i =-1.

[0094] Bidirectional formation refers to the position of two clusters of a multi-agent system presenting a reverse symmetric formation over time. The present invention designs a leading agent as the bidirectional formation target. When one cluster of agents in the multi-agent system synchronizes with the speed of the leading agent, forms and maintains a preset formation in position, and the other cluster is reversely symmetric to it, the multi-agent system is said to achieve bidirectional formation. The conditions for the multi-agent system to achieve bidirectional formation are:

[0095]

[0096] In the formula, Indicates the preset formation. T stands for transpose.

[0097] In step S2, based on the established second-order nonlinear multi-agent system model including competitive relationships, a distributed adaptive controller is designed by introducing an adaptive control gain mechanism in the controller to increase control flexibility and improve control performance.

[0098] Specifically, the mathematical expression of the distributed adaptive controller is:

[0099]

[0100] In the formula, α represents the free weight parameter, α>0; represents the kth triggering time of the ith agent, k∈{1,2,...}; express The position of the jth agent at the moment; Indicates the preset formation; δ 1i represents the feedback control gain, δ 1i ≥0; δ 2i represents the adaptive control gain.

[0101] By defining the error vector, we get the adaptive control gain δ 2i The update formula of (t) is:

[0102] i=1,2,…,N

[0103] in

[0104]

[0105] φ vi (t) = q i v i (t)-v0(t)

[0106] In the formula, Denotes δ 2i The derivative of (t); p represents a constant, p>0; φ xi (t),φ vi (t) represents the error vector.

[0107] In step S3, based on the designed distributed adaptive controller, a dynamic event triggering mechanism with dynamic parameters is constructed, which specifically includes:

[0108] Define the measurement error γ xi (t), γ vi (t) are as follows:

[0109]

[0110] Based on the defined measurement error γ xi (t), γ vi (t), construct a dynamic event triggering mechanism with dynamic parameters, which is expressed as follows:

[0111]

[0112] In the formula, inf{} represents the lower bound; g i (t) represents the trigger function; Indicates S i The derivative of (t), S i (t) represents a dynamic variable and satisfies the initial value S0(t)>0; β i represents the event update parameter, β i >0; c represents the weight coefficient, c>0; λ min represents the minimum eigenvalue; is a positive definite matrix, ψ2=||L+diag{δ 21 (t),...,δ 2N (t)}|| 2 .

[0113] In step S4, based on the distributed adaptive controller and the dynamic event triggering mechanism, a controlled error system is constructed and analyzed to obtain sufficient conditions and exponential convergence speed for the multi-agent system to achieve adaptive bidirectional formation control, including:

[0114] First, based on the distributed adaptive controller and dynamic event triggering mechanism, a controlled error system is constructed:

[0115]

[0116] Define the following vector Then the controlled error system can be written in a more compact form:

[0117]

[0118] In the formula, Respectively represent φ x (t),φ v The derivative of (t), represents convolution, I n is the n-dimensional identity matrix,

[0119] Assumption 1: Assume that the vector function The following conditions are met:

[0120]

[0121] In the formula, z i ∈{1,-1},i=1,2;h k >0,k=1,2,...,n.

[0122] Based on the controlled error system (Formula (5)), we will derive the conditions for the multi-agent system (Formula (1)) and the leader agent (Formula (2)) to achieve bidirectional formation under the action of the distributed adaptive controller (Formula (3)) and the dynamic event trigger mechanism (Formula (4)).

[0123] Furthermore, the present invention constructs the Lyapunov function as:

[0124]

[0125] Where V(t) represents the Lyapunov function.

[0126] definition It can be obtained that V(t) = V1(t) + V2(t), and from the dynamic event trigger mechanism (Formula (4)) Further Recursively extrapolating the time period, we get:

[0127]

[0128] Therefore, we know that S i (t)>0, V2(t)>0. (Assuming this is true, as one of the conclusions), we know from calculation that V1(t)>0. Therefore, V(t)=V1(t)+V2(t)>0.

