Trajectory tracking consistency method for nonlinear heterogeneous multi-agent system

Abstract

The invention discloses a trajectory tracking consistency method for a nonlinear heterogeneous multi-agent system, and relates to the field of artificial intelligence. According to the method, graph theory knowledge is utilized to construct a communication topological graph of a nonlinear heterogeneous multi-agent system; constructing a consistency control protocol based on the dynamic motion model of the follower agent; in the process that the multiple follower agents communicate with one another through the communication topological graph, for each of the multiple follower agents, the state and the expected track of the neighbor follower agent are obtained, and when an event triggering control strategy of the distributed control law is met, the state and the expected track of the neighbor follower agent are obtained; and updating the state of the follower agent according to the state of the neighbor follower agent, the expected trajectory and a consistency control protocol, and realizing the trajectory tracking consistency of the follower agent through a distributed control law within a preset time. The method can solve the communication cost problem when a nonlinear heterogeneous multi-agent system carries out trajectory tracking consistency.

Description

Technical Field

[0001] The present invention relates to the field of artificial intelligence, and in particular to a trajectory tracking consistency method for a nonlinear heterogeneous multi-agent system. Background Art

[0002] The study of consistency in nonlinear, heterogeneous multi-agent systems has been a hot topic in the field of artificial intelligence in recent years. It involves collaboration and competition among multiple agents and has broad applications in fields such as intelligent transportation, intelligent manufacturing, and smart homes. Traditional multi-agent systems typically assume that each agent has the same structure and functionality. However, in real applications, different agents often differ in physical form, functional requirements, and control structures. Therefore, heterogeneous multi-agent systems are being studied to address the problem of how multiple agents can collaborate to complete complex tasks. Furthermore, in engineering practice, heterogeneous multi-agent systems often exhibit nonlinear characteristics, leading to widespread concern regarding the consistency control of these systems.

[0003] In practical engineering, intelligent agents are limited by their own capabilities and the conditions of the communication network. If continuous sampling communication is required between agents, they will need to compete for resources, which can lead to data loss or communication paralysis. To address this problem, event-triggered mechanisms have emerged. However, traditional triggering mechanisms require regular communication and control updates regardless of the system state, which can easily lead to a large amount of redundant communication. Summary of the Invention

[0004] Based on this, it is necessary to provide a trajectory tracking consistency method for nonlinear heterogeneous multi-agent systems to address the above technical issues. This method can solve the communication cost problem when nonlinear heterogeneous multi-agent systems perform trajectory tracking consistency.

[0005] The present invention adopts the following technical solutions:

[0006] The present invention provides a trajectory tracking consistency method for a nonlinear heterogeneous multi-agent system, comprising:

[0007] Using graph theory, we construct a communication topology for a nonlinear heterogeneous multi-agent system. This system consists of a leader agent and multiple follower agents. The leader agent generates the desired trajectory, which is the desired trajectory that the follower agents are required to achieve.

[0008] Based on the dynamic motion model of the follower agent, a consistency control protocol is constructed; the consistency control protocol is a control strategy that drives the states of multiple follower agents to reach a consistent state; the state includes dynamic variables;

[0009] In the process of multiple follower agents communicating with each other through the communication topology graph, for each of the multiple follower agents, the state and expected trajectory of the neighbor follower agent are obtained. When the event triggers the control strategy that satisfies the distributed control law, the state of the follower agent is updated according to the state, expected trajectory and consistency control protocol of the neighbor follower agent, and the consistency of the follower agent trajectory tracking is achieved through the distributed control law within the preset time.

[0010] Preferably, a consistency control protocol is constructed based on the dynamic motion model of the follower agent, specifically including:

[0011] Obtain the tracking error between the follower agent and the desired trajectory based on the dynamic motion model of the follower agent;

[0012] The consistency error is defined based on the tracking error; the consistency error is the state error between the communication topology, tracking error and follower agent;

[0013] Design a time-varying scaling function and map the consistency error tracking problem from infinite time to a finite time interval based on the time-varying scaling function;

[0014] Using the adaptive backstepping method and the Lyapunov stability theorem, a virtual control variable is designed. An adaptive law is introduced to deal with the uncertainty of the state of the follower agent in the nonlinear heterogeneous multi-agent system, and the distributed control law of the nonlinear heterogeneous multi-agent system is obtained by backstepping.

