A multi-agent sampling event-triggered collaborative tracking control method based on cross-species bionics

Abstract

The present invention belongs to the technical field related to multi-agent cluster control, and specifically relates to a multi-agent sampling event-triggered collaborative tracking control method based on cross-species bionics, including: proposing a cross-species bionic representation of a multi-agent system model, realizing the collaborative tracking control effect of the multi-agent system, and improving the biological interpretability and reliability of the control strategy. In addition, three sets of distributed multi-agent sampling event trigger information transmission mechanisms are proposed, which require each agent to monitor its own target agent system parameters and system state estimation values ​​in a discrete first non-periodic sampling sequence and make judgments based on errors, and monitor its own output state value and control protocol in a discrete second non-periodic sampling sequence and make judgments based on errors. If the predetermined three sets of event trigger conditions are met, the information at this moment is transmitted. The present invention can achieve the purpose of efficiently realizing collaborative tracking control under limited computing resources and communication resources.

Description

Technical Field

[0001] The present invention belongs to the technical field related to multi-agent cluster control, and more specifically, relates to a multi-agent sampling event-triggered collaborative tracking control method based on cross-species bionics. Background Art

[0002] In recent years, with the rapid development of artificial intelligence technology, the distributed cooperative control of multi-agent systems has attracted a lot of attention due to its wide application in fields such as robot clusters, unmanned vehicle platoons and microgrids. The consistency problem is the core of the research on multi-agent collaboration. Its main goal is to design distributed control protocols so that all agents tend to be the same or track the state evolution of the leader. This can not only complete complex tasks efficiently, but also provide new ideas for understanding and simulating group behavior in nature. In order to complete complex tasks in an open environment, the composition of multi-agent systems is usually heterogeneous and uncertain, the communication environment they face is usually non-ideal, and their dynamic models are often high-order nonlinear.

[0003] In the process of realizing heterogeneous multi-agent collaboration, information exchange and control updates between agents are essential steps. The microprocessor embedded in each follower agent is responsible for receiving information from neighbors and sending its own information, and updating the control protocol according to the set rules. However, due to bandwidth and energy limitations, the agent's processor cannot work continuously in most engineering scenarios. Therefore, the use of event-triggered working mode can save communication resources and reduce the control updates of actuators. However, many existing event-triggered mechanisms require continuous monitoring of the system status, which not only leads to a large waste of computing resources, but also fails to avoid the problem of continuous operation of the agent processor.

[0004] In the process of dealing with high-order heterogeneous multi-agent systems, the existing mainstream method is to design a backstepping control protocol based on full state information. However, this method requires the agent to transmit and monitor all internal information in real time, which is not easy to achieve in practical applications and greatly increases the information transmission burden of the system. In addition, the virtual controller designed based on backstepping and event triggering often causes huge computational complexity and abnormal operation problems during execution due to complex structure and non-differentiability. In short, the existing methods are difficult to efficiently cope with the challenges brought by non-ideal communication environments and complex dynamic models to multi-agent collaborative control. Therefore, how to develop collaborative control of heterogeneous high-order multi-agent systems that saves computing and communication resources is an urgent problem to be solved. Summary of the invention

[0005] In response to the above defects or improvement needs of the prior art, the present invention provides a multi-agent sampling event-triggered collaborative tracking control method based on cross-species bionics, which aims to efficiently realize collaborative tracking control under limited computing and communication resources.

[0006] To achieve the above-mentioned purpose, according to one aspect of the present invention, a multi-agent sampling event-triggered collaborative tracking control method based on cross-species bionics is provided, wherein the dynamic equation of each follower agent is pre-modeled as a high-order dynamic equation with a structural form equivalent to a food chain mathematical model, and as a food chain mathematical model, the food chain mathematical model of all agents and a directed graph describing the communication and connectivity relationship between multiple agents constitute a cross-species food chain model, thereby obtaining a cross-species bionic representation of the multi-agent system model, and overall collaborative tracking is achieved through communication between the follower agents, and each follower agent controls its own tracking of the target agent in the following manner:

[0007] Based on the error between the estimated value of the same system information of the target agent transmitted by the neighbor agent at the most recent trigger and the estimated value of the same system information of the target agent at the most recent trigger, the estimation curve of the system information is calculated; according to the difference between the estimated value in the estimation curve at the current system information sampling moment and the estimated value of the system information estimated at the most recent trigger, the event trigger judgment of the system information at the sampling moment is performed, and the current estimated value of the system information that meets the judgment condition is transmitted to the neighbor agent; the system information is the system state and / or system parameters;

[0008] According to the error between the output state sampled at the current output state sampling moment and the output state of the self used for the estimation of the self internal state at the most recent trigger, an event trigger judgment is performed on the output state of the self at the sampling moment, and the output state of the self that meets the judgment condition is used for iterative calculation to determine the estimated value of the self internal state; based on the error between the estimated value of the self output state in the determined estimated value of the self internal state and the estimated value of the system output state in the estimated value of the system state transmitted to the neighboring intelligent body at the most recent trigger, the estimated value of the uncertain parameter in the self high-order dynamic equation is calculated; based on the estimated value of the self internal state, the estimated value of the system output state and the estimated value of the uncertain parameter, the control protocol of the self is calculated using the backstepping method;

[0009] According to the error between the control protocol sampled at the current control protocol sampling moment and the control protocol used for motion control last time, an event triggering judgment on the control protocol at the current control protocol sampling moment is performed, and the control protocol that meets the judgment conditions is used to control its own motion.

[0010] Furthermore, the high-order dynamics equation of each follower agent is a high-order dynamics equation whose structural form is equivalent to the food chain mathematical model, specifically:

[0011]

[0012] In the formula, Indicates i The following agent s dimensional state variables over time t The derivative of Indicates i The following agent s +1-dimensional state variable changes with time t, Indicates i a parameter vector following the agent's uncertain parameters, and Indicates i Follower Agent s The output state corresponding to the dimension state Two known nonlinear continuously differentiable functions of , Indicates i The following agent dimensional state variables over time t The derivative of Indicates i a control protocol that follows the agent over time; and Indicates i Follower Agent The output state corresponding to the dimension state Two known nonlinear continuously differentiable functions of ; Indicates i A self-output state that follows the agent over time; Indicates i The relationship between the first-dimensional state variables of a following agent and time t.