[0129] Furthermore, by differentiating V1(t), we can obtain:

[0130]

[0131] in

[0132]

[0133] Based on Assumption 1, we can get the following inequality:

[0134]

[0135] in and Further, we can get:

[0136]

[0137] Based on Hardy's inequality, we can get:

[0138]

[0139] According to formulas (6), (7) and (8), we can get:

[0140]

[0141] Furthermore, based on the dynamic event triggering mechanism (Formula (4)), we can obtain:

[0142]

[0143] Where θ = 2 + h 2 +(c-2α)λ min B-αλ min (L + +L +T )+α 2 , Where f represents the convergence coefficient; h represents the Lipschitz coefficient, L +T Indicates L + The transpose of .

[0144] From formula (9), we can get: V(t)≤V(0)e ft Therefore, if f<0, it can be concluded that the multi-agent system (Formula (1)) realizes a bidirectional formation with the leader agent (Formula (2)) under the action of the dynamic event trigger mechanism (Formula (4)) and the distributed adaptive controller (Formula (3)).

[0145] In summary: If Assumption 1 holds, if the inequality If it holds, the solution of the error system (Formula (5)) converges exponentially to 0, that is, the multi-agent system (Formula (1)) and the leader agent (Formula (2)) achieve a two-way formation.

[0146] In addition, the present invention also includes proving through inequality derivation that under the action of the dynamic event triggering mechanism and the distributed adaptive controller, the Zeno effect will not occur in the process of the multi-agent system realizing bidirectional formation, and verifying it by designing numerical simulation cases.

[0147] Specifically, during the time period In, right || γ vi (t)|| and||γ xi(t)|| Take the derivative and we get:

[0148]

[0149] in

[0150]

[0151] Formula (10) can be further deduced as follows:

[0152]

[0153] Where F = max{||δ 2i (t)α||}, according to the dynamic event trigger mechanism (Formula (4)), the trigger time satisfy Substituting into formula (11) we can get

[0154] It can be further written as: Finally, we can get:

[0155]

[0156] therefore, This shows that the Zeno effect does not occur in the control process.

[0157] In summary, under the action of the dynamic event trigger mechanism (Formula (4)) and the distributed adaptive controller (Formula (3)), the Zeno effect will not occur when the multi-agent system (Formula (1)) realizes the bidirectional formation.

[0158] In order to further illustrate the advantages of the present invention, a specific simulation case is provided below for illustration.

[0159] 1. In order to simulate the actual industrial scene as much as possible, a multi-agent system consisting of eight agents moving in the XYZ three-dimensional space is selected, that is, N = 8, n = 3, and the communication topology diagram is shown in Figure (2). It can be seen from Figure (2) that the eight agents can be divided into two clusters and Select x, y, z as the position coordinates of the agent, and the dynamics function of the agent is as follows:

[0160]

[0161] Among them, v x ,v y ,v z is the agent velocity vector, y x ,u y ,uz Represents the control input, and the target formation vector is as follows:

[0162]

[0163] Based on the target formation, the multi-agent system will eventually form two square formations.

[0164] 2. Set controller parameters diag{δ 11 ,...,δ 1N}=diag{4,3.5,4,4.5,3.5,4,4.4.5}, α=0.95, p=0.01, c=0.125, β i =0.1, i=1,2,…,N.

[0165] 3. According to the sufficient conditions for the multi-agent system to achieve two-way formation, the parameters are calculated It satisfies the derived bidirectional formation criterion for multi-agent systems.

[0167] 4. The construction of the simulation model based on Simulink and the result analysis show that after implementing the control strategy of the present invention, the multi-agent system successfully achieves bidirectional formation behavior. Specifically:

[0168] Speed ​​and position error convergence analysis: Figure 3 Figures (a) and (b) show that as time goes by, the formation error (including speed error and position error) of the multi-agent system gradually approaches zero, which verifies the stability and accuracy of the system's formation control.

[0169] Speed ​​Sync Verification: Figure 4 It clearly demonstrates that the two intelligent agent clusters each achieved speed synchronization of equal value but opposite directions, which meets the design requirements of the two-way formation and reflects the efficiency of the internal collaborative control of the system.