[0015] The distributed control law is determined as a consistency control protocol; the consistency control protocol achieves the consistency of the follower agent's trajectory tracking within a finite time interval.

[0016] Preferably, the time-varying scaling function is:

[0017]

[0018] in, is the calculation result of the time-varying function, t0 is the initial time, l≥max{2,n} is an arbitrarily defined real number, T p is the preset time, v satisfies 0 <v<T P is a constant, and n is the order.

[0019] Preferably, the formula of the distributed control law is:

[0020]

[0021] Among them, Δ i (t) is a computable parameter, k i,n is the control gain parameter, c i,nTo adjust the parameters, is a constant, r i,n To adjust the parameters, ζ i,n is a constant, h is a proportional factor, is the parameter estimate, is a computable bounded function, r i,n To adjust the parameters, is a computable bounded function, r j,n To adjust the parameters, is a computable bounded function, is the time-varying scaling function, z i,n is the error variable, is the estimated parameter, l is a real number arbitrarily defined by the user, n is the order of the nonlinear heterogeneous multi-agent system, β i,n-1 is the derivative of the virtual controller with respect to the estimated parameters, τ is a positive scaling parameter, and δ i,n (T) is the computable control action softening unit, To control the gain parameter, is a constant, β i,n-1 is the derivative of the virtual controller with respect to the estimated parameters, To estimate the parameters, m is the order. is the estimated parameter, α i,n-1 is the virtual controller, n is the order, is a computable bounded function, is the m+1 order derivative of the reference trajectory,

[0022] Preferably, the state of the follower agent is updated according to the state of the neighbor follower agent, the desired trajectory and the consistency control protocol, and the consistency of the follower agent trajectory tracking is achieved through the distributed control law within a preset time, specifically including:

[0023] Inputting the relative state of each follower agent to the states of its neighboring follower agents into the consensus control protocol;

[0024] When an event that satisfies the distributed control law triggers a control strategy, the relative state is updated through the distributed control law to drive the state of the follower agent to converge to the desired trajectory;

[0025] The distributed control law is adjusted by the reference trajectory derivative term and the local error suppression term in the consistency control protocol so that the state of the nonlinear heterogeneous multi-agent system can achieve consistency in the trajectory tracking of the follower agents within a preset time; the local error suppression term is the error between each follower and its neighbors and the error between the follower agent and the desired trajectory.

[0026] Preferably, when the follower agent is a first-order agent, the dynamic variable is position; when the follower agent is a second-order agent, the dynamic variables are position and velocity; when the follower agent is a third-order agent, the dynamic variables are position and acceleration.

[0027] Preferably, the communication topology is represented by a directed graph; the directed graph is:

[0028]

[0029] in, represents the vertex set of multiple follower agents, N is the number of follower agents, ε represents the edge set between the i-th follower agent and the j-th follower agent, Represents a directed graph The adjacency matrix of For a directed graph, when When a i,j >0; when a i,j =0,a i,j = 0 means there is no communication between the i-th follower agent and the j-th follower agent, a i,j >0 indicates that there is communication between the i-th follower agent and the j-th follower agent.

[0030] Preferably, the dynamic motion model of the follower agent is:

[0031]

[0032] in, is the derivative of the state vector of the oth order of the ith follower agent, is the derivative of the state vector of the nth order of the ith follower agent, is the system state of the i-th follower agent, is the state vector of the ith follower agent, n is the order, N is the number of follower agents, is the control input of the nonlinear heterogeneous multi-agent system, is the output of the nonlinear heterogeneous multi-agent system, is an unknown non-vanishing smooth function, is the unknown time-varying control gain, di,o (t)(o=1,…,n) is the unknown time-varying external interference, t is the time, represents the unknown time-varying control gain, represents the concentrated uncertainty, which is an unknown non-vanishing smooth function, d i,n (t) represents the unknown time-varying external interference, x i,1 represents the output variable of agent i, R is a set of real numbers, x i,o+1 (t) is the state vector of the i-th follower agent of order o+1.

[0033] Preferably, the formula corresponding to the event-triggered control strategy of the distributed control law is:

[0034]

[0035] Among them, t k Indicates the triggering time, t k+1 Indicates the next trigger moment, E i (t) = Δ i (t)-u i (t) represents the measurement error, inf represents the infimum, and h1 is the trigger interval.