[0013] Furthermore, the event triggering judgment mechanism of each follower agent for transmitting the target agent system information evaluation value to the neighboring agent is:

[0014] ;

[0015] ;

[0016] ;

[0017] ;

[0018] ;

[0019] In the formula, Indicates i The time when the following agent triggers the first event, , respectively representing the i Each time an event is triggered by a following agent, an estimated value of system information is sent to the neighboring communicative agent at this sampling time; Indicates i The following agent at the sampling time The estimation error judgment function of the target agent system parameters, Indicates i The following agent at the sampling time Estimates of the target agent system parameters; Indicates i The following agent at the trigger time Estimates of the target agent system parameters; is a positive constant; Indicates i The following agent at the sampling time The estimation error judgment function of the target agent system state; Indicates i The following agent at the sampling time An estimate of the system state of the target agent; Indicates i The following agent at the sampling time Based on the time of the most recent event trigger Auxiliary variable of the target agent system state estimate, which is an intermediate parameter; it represents the continuous time starting from 0; Indicates i A non-periodic sampling time series of system information by the following agent, , represents the maximum sampling interval in the sampling time series of all agents, N represents the total number of follower agents in the multi-agent system, Indicates i The maximum sampling interval of the following agents, , , , L is the Laplace matrix, I is the identity matrix, P satisfy The matrix of Indicates the communication relationship between each follower agent and the target agent. The element value is 1 when communication is possible, otherwise it is 0.

[0020] Further, iIn the following agent, the observer used to calculate its own estimation curve of the system information is:

[0021]

[0022] In the formula, is a positive constant; Indicates i The following agent and j The communication coefficient between the following agents is 1 when communicating, otherwise it is 0; Indicates j The agent at the time of the most recent event trigger Estimates of the target agent system parameters; Indicates i The following agent at the time of the most recent event trigger Estimates of the target agent system parameters; Indicates i The derivatives of the follower agents’ estimates of the target agent’s system parameters;

[0023] Indicates i The derivative of the follower agent’s estimate of the target agent’s system state; Indicates i The following agent at the time of the most recent event trigger An estimate of the system state of the target agent; Indicates j The agent triggers the time at time based on the most recent event Auxiliary variables of the target agent system state estimate, which are intermediate parameters; Indicates i A following agent triggers the event at time Auxiliary variables of the target agent system state estimate are intermediate parameters.

[0024] Furthermore, each follower agent has an event triggering judgment mechanism for using its own output state for estimating its own internal state:

[0025] ;

[0026] ;

[0027] ;

[0028] ;

[0029] In the formula, Indicatesi The actual output state of the following agent at time, Indicates i The following agent at the trigger time The actual output state, and Respectively represent i The following agent k Second and k +1 trigger moment; Indicates i The following agent at the sampling time The actual output status of represents a positive constant;

[0030] Indicates i A non-periodic sampling time series of the following agent's output state, and Indicates i The maximum sampling interval in the second non-periodic sampling time series of the following agent, Should meet: , , , , , Represents a preset positive definite matrix The maximum eigenvalue of are preset constants related to the multi-agent system parameters generated during the proof process. include , include .

[0031] Further, i In a following agent, the observer used to iteratively calculate its own internal state estimate is:

[0032]

[0033] In the formula, Indicates i The following agent s The derivative of the estimated value of the dimensional state variable; Indicates i The following agent s +Estimated value of 1-dimensional state variable; Indicatesi The following agent s The observation gain corresponding to the dimensional state variable; Indicates i Follower agent triggers output state With the estimated output state The error of Indicates i The following agent s A known nonlinear continuous differentiable function corresponding to the dimensional state; Indicates i The following agent The derivative of the estimated value of the dimensional state variable; Indicates i The following agent The observation gain corresponding to the dimensional state variable; Indicates i The following agent A known nonlinear continuous differentiable function corresponding to the dimensional state; Indicates i An estimate of the first-dimension state variable of the following agent.

[0034] Further, i The implementation method of a follower agent using the backstepping method to calculate its own control protocol is:

[0035] ;

[0036] ;

[0037]

[0038]

[0039] ;

[0040] In the formula, Indicates i A virtual control protocol of the first dimension of the following agent; Indicates i The control gain corresponding to the first dimension virtual control protocol of the following agent; Indicates i The error between the estimated output state of the following agent and its estimated output state of the target agent. Indicates i The following agent's estimate of the uncertain parameters; Indicates i A known nonlinear continuous differentiable function corresponding to the following agent; Indicates i A known nonlinear continuous differentiable function corresponding to the first-dimensional state of the following agent; Indicates i The output state estimate of the following agent itself; Indicates i The observation gain corresponding to the first dimension state variable of the following agent; Indicates i an upper bound on the number of sensor failures of the following agent; Represents a preset positive constant; express The Lipschitz constant;

[0041] Indicates i Follower Agent s Dimensional virtual control protocol; Indicates i Follower Agent s The control gain corresponding to the virtual control protocol; Indicates i Follower Agent s The internal state estimate of the s The error of the auxiliary variable obtained by the dimensional virtual control protocol after passing through the filter; Indicates i Follower Agent s -1D internal state estimate and s -1D virtual control protocol error of auxiliary variables obtained after filtering; Indicates i The following agent s A known nonlinear continuous differentiable function corresponding to the dimensional state; Indicates i Follower Agent s -1D derivative of the auxiliary variable obtained by filtering the virtual control protocol; Indicates i The observation gain corresponding to the s-th dimension state variable of the following agent; express The Lipschitz constant;

[0042] Indicates i A follower agent-assisted control protocol; Indicates i The following agent targets The control gain corresponding to the auxiliary control protocol of the dimensional state variable; Indicates i Follower Agent The error between the estimated value of the dimensional internal state and the auxiliary variable obtained by the dimensional virtual control protocol after passing through the filter; Respectively represent i Follower Agent The internal state estimate of the The error of the auxiliary variable obtained by the dimensional virtual control protocol after passing through the filter; Indicates i The following agent A known nonlinear continuous differentiable function corresponding to the dimensional state; Indicates The auxiliary variable obtained by the virtual control protocol after passing through the filter; Indicates i The following agent The observation gain corresponding to the dimensional state variable; express The Lipschitz constant; Indicates i The following agent dimensional state variables.