[0170] Formation and maintenance of formation: through Figure 5 and Figure 6 From parts (a), (b), (c), and (d) in the figure, we can observe that the multi-agent system is able to form and maintain a symmetrical square formation at different time points, which proves the effective control ability of the control strategy over the formation configuration in three-dimensional space.

[0171] Control gain parameter optimization: Figure 7 The variation of the optimal control gain parameters determined by the adaptive strategy over time is revealed, indicating that the strategy can dynamically adjust the control parameters to adapt to the system state and optimize the control effect.

[0172] Comparison of event triggering mechanism efficiency: Figure 8 Parts (a) and (b) of the figure compare the difference in triggering frequency between the traditional static event triggering mechanism and the dynamic event triggering mechanism proposed in the present invention. The results show that the dynamic event triggering mechanism significantly reduces the triggering frequency, thereby improving the system resource utilization and communication efficiency.

[0173] In summary, the simulation results strongly prove that the proposed multi-agent system control strategy can effectively realize two-way formation with the leading agent under certain conditions. It also demonstrates the superior performance of the system in formation error control, speed synchronization, formation maintenance, control gain optimization, and event triggering efficiency improvement.

[0174] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0175] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0176] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 These computer program instructions can also be loaded onto a computer or other programmable data processing device, so that a series of operation steps are executed on the computer or other programmable device to produce a computer-implemented process, so that the instructions executed on the computer or other programmable device provide for implementing the process in the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0177] Obviously, the above embodiments are merely examples for clear explanation and are not intended to limit the implementation methods. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the implementation methods here. The obvious changes or modifications derived from them are still within the protection scope of the invention.

Claims

1. A bidirectional formation control method for a multi-agent system based on dynamic event triggering, characterized in that: include: Establish a second-order nonlinear multi-agent system model including competitive relationships; Based on the established second-order nonlinear multi-agent system model with competitive relations, a distributed adaptive controller is designed by introducing an adaptive control gain mechanism into the controller. Based on the designed distributed adaptive controller, a dynamic event triggering mechanism with dynamic parameters is constructed; Based on the distributed adaptive controller and dynamic event triggering mechanism, a controlled error system is constructed and analyzed to obtain the sufficient conditions and exponential convergence speed for the multi-agent system to realize adaptive bidirectional formation control.

2. The method for bidirectional formation control of a multi-agent system based on dynamic event triggering according to claim 1 is characterized in that: The method also includes: proving through inequality derivation that under the action of the dynamic event triggering mechanism and the distributed adaptive controller, the Zeno effect will not occur in the process of the multi-agent system realizing bidirectional formation.

3. The method for bidirectional formation control of a multi-agent system based on dynamic event triggering according to claim 1 is characterized in that: The establishment of a second-order nonlinear multi-agent system model including a competitive relationship specifically includes: The dynamic equations of the second-order nonlinear multi-agent system model are defined, including the position and velocity variables of the agents, as well as nonlinear continuous functions. The mathematical expression is: In the formula, t represents the time; Represents x i The derivative of (t), x i (t) represents the position of the i-th agent at time t; Indicates v i The derivative of (t), v i (t)∈R n represents the speed of the i-th agent at time t, where i = 1, 2, ..., N, R n represents n-dimensional Euclidean space, N represents the number of agents; u i (t)∈R n Represents the control effect exerted on the i-th node; It is a nonlinear continuous function; Define the dynamic behavior of the leader agent, and its mathematical expression is: In the formula, represents the derivative of x0(t), x0(t)∈R n represents the position of the leader agent; represents the derivative of v0(t), v0(t)∈R n represents the speed of the leader agent; A signed directed graph is introduced to represent the communication topology of a multi-agent system, including: Signed directed graph: A signed directed graph G = (V, E, A) is used to represent the communication topology of a multi-agent system, where V = {1, 2, ..., N} is a set of nodes representing each agent; is a set of edges, representing the communication connections between agents; A = [a ij ]∈R N×N is the adjacency matrix of graph G; Adjacency matrix A: element a in the matrix ij The relationship between node i and node j is defined as: a ij >0 indicates that there is a cooperative relationship between nodes i and j; a ij <0 means that there is a competition relationship between node i and node j; a ij =0 means there is no communication connection between node i and node j; Laplace matrix L: In a multi-agent system, all agent nodes are divided into two clusters and The adjacent nodes within each cluster are in a cooperative relationship, while the nodes between two clusters are in a competitive relationship; define the matrix If the node Then q i =1, if the node Then q i = -1; Determine the conditions for the multi-agent system to achieve bidirectional formation, which is expressed as: In the formula, Indicates the preset formation. T stands for transpose.