[0036] The present invention provides a trajectory tracking consistency device for a nonlinear heterogeneous multi-agent system, comprising:

[0037] A building module is used to construct a communication topology graph for a nonlinear heterogeneous multi-agent system using graph theory knowledge. The nonlinear heterogeneous multi-agent system includes a leader agent and multiple follower agents. The leader agent is used to generate a desired trajectory, which is the desired trajectory that the multiple follower agents are required to achieve.

[0038] Design module for building a consistent control protocol based on the dynamic motion model of the follower agent; the consistent control protocol is a control strategy that drives the states of multiple follower agents to reach a consistent state; the state includes dynamic variables;

[0039] The consistency module is used to obtain the state and expected trajectory of neighboring follower agents for each of the multiple follower agents during the process of multiple follower agents communicating with each other through the communication topology graph. When the event triggers the control strategy that satisfies the distributed control law, the state of the follower agent is updated according to the state, expected trajectory and consistency control protocol of the neighboring follower agents, and the consistency of the follower agent trajectory tracking is achieved through the distributed control law within a preset time.

[0040] The present invention provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, it implements the above-mentioned trajectory tracking consistency method of a nonlinear heterogeneous multi-agent system.

[0041] The present invention provides a computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the method for trajectory tracking consistency of a nonlinear heterogeneous multi-agent system is implemented.

[0042] At least one of the above technical solutions adopted by the present invention can achieve the following beneficial effects:

[0043] Utilizing graph theory knowledge, a communication topology diagram of a nonlinear heterogeneous multi-agent system is constructed; a dynamic model of multiple follower agents is constructed, and according to the initial conditions of the dynamic model, a consistency control protocol based on preset time trajectory tracking is designed; multiple follower agents communicate with each other through the communication topology diagram. The present invention is based on event triggering, which avoids unnecessary data transmission, significantly reduces communication frequency, and greatly saves communication costs; during the communication process, for each of the multiple follower agents, the dynamic variables and expected trajectory information of the neighboring follower agents are obtained, and the dynamic variables of the follower agents are updated according to the consistency control protocol. The consistency of the follower agent trajectory tracking is achieved through the distributed preset time event triggering controller within the preset time. The present invention can achieve trajectory tracking consistency within the preset time for nonlinear heterogeneous multi-agent systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0045] Figure 1 A schematic flow chart of a trajectory tracking consistency method for a nonlinear heterogeneous multi-agent system provided by the present invention;

[0046] Figure 2 A schematic diagram of a trajectory tracking consistency device for a nonlinear heterogeneous multi-agent system provided by the present invention;

[0047] Figure 3 Schematic diagram of a computer device for implementing a trajectory tracking consistency method for a nonlinear heterogeneous multi-agent system provided by the present invention. DETAILED DESCRIPTION

[0048] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with specific embodiments of the present invention and corresponding drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0049] Devices such as desktop computers, servers, and laptop computers that can execute the solution of the present invention are described below with the server as the execution subject for the sake of convenience.

[0050] Convergence speed is an important indicator for evaluating the quality of consistency algorithms. Faster convergence speed means better performance. Therefore, researchers have studied the time convergence problem in consistency control. The convergence time of the finite time algorithm depends on the initial conditions, while the convergence time of the fixed time algorithm does not depend on the initial conditions. It depends on the system parameters and cannot be randomly given by the user. Therefore, preset time control is proposed. Preset time trajectory tracking consistency can help nonlinear heterogeneous multi-agent systems complete trajectory tracking within a given time, greatly improving the overall efficiency of nonlinear heterogeneous multi-agent systems. This method is particularly important for time-sensitive tasks, such as emergency rescue and drone formations. The present invention achieves trajectory tracking consistency within a preset time.

[0051] The technical solutions provided by various embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0052] Figure 1 The figure is a flow chart of a trajectory tracking consistency method for a nonlinear heterogeneous multi-agent system in the present invention, which specifically includes the following steps:

[0053] S101: Using graph theory knowledge, construct a communication topology diagram for a nonlinear heterogeneous multi-agent system; the nonlinear heterogeneous multi-agent system includes a leader agent and multiple follower agents; the leader agent is used to generate a desired trajectory; the desired trajectory is the desired trajectory that multiple follower agents are required to achieve.