[0043] Furthermore, each follower agent has an event triggering judgment mechanism for using the control protocol to control its own motion:

[0044] ;

[0045] ;

[0046] ;

[0047] ;

[0048] In the formula, represents a positive constant; Indicates i A control protocol for a following agent at time t; Indicates i The following agent at the trigger time Control protocols; Respectively represent i The following agent k Second and k +1 trigger moment; Indicatesi A non-periodic sampling time series of the following agent's own control protocol; Indicates i The following agent at the sampling time control protocol.

[0049] According to another aspect of the present invention, an intelligent agent is provided, which can implement the above-mentioned method steps of controlling itself to track a target intelligent agent when performing a multi-agent collaborative tracking task.

[0050] According to another aspect of the present invention, a multi-agent system is provided, which can implement the above-mentioned multi-agent sampling event-triggered collaborative tracking control method based on cross-species bionics when executing a multi-agent collaborative tracking task.

[0051] In general, compared with the prior art, the technical solution conceived by the present invention has the following beneficial effects:

[0052] 1. The present invention provides a multi-agent sampling event-triggered collaborative tracking control method and proposes three sets of distributed multi-agent sampling event-triggered information transmission mechanisms. The traditional event triggering mechanism requires continuous monitoring of state information, resulting in unnecessary waste of computing resources. The sampling event triggering mechanism designed by the present invention requires each agent to monitor its own estimated values ​​of the target agent system parameters and system state in the discrete first non-periodic sampling sequence and make judgments based on errors, and to monitor its own output state value and control protocol in the discrete second non-periodic sampling sequence and make judgments based on errors. If the predetermined three sets of event triggering conditions are met, the information at this moment is transmitted. This method can avoid continuous calculation and continuous communication, and naturally avoid Zeno behavior. The overall three triggering mechanisms can achieve the purpose of efficiently realizing collaborative tracking control under limited computing resources and communication resources.

[0053] 2. The present invention also proposes that the high-order dynamics equation of each follower agent is a high-order dynamics equation with a structural form equivalent to the food chain mathematical model. Through appropriate variable substitution, the present invention finds the structural equivalence between the high-order dynamics equation of each agent in the multi-agent system and the food chain mathematical model, gives biological meaning to the multi-agent system, realizes the cross-species bionic characterization of the multi-agent system model, and applies a reasonable control protocol to the multi-agent system based on the equivalent meaning of human intervention and multi-agent system control protocol in multiple food chains, realizes the collaborative tracking control effect of the multi-agent system, and improves the biological interpretability and reliability of the control strategy. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1It is a framework diagram of a multi-agent sampling event-triggered collaborative tracking control method based on cross-species bionics provided by an embodiment of the present invention.

[0055] Figure 2 It is an observation effect diagram of the distributed target observer provided by an embodiment of the present invention.

[0056] Figure 3 Trajectory diagram of output variables of a multi-agent system provided in an embodiment of the present invention.

[0057] Figure 4 Schematic diagram of three sets of event triggering time sequence values ​​provided for an embodiment of the present invention.

[0058] Figure 5 An evolution trajectory diagram of the feedback controller provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0059] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0060] Embodiment 1

[0061] A multi-agent sampling event-triggered collaborative tracking control method based on cross-species bionics is proposed. The dynamic equation of each follower agent is pre-modeled as a high-order dynamic equation with a structural form equivalent to the food chain mathematical model. As a food chain mathematical model, the food chain mathematical model of all agents and the directed graph describing the communication and connectivity relationship between multiple agents constitute a cross-species food chain model, and a cross-species bionic representation of the multi-agent system model is obtained. The overall collaborative tracking is achieved through communication between the follower agents. Each follower agent controls its own tracking of the target agent in the following ways, such as Figure 1 As shown:

[0062] Based on the error between the estimated value of the same system information of the target agent transmitted by the neighbor agent at the most recent trigger and the estimated value of the same system information of the target agent at the most recent trigger, the estimation curve of the system information is calculated; according to the difference between the estimated value in the estimation curve at the current system information sampling moment and the estimated value of the system information estimated at the most recent trigger, the event trigger judgment of the system information at the sampling moment is performed, and the current estimated value of the system information that meets the judgment condition is transmitted to the neighbor agent; the system information is the system state and / or system parameters;

[0063] According to the error between the output state sampled at the current output state sampling moment and the output state of the self used for the estimation of the self internal state at the most recent trigger, an event trigger judgment is performed on the output state of the self at the sampling moment, and the output state of the self that meets the judgment condition is used for iterative calculation to determine the estimated value of the self internal state; based on the error between the estimated value of the self output state in the determined estimated value of the self internal state and the estimated value of the system output state in the estimated value of the system state transmitted to the neighboring intelligent body at the most recent trigger, the estimated value of the uncertain parameter in the self high-order dynamic equation is calculated; based on the estimated value of the self internal state, the estimated value of the system output state and the estimated value of the uncertain parameter, the control protocol of the self is calculated using the backstepping method;

[0064] According to the error between the control protocol sampled at the current control protocol sampling moment and the control protocol used for motion control last time, an event triggering judgment on the control protocol at the current control protocol sampling moment is performed, and the control protocol that meets the judgment conditions is used to control its own motion.

