Method for group consensus control of leader-follower nonlinear multi-agent system

Abstract

The application discloses a kind of group consensus control methods of leader-following nonlinear multi-agent system, comprising: step one: in group multi-agent system, sub-system is divided;Select an agent as leader agent in each sub-system;Step two: each agent is regarded as a mass point obeying single integrator motion model, and the nonlinear dynamics model of each agent in group multi-agent system is established;Step three: the communication connection network between agent is established;Step four: design control protocol and adaptive state observer, initialize each agent state value and state observation value;Step five: the corresponding control protocol is calculated by the current state value of each agent and convergence target, and each agent executes next action;Step six: the adaptive law is calculated using the current state and observation value of agent;Step seven: the state value of each agent after executing action is obtained using state observer.

Description

Technical Field

[0001] This invention belongs to the field of intelligent agent cooperative control technology, specifically a group consensus control method for a leader-follower nonlinear multi-agent system. Background Technology

[0002] Clustering phenomena are widespread in nature and human society. Viewing the individuals within a cluster as a single intelligent agent constitutes a multi-agent system (MAS). A MAS is composed of multiple simple, individual intelligent agents with certain perception, computation, communication, and execution capabilities. In a MAS, agents share information and cooperate to jointly perform complex tasks that a single agent cannot accomplish. Cooperative control of MAS has broad application prospects in smart grids, smart manufacturing, and drone swarms, becoming a major research hotspot. Taking smart manufacturing as an example, intelligent collaborative production and flexible discrete manufacturing processes can be achieved through mutual cooperation between humans, machines, and materials on the production line.

[0003] Single-agent multi-agent systems converge to a single state value, but in many cases, multiple tasks need to be completed simultaneously, making single-agent systems unsuitable for practical needs. Group consensus, as an extension of consensus in multi-agent systems, divides the system into different sub-networks. Information exchange exists not only between agents within the same sub-network but also between different sub-networks, ultimately leading to system convergence to multiple states. Extensive research has been conducted on group consensus in multi-agent systems. In most studies, information transfer between agents is bidirectional, and the agent models are linear. However, in real-world scenarios, nonlinear systems with unidirectional information transfer are more common. Furthermore, for complex systems, relying solely on information exchange between agents is insufficient to achieve group consensus; external control is also crucial. Additionally, with the development of network technology, multi-agent systems are vulnerable to network attacks. Moreover, as the distance between agents within or between groups increases, network degradation may occur, potentially disrupting the established group consensus state. To address this, we propose an adaptive control protocol and design an adaptive neural network state observer. This state observer recovers the disturbed signal, enabling the multi-agent system to regain collective consensus. Summary of the Invention

[0004] In view of this, the purpose of this invention is to provide a group consensus control method for a leader-follower nonlinear multi-agent system, which restores the disturbed signal through a designed control protocol and an adaptive neural network state observer, enabling the multi-agent system whose group consensus has been disrupted to regain group consensus.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A group consensus control method for a leader-follower nonlinear multi-agent system includes:

[0007] Step 1: Set the convergence objective of the agents. Divide the agents with the same convergence objective in the group multi-agent system into a subsystem to obtain several subsystems. In each subsystem, select an agent as the leader agent and the other agents as follower agents.

[0008] Step 2: Establish a global coordinate system in the activity space of the agents, treat each agent as a point mass that follows a single integrator motion model, and establish a nonlinear dynamic model for each agent in the group multi-agent system;

[0009] Step 3: Establish a communication network between intelligent agents;

[0010] Step 4: Design the control protocol and initialize the state values ​​and state observations of each agent;

[0011] Step 5: Calculate the corresponding control protocol based on the current state value of each agent and the convergence target, and each agent executes the next action;

[0012] Step 6: Calculate the adaptive law using the agent's current state and observations, and design an adaptive state observer;

[0013] Step 7: Use the state observer to obtain the state value of each agent after the action is performed.