[0054] Specifically, a communication topology graph of a nonlinear heterogeneous multi-agent system is constructed through the vertex sets of multiple follower agents, the edge sets between follower agents, and the adjacency matrix.

[0055] In an exemplary embodiment, the communication topology of the nonlinear heterogeneous multi-agent system is represented by a directed graph; the directed graph is shown in formula (1):

[0056]

[0057] in, Represents the vertex set of multiple agent followers, N is the number of agent followers, ε represents the edge set between the followers of the i-th agent and the followers of the j-th agent, Represents a directed graph The adjacency matrix of For a directed graph, when When a i,j >0; when a i,i =0;a i,j Indicates whether there is communication between the i-th agent follower and the j-th agent follower.

[0058] The Laplace matrix corresponding to the directed graph is shown in formula (2):

[0059]

[0060] in, is the Laplace matrix, is the in-degree matrix, For a directed graph The adjacency matrix of , when i = j, When i≠j, is a set of N×N real matrices.

[0061] The in-degree matrix is shown in formula (3):

[0062]

[0063] in, is the in-degree matrix, diag represents the diagonal matrix, d1 is the total amount of information received by the first follower agent from the rest of the follower agents, is the total amount of information received by the Nth follower agent from the rest of the follower agents.

[0064] Specifically, an adjacency matrix and a Laplace matrix are determined according to a communication topology graph of a nonlinear heterogeneous multi-agent system.

[0065] S102: Based on the dynamic motion model of the follower agent, a consistency control protocol is constructed; the consistency control protocol is a control strategy that drives the states of multiple follower agents to reach a consistent state; the state includes dynamic variables.

[0066] In an exemplary embodiment, a consistency control protocol is constructed based on the dynamic motion model of the follower agent, specifically including: obtaining the tracking error between the follower agent and the desired trajectory based on the dynamic motion model of the follower agent; and defining the consistency error based on the tracking error; the consistency error is the state error between the communication topology, the tracking error and the follower agent; designing a time-varying scaling function, and mapping the tracking problem of the consistency error from infinite time to a finite time interval based on the time-varying scaling function; utilizing the adaptive backstepping method, according to the Lyapunov stability theorem, designing a virtual control quantity, and introducing an adaptive law to deal with the uncertainty of the state of the follower agent in the nonlinear heterogeneous multi-agent system, and performing inverse deduction to obtain the distributed control law of the nonlinear heterogeneous multi-agent system; determining the distributed control law as a consistency control protocol; the consistency control protocol achieves consistency in the trajectory tracking of the follower agent within a finite time interval.

[0067] In an exemplary embodiment, the dynamic model of the follower agent is shown in formula (4):

[0068]

[0069] in, is the derivative of the state vector of the oth order of the ith follower agent, is the derivative of the state vector of the nth order of the ith follower agent, is the system state of the i-th follower agent, is the state vector of the ith follower agent, n is the order, N is the number of follower agents, is the control input of the nonlinear heterogeneous multi-agent system, is the output of the nonlinear heterogeneous multi-agent system, is an unknown non-vanishing smooth function, is the unknown time-varying control gain, d i,o (t)(o=1,…,n) is the unknown time-varying external interference, t is the time, represents the unknown time-varying control gain, represents the concentrated uncertainty, which is an unknown non-vanishing smooth function, d i,n (t) represents the unknown time-varying external interference, x i,1 represents the output variable of agent i, R is a set of real numbers, x i,o+1 (t) is the state vector of the i-th follower agent of order o+1.

[0070] The time-varying function is shown in formula (5):

[0071]

[0072] in, is the calculation result of the time-varying function, t0 is the initial time, l≥max{2,n} is an arbitrarily defined real number, T p is the preset time, v satisfies 0 <v<T P is a constant, and n is the order.