[0065] Existing event triggering mechanisms are rarely installed on the entire channel of agent-agent, sensor-controller, and controller-actuator at the same time, which still causes unnecessary waste of resources. This embodiment provides a multi-agent sampling event-triggered collaborative tracking control method, which introduces three sets of distributed multi-agent sampling event triggering information transmission mechanisms, requiring each agent to monitor its own estimated values ​​of the target agent system parameters and system state in the discrete first non-periodic sampling sequence and make judgments based on errors, and to monitor its own output state value and control protocol in the discrete second non-periodic sampling sequence and make judgments based on errors. If the predetermined three sets of event triggering conditions are met, the information at this moment is transmitted. This method can avoid continuous calculation and continuous communication, and naturally avoid Zeno behavior. The overall three triggering mechanisms can achieve the purpose of efficiently realizing collaborative tracking control under limited computing resources and communication resources.

[0066] When actually designing the control method, firstly, a heterogeneous multi-agent system model corresponding to the control system to be controlled is established, in which each agent corresponds to an entity object in the control system to be controlled; based on the ODE model, a high-order dynamic equation of each agent in the heterogeneous multi-agent system is established to describe the relationship between physical quantities such as the position, velocity, acceleration and communication control protocol between agents; a directed graph is established to describe the communication connectivity relationship between multiple agents. Based on the structural equivalence of the agent's high-order dynamic equation and the mathematical model of a multi-species single food chain, considering that the mathematical model of the food chain has advantages such as asymptotic stability and persistence, the high-order dynamic equation of each agent in the multi-agent system model is regarded as a food chain mathematical model; the food chain mathematical model of all agents and the directed graph describing the communication connectivity relationship between multiple agents constitute a cross-species food chain model, and a cross-species bionic representation of the multi-agent system model is obtained, thereby giving the following preferred scheme of this embodiment a cross-material bionic meaning to understand its effectiveness.

[0067] Preferably, the high-order dynamics equation of each follower agent is a high-order dynamics equation whose structure is equivalent to the food chain mathematical model, specifically:

[0068]

[0069] In the formula, Indicates i The following agent s dimensional state variables over time t The derivative of Indicates i The following agent s +1-dimensional state variable changes with time t, Indicates i a parameter vector following the agent's uncertain parameters, and Indicates i Follower Agent s The output state corresponding to the dimension state Two known nonlinear continuously differentiable functions of , Indicates i The following agent dimensional state variables over time t The derivative of Indicates i a control protocol that follows the agent over time; and Indicates i Follower Agent The output state corresponding to the dimension state Two known nonlinear continuously differentiable functions of ; Indicates i A self-output state that follows the agent over time; Indicates i The relationship between the first-dimensional state variables of a following agent and time t.

[0070] The dynamic equation of the leader agent to be tracked is , where the matrix is ​​antisymmetric and represents the real system parameters of the leader agent, Represents the real system state of the leader agent. To represent the communication topology between multiple agents; The first dimension variable representing the internal state of the target agent, Represents the output state of the target agent.

[0071] The n-species single food chain model with time-varying food conversion efficiency (i.e., food chain mathematical model) is:

[0072]

[0073] in, represents the number of organisms at the bottom, and the model has asymptotic stability and persistence characteristics. Redefine Corresponding to the highest level of organisms, Corresponding to the lowest level organisms, for example, in the food chain of grass → sheep → wolf, represents the number of wolves, represents the amount of grass. And let , that is, taking a specific predator response function and food conversion efficiency in the definition domain, the above high-order ODE model is rewritten as the following equivalent n-species single food chain model (that is, the model form of the above-mentioned food chain mathematical model):

[0074]

[0075] In this formula, is the number of organisms at the highest level, is the number of organisms at the bottom layer, Indicates the first j The number of organisms in the layer, Represents the unknown nonlinear function of the number of organisms at the highest level and time. According to the working principle of neural network fitting any nonlinear function, it is recorded as ; Indicates the growth rate of the lowest level organisms.

[0076] It can be observed that the above-mentioned agent high-order dynamic equation is equivalent to the above-mentioned population single food chain model in structural form, so the coordination problem of heterogeneous multi-agent system can be equivalently transformed into the coordination of N stable population single food chain models, that is, the coordination of cross-species food chains, and the cross-species bionic representation of the multi-agent system model is obtained. It can be understood that this embodiment aims to control the number of organisms at the bottom of each food chain (by controlling the highest-order internal state in the equation) so that the change law of the number of organisms at the highest level of all food chains is consistent with the ideal population size (that is, the output state of all following agents can track the output state of the target agent). For example, there are two food chains, namely grass → sheep → wolf, grass → insect → bird → snake → owl → weasel → wolf, then through human intervention (in the agent collaborative tracking control, that is, control protocol generation and execution) the number of grass in the two food chains, and use the self-evolution characteristics of a single food chain to make the number of wolves in the two food chains reach the ideal number.

[0077] As a preferred embodiment, the event triggering judgment mechanism of each follower agent (each food chain) for transmitting the target agent system information evaluation value to the neighboring agent is:

[0078] The event trigger judgment mechanism for each follower agent to transmit the target agent system information evaluation value to the neighboring agent is:

[0079] ;

[0080] ;

[0081] ;

[0082] ;

[0083] ;

[0084] In the formula, Indicates i The time when the following agent triggers the first event, , respectively representing the i Each time an event is triggered by a following agent, an estimated value of system information is sent to the neighboring communicative agent at this sampling time; Indicates i The following agent at the sampling time The estimation error judgment function of the target agent system parameters, Indicates i The following agent at the sampling time Estimates of the target agent system parameters; Indicates i The following agent at the trigger time Estimates of the target agent system parameters; is a positive constant; Indicates i The following agent at the sampling time The estimation error judgment function of the target agent system state; Indicates i The following agent at the sampling time An estimate of the system state of the target agent; Indicates i The following agent at the sampling time Based on the time of the most recent event trigger Auxiliary variable of the target agent system state estimate, which is an intermediate parameter; it represents the continuous time starting from 0; Indicates i A non-periodic sampling time series of system information by the following agent, , represents the maximum sampling interval in the sampling time series of all agents, N represents the total number of follower agents in the multi-agent system, Indicates i The maximum sampling interval of the following agents, , , , L is the Laplace matrix, I is the identity matrix, P satisfy The matrix of Indicates the communication relationship between each follower agent and the target agent. The element value is 1 when communication is possible, otherwise it is 0.