4. The method for bidirectional formation control of a multi-agent system based on dynamic event triggering according to claim 3 is characterized in that: By introducing an adaptive control gain mechanism into the controller, a distributed adaptive controller is designed, including: By introducing the adaptive control gain mechanism into the controller, the mathematical expression of the designed distributed adaptive controller is: In the formula, α represents the free weight parameter, α>0; represents the kth triggering time of the ith agent, k∈{1,2,...}; express The position of the jth agent at the moment; Indicates the preset formation; δ 1i represents the feedback control gain, δ 1i ≥0; δ 2i represents the adaptive control gain; By defining the error vector, we get the adaptive control gain δ 2i The update formula of (t) is: in φ vi (t)=q i v i (t)-v0(t) In the formula, Denotes δ 2i The derivative of (t); p represents a constant, p>0; φ xi (t),φ vi (t) represents the error vector.

5. The method for bidirectional formation control of a multi-agent system based on dynamic event triggering according to claim 4 is characterized in that: Construct a dynamic event trigger mechanism with dynamic parameters, including: Define the measurement error γ xi (t), γ vi (t) are as follows: Based on the defined measurement error γ xi (t), γ vi (t), construct a dynamic event triggering mechanism with dynamic parameters, which is expressed as follows: In the formula, inf{} represents the lower bound; g i (t) represents the trigger function; Indicates S i The derivative of (t), S i (t) represents a dynamic variable and satisfies the initial value S0(t)>0; β i represents the event update parameter, β i >0; c represents the weight coefficient, c>0; λ min represents the minimum eigenvalue; is a positive definite matrix, ψ2=||L+diag{δ 21 (t), ..., δ 2N (t)}|| 2 .

6. The method for bidirectional formation control of a multi-agent system based on dynamic event triggering according to claim 5 is characterized in that: Based on the distributed adaptive controller and dynamic event triggering mechanism, a controlled error system is constructed and analyzed to obtain the sufficient conditions and exponential convergence speed for the multi-agent system to realize adaptive bidirectional formation control, including: Construct a controlled error system based on distributed adaptive controller and dynamic event triggering mechanism; Using Lyapunov stability theory, we analyze the stability and convergence of multi-agent systems by constructing and deriving Lyapunov functions. According to the derivation results of the Lyapunov function, sufficient conditions and exponential convergence speed for the multi-agent system to achieve adaptive bidirectional formation control are obtained.

7. The method for bidirectional formation control of a multi-agent system based on dynamic event triggering according to claim 6 is characterized in that: The controlled error system is: In the formula, Respectively represent φ x (t),φ v The derivative of (t), represents convolution, I n is the n-dimensional identity matrix, 8. The method for bidirectional formation control of a multi-agent system based on dynamic event triggering according to claim 7 is characterized in that: The Lyapunov function is: Where V(t) represents the Lyapunov function.

9. The method for bidirectional formation control of a multi-agent system based on dynamic event triggering according to claim 8, characterized in that: According to the derivation result of the Lyapunov function, the sufficient condition for the multi-agent system to achieve adaptive bidirectional formation control is obtained as follows: Where f represents the convergence coefficient; θ = 2 + h 2 +(c-2α)λ min B-αλ min (L + +L +T )+α 2 , h represents the Lipschitz coefficient, L +T Indicates L + The transpose of 10. The method for bidirectional formation control of a multi-agent system based on dynamic event triggering according to claim 9, characterized in that: According to the derivation results of the Lyapunov function, the exponential convergence speed of the multi-agent system to achieve adaptive bidirectional formation control is obtained as -f.

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