[0014] Furthermore, in step two, the nonlinear dynamic model of the leader agent is as follows:

[0015]

[0016] in, Indicates the first The state of the leader agent in each subsystem; express The first derivative with respect to time; Indicates a time step; Indicates the first A collection of intelligent agents in a subsystem;

[0017] The nonlinear dynamics model of the follower agent is as follows:

[0018]

[0019] in, Indicates the first The state of each agent; express The first derivative with respect to time; Indicates the first The nonlinear component of an agent; Represents the control input matrix; Indicates the first The control parameters of each agent; and

[0020] =

[0021] :=

[0022]

[0023] in, Represents intelligent agents The state of item; Indicates the first The nonlinear part of the agent's first... item; , Indicates the first The number of agents in each subsystem; Represents a real number of dimension n; The dimension is The real number.

[0024] Furthermore, in step four, the control protocol is as follows:

[0025]

[0026] The definition is as follows:

[0027]

[0028] in The definition is as follows:

[0029]

[0030] in, This represents a matrix with g rows and r columns; Represents intelligent agents Poor condition; Represents intelligent agents No. The state difference of the item; Represents a constant that is greater than or equal to 1; and Representing vectors respectively sum vector The One element; Yes The estimated value, This represents the state value of agent i in the s-th subsystem at the k-th item; It represents a constant greater than zero; and satisfies:

[0031]

[0032] vector sum vector They are represented as follows:

[0033] := ,

[0034]

[0035] in, This represents the communication weights between agents i and j in a communication network; This represents the total number of agents in a grouped multi-agent system.

[0036] The derivative is defined as:

[0037]

[0038] The error equation is defined as:

[0039] ,

[0040] in, express The first subsystem The state difference between an agent and its neighboring agents; This represents the connection weight between follower i and the leader in the subsystem; The leader's status value.

[0041] Furthermore, in step six, the designed adaptive observer is as follows:

[0042]

[0043] in, express The estimated value; express The derivative; It is a positive number greater than zero; This represents an estimate of the signal attenuation rate. Represents the control input matrix; Indicates the first Control parameters for each agent; , representing the adaptive observation gain; and:

[0044] when hour:

[0045]

[0046] when hour:

[0047]

[0048]

[0049] in, Represents the adaptive observation matrix The item; This indicates that the k-th term of agent j is affected by signal attenuation; right The estimated value; This represents the estimated values ​​of the neural network weights; This represents an estimate of the neural network error. Represents the basis functions of a neural network; This indicates the state value after being affected; Indicates to The estimate; This indicates that agent j is affected by signal attenuation; Indicates to The estimated value; This represents the k-th term of the state value of agent j; and It represents a very small positive number.

[0050] Furthermore, in step seven, the method for obtaining the state value of each agent using a state observer is as follows:

[0051] 71) Construct an adaptive neural network and determine its parameters. , and ;in, This represents the width of the Gaussian function in the state observer i neural network; Indicates the central value of the Gaussian function; Indicates the number of nodes in the neural network;

[0052] 72) Initialization , and ; Represents the weights of a neural network; Indicates the upper bound of the neural network error; This represents the signal attenuation value received by the agent;

[0053] 73) Using the agent's state value as input, an adaptive neural network is used to approximate the unknown nonlinear equation:

[0054]

[0055] in, It is an unknown positive constant; Indicates a statement about An unknown function;

[0056] This represents the optimal weight vector for the neural network. Indicates the first The weights of neural network nodes, , This represents the number of nodes in the neural network. Represents a fuzzy basis function vector; The Gaussian equation was chosen, and it takes the following form:

[0057]

[0058] in, Indicates about intelligent agents The first basis function of the neural network in the state observer item; Indicates the first Width in the term basis function; Indicates the first The central value in the term basis function;

[0059] Obtaining unknown nonlinear equations An approximate solution;

[0060] 74) Utilizing interference signals from communication connection networks (t), calculate the observation matrix ;

[0061] 75) will Approximate solution and observation matrix Substituting these values ​​into the state observer yields the recovered state value estimate. ;

[0062] 76) Judgment Is it equal to zero? If so, then... As the current state value of the agent If not, proceed to step 77).

[0063] 77) Using state value estimates and state value renew , and :

[0064]

[0065]

[0066]

[0067] in, , , , All are constants greater than zero; This represents the k-th element of the observation matrix; This represents the k-th term of the state value of agent j; Indicates to Estimated value;

[0068] 78) Repeat step 73).