[0085] It can be further preferred that i In the following agent, the observer used to calculate its own estimation curve of the system information is:

[0086]

[0087] In the formula, is a positive constant; Indicates i The following agent and j The communication coefficient between the following agents is 1 when communicating, otherwise it is 0; Indicates j The agent at the time of the most recent event trigger Estimates of the target agent system parameters; Indicatesi The following agent at the time of the most recent event trigger Estimates of the target agent system parameters; Indicates i The derivatives of the follower agents’ estimates of the target agent’s system parameters;

[0088] Indicates i The derivative of the follower agent’s estimate of the target agent’s system state; Indicates i The following agent at the time of the most recent event trigger An estimate of the system state of the target agent; Indicates j The agent triggers the time at time based on the most recent event Auxiliary variables of the target agent system state estimate, which are intermediate parameters; Indicates i A following agent triggers the event at time Auxiliary variables of the target agent system state estimate are intermediate parameters.

[0089] It should be noted that the event triggering judgment mechanism based on each follower agent (each food chain) transmitting the target agent system information evaluation value to the neighboring agent and the first i The design of the observer used by the following agent to calculate its own estimation curve of the system information shows that if the maximum sampling interval satisfies , there will be and The exponential converges to 0, which means that each agent (each food chain) can accurately predict the state of the target (ideal population size).

[0090] As a further preferred implementation, each follower agent has an event triggering judgment mechanism for using its own output state for estimating its own internal state as follows:

[0091] ,

[0092] ,

[0093] ,

[0094] ,

[0095] In the formula, Indicates i The actual output state of the following agent at time, Indicates i The following agent at the trigger time The actual output state, and Respectively represent i The following agent k Second and k +1 trigger moment; Indicates i The following agent at the sampling time The actual output status of represents a positive constant;

[0096] It should be noted that It is the output state sampling time series that is independent of the system information sampling time series.

[0097] Indicates i A non-periodic sampling time series of the following agent's output state, and Indicates i The maximum sampling interval in the second non-periodic sampling time series of the following agent, Should meet: , , ,

[0098] , , Represents a preset positive definite matrix The maximum eigenvalue of are preset constants related to the multi-agent system parameters generated during the proof process. include , include .

[0099] Further, as a preferred embodiment, i In a following agent, the observer used to iteratively calculate its own internal state estimate is:

[0100]

[0101] In the formula, Indicates i The following agent s The derivative of the estimated value of the dimensional state variable; Indicates i The following agent s +Estimated value of 1-dimensional state variable; Indicates i The following agent s The observation gain corresponding to the dimensional state variable; Indicates i Follower agent triggers output state With the estimated output state The error of Indicates i The following agent s A known nonlinear continuous differentiable function corresponding to the dimensional state; Indicates i The following agent The derivative of the estimated value of the dimensional state variable; Indicates i The following agent The observation gain corresponding to the dimensional state variable; Indicates i The following agent A known nonlinear continuous differentiable function corresponding to the dimensional state; Indicates i An estimate of the first-dimension state variable of the following agent.

[0102] In order to achieve the ideal number of cross-species food chain models, the lowest-level organisms need to be Performing human intervention, i.e. applying a control protocol, can be further used as a preferred embodiment. i The implementation method of a follower agent using the backstepping method to calculate its own control protocol is:

[0103] ;

[0104] ;

[0105]

[0106]

[0107] ;

[0108] In the formula, Indicates iA virtual control protocol of the first dimension of the following agent; Indicates i The control gain corresponding to the first dimension virtual control protocol of the following agent; Indicates i The error between the estimated output state of the following agent and its estimated output state of the target agent. , , , It is i Follower Agent (No. i food chain) estimates the output state of the target agent; Indicates i The following agent's estimate of the uncertain parameters; Indicates i A known nonlinear continuous differentiable function corresponding to the following agent; Indicates i A known nonlinear continuous differentiable function corresponding to the first-dimensional state of the following agent; Indicates i The output state estimate of the following agent itself; Indicates i The observation gain corresponding to the first dimension state variable of the following agent; Indicates i an upper bound on the number of sensor failures of the following agent; Represents a preset positive constant; express The Lipschitz constant;

[0109] Indicates i Follower Agent s Dimensional virtual control protocol; Indicates i Follower Agent s The control gain corresponding to the virtual control protocol; Indicates i Follower Agent s The internal state estimate of the s The error of the auxiliary variable obtained by the dimensional virtual control protocol after passing through the filter; Indicates i Follower Agent The internal state estimate of the The error of the auxiliary variable obtained by the dimensional virtual control protocol after passing through the filter; Indicates i The following agent sA known nonlinear continuous differentiable function corresponding to the dimensional state; Indicates i Follower Agent The derivative of the auxiliary variable obtained by the dimensional virtual control protocol after passing through the filter, which can be a first-order low-pass filter , Represents the coefficient of the filter, which can solve the problem of difficult controller execution caused by the non-differentiability of the virtual controller and the complexity of calculation; Indicates i The following agent s The observation gain corresponding to the dimensional state variable; express The Lipschitz constant;

[0110] Indicates i A follower agent-assisted control protocol; Indicates i The following agent targets The control gain corresponding to the auxiliary control protocol of the dimensional state variable; Indicates i Follower Agent The internal state estimate of the The error of the auxiliary variable obtained by the dimensional virtual control protocol after passing through the filter; Respectively represent i Follower Agent The internal state estimate of the The error of the auxiliary variable obtained by the dimensional virtual control protocol after passing through the filter; Indicates i The following agent A known nonlinear continuous differentiable function corresponding to the dimensional state; Indicates The auxiliary variable obtained by the virtual control protocol after passing through the filter; Indicates i The following agent The observation gain corresponding to the dimensional state variable; express The Lipschitz constant; Indicates i The following agent dimensional state variables; Indicated by is the vector of Lipschitz constants.