[0073] The formula of the distributed control law is:

[0074]

[0075] Among them, Δ i (t) is a computable parameter, k i,n is the control gain parameter, c i,n To adjust the parameters, is a constant, r i,n To adjust the parameters, ζ i,n is a constant, h is a proportional factor, is the parameter estimate, is a computable bounded function, r i,n To adjust the parameters, is a computable bounded function, r j,n To adjust the parameters, is a computable bounded function, is the time-varying scaling function, z i,n is the error variable, is the estimated parameter, l is a real number arbitrarily defined by the user, n is the order of the nonlinear heterogeneous multi-agent system, β i,n-1 is the derivative of the virtual controller with respect to the estimated parameters, τ is a positive scaling parameter, and δ i,n (T) is the computable control action softening unit, To control the gain parameter, is a constant, β i,n-1 is the derivative of the virtual controller with respect to the estimated parameters, To estimate the parameters, m is the order. is the estimated parameter, α i,n-1 is the virtual controller, n is the order, is a computable bounded function, is the m+1 order derivative of the reference trajectory,

[0076] S103: In the process of multiple follower agents communicating with each other through the communication topology graph, for each of the multiple follower agents, the state and expected trajectory of the neighbor follower agent are obtained. When the event triggers the control strategy that satisfies the distributed control law, the state of the follower agent is updated according to the state, expected trajectory and consistency control protocol of the neighbor follower agent, and the consistency of the follower agent trajectory tracking is achieved through the distributed control law within a preset time.

[0077] Each agent uses the communication topology to determine its neighboring agents, which are directly connected to it. During the communication process, the agent can obtain the state information of the neighboring agents, such as location, speed, posture, etc.

[0078] In an exemplary embodiment, the state of the follower agent is updated according to the state of the neighbor follower agent, the desired trajectory and the consistency control protocol, and the consistency of the follower agent trajectory tracking is achieved through the distributed control law within a preset time, specifically including: inputting the relative state between the state of each follower agent and the state of the neighbor follower agent into the consistency control protocol; when an event that satisfies the distributed control law triggers a control strategy, the relative state is updated through the distributed control law to drive the state of the follower agent to converge to the desired trajectory; the distributed control law is adjusted through the reference trajectory derivative term and the local error suppression term in the consistency control protocol, so that the state of the nonlinear heterogeneous multi-agent system achieves the consistency of the follower agent trajectory tracking within a preset time; the local error suppression term is the error between each follower and its neighbor and the error part between the follower agent and the desired trajectory.

[0079] Specifically, the tracking agent updates and adjusts its state based on the information it receives from neighboring tracking agents and the consistency control protocol. For example, in formation control, the follower agent adjusts its motion state based on the position and velocity information of neighboring agents to maintain the desired formation shape or complete a specific task.

[0080] Specifically, most of the current research on the preset time of heterogeneous multi-agent systems is focused on linear multi-agents, while the present invention targets nonlinear heterogeneous multi-agent systems and considers unknown time-varying control gains, achieving trajectory tracking consistency within the preset time.

[0081] In an exemplary embodiment, the formula corresponding to the event triggering control strategy of the distributed preset time event triggering controller is shown in formula (7):

[0082]

[0083] Among them, t kIndicates the triggering time, t k+1 Indicates the next trigger moment, E i (t) = Δ i (t)-u i (t) represents the measurement error, inf represents the infimum, and h1 is the trigger interval.

[0084] In an exemplary embodiment, the controller is designed by first performing a coordinate transformation, as shown in formula (8):

[0085]

[0086] Where q = 2, 3, ..., n, It is a virtual controller. is the consistency error of the ith agent, is the error variance of the ith agent.

[0087] Let T = T p +t0-ν, the discussion is mainly divided into two parts: t∈[t0,T) and t∈[T,+∞).

[0088] Part 1: t∈[t0,T).

[0089] Step 1: For the i-th agent, select the Lyapunov function of the first step. The Lyapunov function is shown in formula (9);

[0090]

[0091] Among them, V i,1 is the Lyapunov function, represents the parameter estimation error, It is the parameter estimated value.

[0092] According to the Lyapunov stability theorem, the virtual controller α of the i-th agent is designed i,1 , α i,1 As shown in formula (10):

[0093]

[0094] The corresponding adaptive law is shown in formula (11):

[0095]

[0096] Among them, k i,1 >0 is the control gain parameter, To adjust the parameters,

[0097] is a constant, is a constant.

[0098] Step 2: For the i-th follower, design the Lyapunov function of the second step. The Lyapunov function of the second step is shown in formula (12):

[0099]

[0100] According to the Lyapunov stability theorem, the virtual controller α is designed i,2 As shown in formula (13):

[0101]

[0102] The corresponding adaptive law is shown in formula (14):

[0103]

[0104] in, It is the parameter The estimated value of k i,2 >0 is the control gain parameter, To adjust the parameters, is a constant, is a constant.