[0069] The beneficial effects of this invention are as follows:

[0070] When a multi-agent system is affected by signal attenuation or network attacks, the consensus reached by the multi-agent system can be disrupted. This invention provides a group consensus control method for leader-follower nonlinear multi-agent systems. Through a designed control protocol, the nonlinear agents in different groups eventually converge to the state of their respective leaders. By designing an adaptive state observer, the system can recover signals that have been attacked or weakened, thereby enabling the multi-agent system to re-converge and reach consensus. Ultimately, this method enables the multi-agent system whose group consensus has been disrupted to regain group consensus. Attached Figure Description

[0071] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration:

[0072] Figure 1 The network topology for communication methods between multiple agents in a grouped multi-agent system comprising two subsystems;

[0073] Figure 2 A state simulation diagram of a multi-group, multi-agent system;

[0074] Figure 3 The prediction error curve for a multi-group, multi-agent system. Detailed Implementation

[0075] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0076] The group consensus control method for a leader-follower nonlinear multi-agent system in this embodiment includes:

[0077] Step 1: Define the convergence objective for the agents. Divide agents with the same convergence objective into several subsystems. In each subsystem, select one agent as the leader agent and the others as followers. The convergence objective can be velocity, angular velocity, displacement, etc.

[0078] Step 2: Establish a global coordinate system in the activity space of the agents, treat each agent as a point mass that follows a single integrator motion model, and establish a nonlinear dynamic model for each agent in the group multi-agent system.

[0079] The nonlinear dynamic model of the leader agent is as follows:

[0080]

[0081] in, Indicates the first The state of the leader agent in each subsystem; express The first derivative with respect to time; Indicates a time step; Indicates the first A collection of intelligent agents in a subsystem;

[0082] The nonlinear dynamics model of the follower agent is as follows:

[0083]

[0084] in, Indicates the first The state of each agent; express The first derivative; Indicates the first The nonlinear component of an agent; Represents the control input matrix; Indicates the first The control parameters of each agent; and

[0085] =

[0086] :=

[0087]

[0088] in, Represents intelligent agents The state of item; Indicates the first The nonlinear part of the agent's first... item; , Indicates the first The number of agents in each subsystem; Represents a real number of dimension n; The dimension is The real number.

[0089] Step 3: Establish a communication network between intelligent agents.

[0090] The initial positions of each agent are determined, and a topology network diagram is established based on the communication links between agents. Considering that in actual flexible manufacturing lines, the speed or acceleration of coordinating equipment is not necessarily the same during coordination, and most of the time it operates at a certain ratio, certain weights are set between the communication connections in the topology network diagram. If agent i communicates with agents in other subsystems, then the number of connections between agent i and agents in other subsystems is 2, and the connection weights between them are opposites.

[0091] Step 4: Design the control protocol and initialize the state values ​​and state observations of each agent.

[0092] In this embodiment, the control protocol is:

[0093]

[0094] The definition is as follows:

[0095]

[0096] in The definition is as follows:

[0097]

[0098] in, This represents a matrix with g rows and r columns; Represents intelligent agents Poor condition; Represents intelligent agents No. The state difference of the item; Represents a constant that is greater than or equal to 1; and Representing vectors respectively sum vector The One element; Yes The estimated value, This represents the k-th term of the state value of agent i in the s-th subsystem; It represents a constant greater than zero; and satisfies:

[0099]

[0100]

[0101] vector sum vector They are represented as follows:

[0102] := ,

[0103] in, The communication weights between agents i and j in a communication network; This represents the total number of agents in a group multi-agent system; where Defined as:

[0104]

[0105] The derivative is defined as:

[0106]

[0107] The error equation is defined as:

[0108] ,

[0109] in, Indicates the first The first subsystem The state difference between an agent and its neighboring agents; Represents the followers in the s group subsystem The weight of the connection with the leader; The leader; This represents the set of agents in the s-th subsystem.

[0110] Step 5: Based on the current state values ​​of each agent and the convergence objective, each agent uses its own microprocessor to calculate the corresponding control protocol. Each agent then executes the next action. After each agent's state is refreshed, the controller's state is recalculated. .

[0111] Step 6: Calculate the adaptive law using the agent's current state and observations, and design an adaptive state observer.