[0111] As a further preferred implementation, each follower agent has an event triggering judgment mechanism for using the control protocol to control its own motion:

[0112]

[0113]

[0114]

[0115]

[0116] In the formula, represents a positive constant; Indicates i A control protocol for a following agent at time t; Indicates i The following agent at the trigger time Control protocols; Respectively represent i The following agent k Second and k +1 trigger moment; Indicates i A non-periodic sampling time series of the following agent's own control protocol; Indicates i The following agent at the sampling time control protocol.

[0117] It should be noted that each agent samples and monitors its own output state value and control protocol and shares the same sampling time series, that is, , defined here as the second non-periodic sampling time series. Further, Indicates i The maximum sampling interval in the second non-periodic sampling time series of the following agent should satisfy the condition , ,

[0118] , , , Represents a preset positive definite matrix The maximum eigenvalue of etc. are preset constants related to the multi-agent system parameters generated during the proof process. include , include .

[0119] Abouti The observer used in the following agent to iteratively calculate the estimated value of its internal state can be designed according to its specific formula, and the observation error system can be obtained as follows: ,in, is the error vector and , , , , is a positive constant that needs to be designed so that is the Hurwitz matrix.

[0120] Regarding the estimation of uncertain parameters, Indicates the uncertainty of the parameters The estimate of , d represents the constant to be designed, represents the preset positive definite matrix, Indicated by is the vector of Lipschitz constants.

[0121] In general, the sampling event trigger mechanism designed in this embodiment only needs to monitor the system status at discrete sampling moments, which greatly saves computing and communication resources and naturally avoids Zeno behavior. At the same time, this embodiment assembles the sampling event trigger mechanism on three information channels, so that all signal channels between modules in the system communicate through trigger signals, which is highly consistent with the digital work requirements in actual engineering applications, and enhances the feasibility of the application of the method of this embodiment.

[0122] This embodiment also preferably proposes that the high-order dynamics equation of each follower agent is a high-order dynamics equation with a structural form equivalent to the food chain mathematical model. Through appropriate variable substitution, it is found that the structural equivalence of the high-order dynamics equation of each agent in the multi-agent system and the food chain mathematical model is found, giving biological meaning to the multi-agent system. Further, a target agent system information observer (i.e. Figure 1The leader observer in the system), its own internal state observer, and the controller used to generate the control protocol are used to achieve the complete acquisition of the collaborative state information of multiple agents under the trigger mechanism and the coordination of heterogeneous high-order multi-agent systems with uncertain parameters. Specifically, designing an observer based on the output information at the trigger time refers to designing a target observer and an internal state observer to achieve effective compensation for unknown information. First, since only a part of the agents know the state of the target agent, based on the communication topology, each agent sends its own observation value of the target to the neighboring agent at the trigger time. The neighbor updates the observer by collecting all the feedback information sent. Finally, it can be proved through matrix analysis and the stability theory of time-delay systems that the target observer can effectively observe accurate target information. Secondly, since the internal state information of the agent is unmeasurable, the output state at the trigger time is used for feedback iterative calculation. The high-order dynamics model can be combined to select the appropriate observer gain to design the internal state observer. The effectiveness of the internal state observer can be proved by mathematical analysis by designing the Lyapunov function. An adaptive update rate is also designed and a controller is designed based on the backstepping method. First, it refers to the design of an adaptive update rate based on error feedback for uncertain parameters in high-order dynamic equations. The effectiveness of the adaptive update rate can be proved by taking it into account in the design of the Lyapunov function. Secondly, a controller is designed based on the backstepping method. Based on the strict feedback characteristics of the dynamic equations of the multi-agent system, combined with the designed objectives and internal state observers, the backstepping method can be used to iteratively design a virtual controller for each agent and a feedback controller that matches the input of the multi-agent system. By designing a suitable Lyapunov function and combining it with analysis techniques such as the Granval inequality, it can be proved that the designed feedback controller can effectively drive the heterogeneous high-order multi-agent system to achieve collaborative tracking.

[0123] This embodiment theoretically proposes a cross-species bionic collaborative control idea, so that the above-mentioned specific observer and controller design are interpretable. Through appropriate variable substitution, the dynamic model of heterogeneous multi-agents is modeled as a mathematical model of multiple food chains with multiple populations, which is called a cross-species food chain model, to achieve cross-species bionic characterization of the multi-agent system model. Then, by applying human intervention in the food chain (i.e., the generation and execution of the control protocol), the tracking consistency of the multi-agent system is achieved by utilizing the advantages of the food chain model such as asymptotic stability and persistence. Compared with the existing multi-agent collaborative control method, cross-species bionic collaborative control has obvious biological interpretability and improves the reliability of the control strategy. That is, combined with the stable evolution of the food chain in nature, a collaborative control method based on cross-species bionics is proposed. By considering the structural equivalence of the heterogeneous multi-agent system and the cross-species food chain model, the biological advantages in nature can be introduced into the analysis of multi-agent collaboration, and the biological interpretability of the method can be achieved, thereby explaining its effectiveness.

[0124] Embodiment 2

[0125] An intelligent agent can implement the above-mentioned method steps for controlling itself to track a target intelligent agent when performing a multi-agent collaborative tracking task.

[0126] The relevant technical solution is the same as that in Embodiment 1 and will not be described in detail here.

[0127] Embodiment 3

[0128] A multi-agent system can implement the above-mentioned multi-agent sampling event-triggered collaborative tracking control method based on cross-species bionics when performing a multi-agent collaborative tracking task.

[0129] The relevant technical solution is the same as that in Embodiment 1 and will not be described in detail here.

[0130] The following is an example of the cooperative control of a multi-agent system composed of multiple inverted pendulums to further explain the beneficial effects that can be achieved by the present invention. The inverted pendulum system includes 6 inverted pendulums and a target trajectory. The high-order dynamic equation of each inverted pendulum is , after variable substitution, we get

[0131]

[0132] in, , , is used in the simulation but is unknown to the controller. The remaining parameters are , , , , , , as well as Consider the following sensor failure and target trajectory

[0133] ,

[0134] ,

[0135] .