[0105] Step q (q = 3, ..., n-1), select the Lyapunov function of step q as shown in formula (15):

[0106]

[0107] Recursively obtain the virtual controller α i,q (q=3,...,n-1) as shown in formula (16):

[0108]

[0109] The corresponding adaptive law is shown in formula (17):

[0110]

[0111] in, is the derivative of the virtual controller with respect to the estimated parameters, k i,q >0 is the control gain parameter, To adjust the parameters, is a constant, is a constant, is a computable bounded function,

[0112]

[0113] is a computable bounded function.

[0114] Step n: Select the Lyapunov function of step n as shown in formula (18):

[0115]

[0116] The designed adaptive law is as shown in formula (19):

[0117]

[0118] in is an unknown virtual constant,

[0119] Part 2: t∈[T,+∞).

[0120] Virtual Controller α i,1 Same as in the first part. It should be noted that in the conventional backstepping design, repeated differentiation of the virtual controller is involved. In the second part, the function The definition of is a constant, so its derivative is 0, which will affect the design of the virtual control strategy. The definition of the computable control action softening unit is shown in formula (20):

[0121]

[0122] To compensate for the discontinuity of the control input at time t = T, the designed virtual controller is shown in formula (21):

[0123]

[0124] Among them, q=2,…,n-1 is the order.

[0125] The actual controller designed is shown in formula (22):

[0126]

[0127] in,

[0128]

[0129] The corresponding adaptive law is shown in formula (23):

[0130]

[0131] Where, q=2,…,n, is an unknown virtual constant,

[0132] Theoretical analysis.

[0133] Part 1: t∈[t0,T)

[0134] Case 1: At the time t when two events are triggered k and t k+1 Between, that is, t∈[t k ,t k+1 ), analyze the stability of the system, and prove that the output signal y(t) can track the target trajectory within the preset time.

[0135] For the i-th agent, the total Lyapunov function is selected as shown in formula (24):

[0136]

[0137] The derivative of formula (24) can be obtained as shown in formula (25):

[0138]

[0139] in, is a finite positive constant k i,m >0 is the control gain parameter, To adjust the parameters, is a constant, is a constant,

[0140] Case 2: When t = t k+1 , proving the stability of the system.

[0141] According to the event trigger control strategy and event trigger mechanism, there is u i =Δ i (t k+1 ), the derivative of the total Lyapunov function is shown in formula (26):

[0142]

[0143] in,

[0144] Further analysis is similar to case 1, and it is concluded that at t k+1 The moment is also valid. k ,t k+1 ]The analysis other than that will repeat the process of Case 1 and Case 2.

[0145] Part 2: t∈[T,+∞)

[0146] It is proved that the system target trajectory tracking consistency can be maintained after exceeding the preset time.

[0147] First, we prove that the control strategy is continuous at time t = T. According to the control action softening unit δ defined in (53), i,q (T), we get the formula (27):

[0148]

[0149] Therefore, it is explained that α i,q (q=2,…,n-1) is continuous at time t=T. Similar to formula (27), it can be explained that Δ i Continuous at time t = T. In addition, it can be inferred that the control action softening unit δ i,q (T) is a finite constant.

[0150] The convergence of the system in the interval [T,+∞). Only need to deal with According to Young's inequality, where λ i,m (m=2,…,n) is an arbitrarily given constant.

[0151] Therefore, we can get the following formula (28):

[0152]

[0153] in, is a finite positive constant, k i,m >λ i,m >0,

[0154] For event-triggered control strategies, E i (t) = Δ i (t)-u i (t), There is {t k+1 -t k}≥t * .

[0155] Therefore, we can get the following formula (29):

[0156]

[0157] in, Is a continuous function, applicable to nth order and the nth-order continuous function d r , considering Contains bounded signal z i,q and but δ>0 is a constant. This shows that Zeno's behavior was successfully avoided.

[0158] When applying the trajectory tracking consistency method of a nonlinear heterogeneous multi-agent system provided by the present invention, it is not necessary to Figure 1 The steps are executed in the order shown. The specific execution order of the steps can be determined according to needs, and the present invention does not limit this.

[0159] The above is a trajectory tracking consistency method for a nonlinear heterogeneous multi-agent system provided by one or more embodiments of the present invention. Based on the same idea, the present invention also provides a corresponding trajectory tracking consistency device for a nonlinear heterogeneous multi-agent system, such as Figure 2 shown.