[0136] Secondly, the parameters of the distributed target state observer designed based on the trigger time information are , , , , , the maximum sampling time interval of different agents is , , The parameters in the distributed feedback controller are selected as , , , , , , , the parameters of the sampling event trigger mechanism are selected as , , , , , , , , At the same time, the maximum sampling interval of different agents is designed based on these parameters. , , , .

[0137] Under the above parameter settings, the observation effect of the distributed target observer can be obtained through MATLAB simulation, such as Figure 2 In addition, Figure 3 Given the trajectory of the output variables of the multi-agent system, Figure 4 Three sets of event triggering time sequence values ​​are shown. Figure 5 The state trajectory of the designed feedback controller is given. Figure 2 , Figure 3 , Figure 4 and Figure 5 It can be seen that the observer and controller designed by the present invention based on sampling event triggering are effective and can realize the collaborative tracking task of heterogeneous high-order multi-agent systems under the condition of limited communication resources.

[0138] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A multi-agent sampling event-triggered collaborative tracking control method based on cross-species bionics, characterized in that: The dynamic equation of each follower agent is pre-modeled as a high-order dynamic equation with a structural form equivalent to the food chain mathematical model. As a food chain mathematical model, the food chain mathematical model of all agents and the directed graph describing the communication and connectivity relationship between multiple agents constitute a cross-species food chain model, and a cross-species bionic representation of the multi-agent system model is obtained. The overall collaborative tracking is achieved through communication between the follower agents. Each follower agent controls its own tracking of the target agent in the following ways: Based on the error between the estimated value of the same system information of the target agent transmitted by the neighbor agent at the most recent trigger and the estimated value of the same system information of the target agent at the most recent trigger, the estimation curve of the system information is calculated; according to the difference between the estimated value in the estimation curve at the current system information sampling moment and the estimated value of the system information estimated at the most recent trigger, the event trigger judgment of the system information at the sampling moment is performed, and the current estimated value of the system information that meets the judgment condition is transmitted to the neighbor agent; the system information is the system state and / or system parameters; According to the error between the output state sampled at the current output state sampling moment and the output state of the self used for the estimation of the self internal state at the most recent trigger, an event trigger judgment is performed on the output state of the self at the sampling moment, and the output state of the self that meets the judgment condition is used for iterative calculation to determine the estimated value of the self internal state; based on the error between the estimated value of the self output state in the determined estimated value of the self internal state and the estimated value of the system output state in the estimated value of the system state transmitted to the neighboring intelligent body at the most recent trigger, the estimated value of the uncertain parameter in the self high-order dynamic equation is calculated; based on the estimated value of the self internal state, the estimated value of the system output state and the estimated value of the uncertain parameter, the control protocol of the self is calculated using the backstepping method; According to the error between the control protocol sampled at the current control protocol sampling moment and the control protocol used for motion control last time, an event triggering judgment on the control protocol at the current control protocol sampling moment is performed, and the control protocol that meets the judgment conditions is used to control its own motion.

2. The multi-agent sampling event-triggered collaborative tracking control method according to claim 1, characterized in that: The high-order dynamics equation of each follower agent is a high-order dynamics equation with a structural form equivalent to the food chain mathematical model, specifically: In the formula, represents the derivative of the s-dimensional state variable of the i-th following agent with time t, x i,s+1 (t) represents the change relationship between the s+1th dimension state variable of the ith follower agent and time t, represents the parameter vector of the uncertain parameters of the ith following agent, ψ i,s (y i ) and h i,s (y i ) represents the output state y corresponding to the s-dimensional state of the i-th follower agent i Two known nonlinear continuously differentiable functions of , represents the nth following agent of the ith i The derivative of the dimensional state variable with time t; u i (t) represents the time-varying control protocol of the i-th follower agent; and Indicates the nth following agent of the ith i The output state y corresponding to the dimensional state i Two known nonlinear continuously differentiable functions of y i (t) represents the output state of the i-th following agent that changes over time; x i,1 (t) represents the change relationship between the first-dimensional state variable of the i-th follower agent and time t.

3. The multi-agent sampling event-triggered collaborative tracking control method as claimed in claim 2, characterized in that: The event trigger judgment mechanism for each follower agent to transmit the target agent system information evaluation value to the neighboring agent is: In the formula, represents the time when the l+1th event of the i-th following agent is triggered, They represent the triggering moments of each event of the i-th following agent, and send the estimated value of system information to the neighboring communicative agent at this sampling moment; represents the estimation error judgment function of the target agent system parameters by the i-th follower agent at sampling time τ, represents the estimated value of the target agent system parameters by the i-th follower agent at sampling time τ; Indicates the i-th following agent at the triggering time The estimated values ​​of the target agent system parameters; A ,l v ,r A ,r v is a positive constant; represents the estimation error judgment function of the target agent system state by the i-th follower agent at sampling time τ; represents the estimated value of the system state of the target agent by the i-th follower agent at the sampling time τ; It indicates that the i-th follower agent at the sampling time τ is based on the most recent event triggering time The auxiliary variable of the target agent system state estimate is an intermediate parameter; t represents the continuous time starting from 0; {s i 0,s1 i ,…} represents the non-periodic sampling time series of the system information by the ith following agent, represents the maximum sampling interval in the sampling time series of all agents, N represents the total number of follower agents in the multi-agent system, and T i represents the maximum sampling interval of the ith following agent, H=(L+B), L is the Laplace matrix, I is the identity matrix, and P satisfies The matrix, B = diag(a 10 ,…,a N0 ) represents the communication relationship between each follower agent and the target agent. The element value is 1 when communication is possible, otherwise it is 0.

4. The multi-agent sampling event-triggered collaborative tracking control method as claimed in claim 3, characterized in that: In the i-th follower agent, the observer used to calculate its own estimation curve of the system information is: In the formula, μ1, μ2 are positive constants; a ij It represents the communication coefficient between the ith follower agent and the jth follower agent. It takes the value of 1 when communicating and 0 otherwise. Indicates the jth agent at the time of the most recent event triggering Estimates of the target agent system parameters; Indicates the i-th follower agent at the time of the most recent event triggering Estimates of the target agent system parameters; represents the derivative of the estimated value of the target agent system parameter of the i-th follower agent; represents the derivative of the estimated value of the target agent system state by the i-th follower agent; Indicates the i-th follower agent at the time of the most recent event triggering An estimate of the system state of the target agent; Indicates that the jth agent triggers the most recent event at time t Auxiliary variables of the target agent system state estimate, which are intermediate parameters; Indicates the i-th follower agent at time t based on the most recent event triggering time Auxiliary variables of the target agent system state estimate are intermediate parameters.

5. The multi-agent sampling event-triggered collaborative tracking control method as claimed in claim 2, characterized in that: Each follower agent has an event triggering judgment mechanism for using its own output state for estimating its own internal state: In the formula, represents the true output state of the i-th follower agent at time t, Indicates the i-th following agent at the triggering time The actual output state, and They represent the kth and k+1th triggering moments of the i-th following agent respectively; represents the actual output state of the i-th follower agent at sampling time τ; represents a positive constant; represents the non-periodic sampling time series of the i-th follower agent's output state, and represents the maximum sampling interval in the second non-periodic sampling time series of the i-th following agent, Should meet: λ max (P i ) represents the preset positive definite matrix P i The maximum eigenvalue of are preset constants related to the multi-agent system parameters generated during the proof process, c i,s include β i,s include 6. The multi-agent sampling event-triggered collaborative tracking control method according to claim 5, characterized in that: In the i-th follower agent, the observer used to iteratively calculate its own internal state estimate is: In the formula, represents the derivative of the estimated value of the s-th dimension state variable of the ith following agent; represents the estimated value of the s+1th dimension state variable of the ith following agent; l i,s represents the observation gain corresponding to the s-dimensional state variable of the i-th following agent; Indicates the output state triggered by the i-th follower agent With the estimated output state The error of h i,s Represents the known nonlinear continuous differentiable function corresponding to the s-dimensional state of the i-th following agent; represents the nth following agent of the ith i The derivative of the estimated value of the dimensional state variable; represents the nth following agent of the ith i The observation gain corresponding to the dimensional state variable; represents the nth following agent of the ith i A known nonlinear continuous differentiable function corresponding to the dimensional state; Represents the estimated value of the 1st dimension state variable of the i-th follower agent.

7. The multi-agent sampling event-triggered collaborative tracking control method according to claim 6, characterized in that: The implementation method of the i-th follower agent using the backstepping method to calculate its own control protocol is: In the formula, α i,1 represents the first dimension virtual control protocol of the ith follower agent; c i,1 represents the control gain corresponding to the first dimension virtual control protocol of the i-th follower agent; z i,1 represents the error between the estimated output state of the i-th follower agent and its estimated output state of the target agent; represents the estimated value of the uncertain parameter by the i-th following agent; φ i represents the known nonlinear continuous differentiable function corresponding to the i-th following agent; represents the known nonlinear continuous differentiable function h corresponding to the first-dimensional state of the i-th following agent i,1 exist The value of when represents the estimated output state of the i-th following agent; l i,1 represents the observation gain corresponding to the first-dimensional state variable of the i-th following agent; represents the upper bound of the sensor failure of the ith follower agent; μ represents a preset normal constant; α i,s represents the s-dimensional virtual control protocol of the i-th follower agent; c i,s represents the control gain corresponding to the s-dimensional virtual control protocol of the i-th follower agent; z i,s represents the error between the estimated value of the s-dimensional internal state of the i-th follower agent and the auxiliary variable obtained after the s-dimensional virtual control protocol passes through the filter; z i,s-1 represents the error between the estimated value of the internal state of the s-1th dimension of the i-th follower agent and the auxiliary variable obtained after the s-1th dimension virtual control protocol passes through the filter; represents the known nonlinear continuous differentiable function h corresponding to the s-dimensional state of the i-th following agent i,s exist The value of when represents the derivative of the auxiliary variable α obtained after the s-dimensional virtual control protocol of the i-th following agent passes through the filter; l i,s represents the observation gain corresponding to the s-dimensional state variable of the i-th following agent; ν i (t) represents the auxiliary control protocol of the i-th follower agent; Indicates that the i-th follower agent targets the n-th i The control gain corresponding to the auxiliary control protocol of the dimensional state variable; Indicates the nth following agent of the ith i The estimated value of the internal state of the nth i -1D virtual control protocol error of auxiliary variables obtained after filtering; Respectively represent the nth following agent of the ith i -1D internal state estimate and the nth i -2D virtual control protocol error of auxiliary variables obtained after filtering; represents the nth following agent of the ith i A known nonlinear continuous differentiable function corresponding to the dimensional state; Indicates the nth i The auxiliary variable obtained by the virtual control protocol after passing through the filter; represents the nth following agent of the ith i The observation gain corresponding to the dimensional state variable; represents the nth following agent of the ith i dimensional state variables.

8. The multi-agent sampling event-triggered collaborative tracking control method according to claim 7, characterized in that: The event trigger judgment mechanism for each follower agent to use the control protocol to control its own motion is: In the formula, represents a positive constant; u i (t) represents the control protocol of the i-th follower agent at time t; Indicates the i-th following agent at the triggering time Control protocols; They represent the kth and k+1th triggering moments of the i-th following agent respectively; represents the non-periodic sampling time series of the ith follower agent for its own control protocol; ν i (τ) represents the control protocol of the i-th follower agent at sampling time τ.

9. An intelligent agent, characterized in that: When executing a multi-agent collaborative tracking task, the method steps of controlling the tracking of the target agent by itself as described in any one of claims 1 to 8 can be implemented.

10. A multi-agent system, characterized in that: When executing a multi-agent collaborative tracking task, a multi-agent sampling event-triggered collaborative tracking control method based on cross-species bionics as described in any one of claims 1 to 8 can be implemented.

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