[0160] Figure 2 A schematic diagram of a trajectory tracking consistency device for a nonlinear heterogeneous multi-agent system provided by the present invention includes:

[0161] The construction module 201 is used to construct a communication topology graph of a nonlinear heterogeneous multi-agent system using graph theory knowledge; the nonlinear heterogeneous multi-agent system includes a leader agent and multiple follower agents.

[0162] The design module 202 is used to construct a dynamic model of multiple follower agents and design a consistency control protocol based on preset time trajectory tracking according to the initial conditions of the dynamic model.

[0163] The consistency module 203 is used to obtain the dynamic variables and expected trajectory information of the neighbor follower agents for each of the multiple follower agents during the communication process, and update the dynamic variables of the follower agents according to the consistency control protocol, so as to achieve the consistency of the follower agent trajectory tracking through the distributed preset time event triggering controller within the preset time.

[0164] Regarding the specific definition of a trajectory tracking consistency device for a nonlinear heterogeneous multi-agent system, please refer to the definition of a trajectory tracking consistency method for a nonlinear heterogeneous multi-agent system above, which will not be repeated here. The various modules in the above-mentioned trajectory tracking consistency device for a nonlinear heterogeneous multi-agent system can be implemented in whole or in part by software, hardware and a combination thereof. The above-mentioned modules can be embedded in or independent of the processor in the computer device in the form of hardware, or can be stored in the memory of the computer device in the form of software, so that the processor can call and execute the operations corresponding to the above modules.

[0165] The present invention also provides a computer-readable storage medium, which stores a computer program, which can be used to execute the above Figure 1A trajectory tracking consistency method for nonlinear heterogeneous multi-agent systems is provided.

[0166] The present invention also provides Figure 3 The structural diagram of the computer equipment shown in FIG. Figure 3 As shown in the figure, at the hardware level, the computer device includes a processor, an internal bus, a network interface, a memory, and a non-volatile memory. Of course, it may also include other hardware required for the business. The processor reads the corresponding computer program from the non-volatile memory into the memory and then runs it to achieve the above Figure 1 A trajectory tracking consistency method for nonlinear heterogeneous multi-agent systems is provided.

[0167] Those skilled in the art will appreciate that all or part of the processes in the above-mentioned embodiment methods can be implemented by instructing the relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided by the present invention can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory or optical memory, etc. Volatile memory can include random access memory (RAM) or external cache memory. As an illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).

[0168] The technical features of the above embodiments can be combined arbitrarily. In order to make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of the present invention.

Claims

1. A trajectory tracking consistency method for nonlinear heterogeneous multi-agent systems, characterized by: include: Using graph theory knowledge, construct the communication topology graph of nonlinear heterogeneous multi-agent systems; The nonlinear heterogeneous multi-agent system includes a leader agent and multiple follower agents; the leader agent is used to generate a desired trajectory; the desired trajectory is the desired trajectory that the multiple follower agents are required to achieve; Based on the dynamic motion model of the follower agent, a consistency control protocol is constructed; the consistency control protocol is a control strategy that drives the states of multiple follower agents to reach a consistent state; the states include dynamic variables; In the process of multiple follower agents communicating with each other through the communication topology graph, for each of the multiple follower agents, the state of the neighbor follower agent and the expected trajectory are obtained. When an event that satisfies the distributed control law triggers a control strategy, the state of the follower agent is updated according to the state of the neighbor follower agent, the expected trajectory and the consistency control protocol, and the consistency of the follower agent trajectory tracking is achieved through the distributed control law within a preset time.

2. The method according to claim 1, wherein Based on the dynamic motion model of the follower agent, a consistency control protocol is constructed, which specifically includes: Obtaining a tracking error between the follower agent and the desired trajectory according to a dynamic motion model of the follower agent; and defining a consistency error based on the tracking error; the consistency error being a state error between the communication topology graph, the tracking error, and the follower agent; Designing a time-varying scaling function, and mapping the tracking problem of the consistency error from infinite time to a finite time interval according to the time-varying scaling function; Using the adaptive backstepping method and the Lyapunov stability theorem, a virtual control variable is designed. An adaptive law is introduced to deal with the uncertainty of the state of the follower agent in the nonlinear heterogeneous multi-agent system, and the distributed control law of the nonlinear heterogeneous multi-agent system is obtained by backstepping. The distributed control law is determined as the consistency control protocol; the consistency control protocol achieves consistency in the trajectory tracking of the follower intelligent agent within a limited time interval.

3. The method according to claim 2, wherein The time-varying scaling function is: in, is the calculation result of the time-varying function, t0 is the initial time, l≥max{2,n} is an arbitrarily defined real number, T p is the preset time, v satisfies 0 <v<T P is a constant, and n is the order.

4. The method according to claim 2, wherein The formula of the distributed control law is: Among them, Δ i (k) is a computable parameter, k i,n is the control gain parameter, c i,n To adjust the parameters, is a constant, r i,n To adjust the parameters, ζ i,n is a constant, h is a proportional factor, is the parameter estimate, is a computable bounded function, r i,n To adjust the parameters, is a computable bounded function, r j,n To adjust the parameters, is a computable bounded function, is the time-varying scaling function, z i,n is the error variable, is the estimated parameter, l is a real number arbitrarily defined by the user, n is the order of the nonlinear heterogeneous multi-agent system, β i,n-1 is the derivative of the virtual controller with respect to the estimated parameters, τ is a positive scaling parameter, and δ i,n (T) is the computable control action softening unit, To control the gain parameter, is a constant, β i,n-1 is the derivative of the virtual controller with respect to the estimated parameters, To estimate the parameters, m is the order. is the estimated parameter, α i,n-1 is the virtual controller, n is the order, is a computable bounded function, is the m+1 order derivative of the reference trajectory, 5. The method according to claim 4, wherein The updating of the state of the follower agent according to the state of the neighbor follower agent, the desired trajectory and the consistency control protocol, and achieving the consistency of the follower agent trajectory tracking through the distributed control law within a preset time, specifically includes: inputting the relative state of each follower agent to the state of neighboring follower agents into the consensus control protocol; When an event that satisfies the distributed control law triggers a control strategy, the relative state is updated through the distributed control law to drive the state of the follower agent to converge to the desired trajectory; The distributed control law is adjusted by the reference trajectory derivative term and the local error suppression term in the consistency control protocol so that the state of the nonlinear heterogeneous multi-agent system can achieve consistency in the trajectory tracking of the follower agents within a preset time; the local error suppression term is the error between each follower and its neighbor and the error part between the follower agent and the desired trajectory.

6. The method according to claim 1, wherein When the follower agent is a first-order agent, the dynamic variable is position; when the follower agent is a second-order agent, the dynamic variables are position and velocity; when the follower agent is a third-order agent, the dynamic variables are position and acceleration.

7. The method according to claim 1, wherein The communication topology diagram is represented by a directed graph; the directed graph is: in, represents the vertex set of multiple follower agents, N is the number of follower agents, ε represents the edge set between the i-th follower agent and the j-th follower agent, Represents a directed graph The adjacency matrix of For a directed graph, when When a i,j >0; when a i,j =0,a i,j = 0 means there is no communication between the i-th follower agent and the j-th follower agent, a i,j >0 indicates that there is communication between the i-th follower agent and the j-th follower agent.

8. The method according to claim 1, wherein The dynamic motion model of the follower agent is: and i =x i,1 in, is the derivative of the state vector of the oth order of the ith follower agent, is the derivative of the state vector of the nth order of the ith follower agent, is the system state of the i-th follower agent, is the state vector of the ith follower agent, n is the order, N is the number of follower agents, is the control input of the nonlinear heterogeneous multi-agent system, is the output of the nonlinear heterogeneous multi-agent system, is an unknown non-vanishing smooth function, is the unknown time-varying control gain, d i,o (t)(o=1,…,n) is the unknown time-varying external interference, t is the time, represents the unknown time-varying control gain, represents the concentrated uncertainty, which is an unknown non-vanishing smooth function, d i,n (t) represents the unknown time-varying external interference, x i,1 represents the output variable of agent i, R is a set of real numbers, x i,o+1 (t) is the state vector of the i-th follower agent of order o+1.

9. The method according to claim 1, wherein The formula corresponding to the event-triggered control strategy of the distributed control law is: Among them, t k Indicates the triggering time, t k+1 Indicates the next trigger moment, E i (t) = Δ i (t)-u i (t) represents the measurement error, inf represents the infimum, and h1 is the trigger interval.

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