[0112] In this embodiment, the designed adaptive state observer is:

[0113]

[0114] in, express The estimated value; express The derivative; It is a positive number greater than zero; Indicates the signal attenuation parameter The estimate; Represents the control input matrix; Indicates the first Control parameters for each agent; , representing the adaptive observation gain; and:

[0115] when hour:

[0116]

[0117] when hour:

[0118]

[0119]

[0120] in, Represents the adaptive observation matrix The item; This indicates that the k-th term of agent j is affected by signal attenuation; right The estimated value; This represents the estimated values ​​of the neural network weights; This represents an estimate of the neural network error. Represents the basis functions of a neural network; This indicates the state value after being affected; Indicates to The estimate; This indicates that agent j is affected by signal attenuation; Indicates to The estimated value; This represents the k-th term of the state value of agent j; and It represents a very small positive number.

[0121] Step 7: Use the state observer to obtain the state value of each agent after the action is performed.

[0122] In this embodiment, the method for obtaining the state value of each agent using a state observer involves the following steps:

[0123] 71) Construct an adaptive neural network and determine its parameters. , and ;in, This represents the width of the Gaussian function in the state observer i neural network; Indicates the center value; Indicates the number of nodes in the neural network;

[0124] 72) Initialization , and ; Represents the weights of a neural network; Indicates the upper bound of the neural network error; This represents the signal attenuation value received by the agent;

[0125] 73) Using the state value of the agent as input, an adaptive neural network is used to approximate the unknown nonlinear equation.

[0126] Specifically, assuming It is continuously differentiable in the real field R, and ; ;; ; ; Indicates the first The number of agents in each subsystem; This indicates the number of agents in a multi-agent system. (The question seems to be incomplete and requires further context.) It satisfies the Mean Value Theorem:

[0127]

[0128] exist The nonlinear part can be expressed as:

[0129]

[0130] in, This represents the nonlinear term in the dynamic model of agent i; This represents the nonlinear term in the dynamic model of agent j;

[0131] There exists a bounded positive number satisfy , Yes The estimated value. Then there exists a bounded positive number. satisfy ,in It is a continuous, unknown nonlinear equation, which can be approximated using an RBF neural network. :

[0132]

[0133] in, It is a constant greater than zero; Indicates a statement about An unknown function; This represents the optimal weight vector for the neural network. Indicates the first The weights of neural network nodes, , This represents the number of nodes in the neural network. Represents a fuzzy basis function vector; The Gaussian equation was chosen, and it takes the following form:

[0134]

[0135] in, Indicates about intelligent agents The first basis function of the neural network in the state observer item; Indicates the first Width in the term basis function; Indicates the first The central value in the term basis function;

[0136] Obtaining unknown nonlinear equations An approximate solution;

[0137] 74) Utilizing interference signals from communication connection networks (t), calculate the observation matrix ;

[0138] 75) will Approximate solution and observation matrix Substituting these values ​​into the state observer yields the recovered state value estimate. ;

[0139] 76) Judgment Is it equal to zero? If so, then... As the current state value of the agent If not, proceed to step 77).

[0140] 77) Utilizing state values renew , and :

[0141]

[0142]

[0143]

[0144] in, , , All of them are constants greater than zero; Represents the observation matrix The kth term; This represents the k-th term of the state value of agent j; Indicates to Estimated value;

[0145] 78) Repeat step 73).

[0146] When a multi-agent system is affected by signal attenuation or network attacks, the consensus reached by the multi-agent system will be disrupted. This embodiment presents a leader-follower nonlinear multi-agent system consensus control method. Through a designed control protocol, the nonlinear agents in different groups eventually converge to the state of their respective leaders. By designing an adaptive state observer, the signal affected by network attacks or attenuation can be recovered, thereby enabling the multi-agent system to re-converge and reach consensus. Ultimately, the multi-agent system whose consensus has been disrupted can regain consensus.

[0147] This embodiment uses simulation verification with two subsystems consisting of 4 and 5 agents respectively, where agents 1 and 5 are the leaders of the two subsystems, and the state equations are respectively... , The state equations of the other followers are: , The initial state of each agent is The system network topology diagram is as follows: Figure 1 , Figure 2 and Figure 3 The results are from the simulation.

[0148] Simulation results show that the multi-agent system converges in approximately 2.5 seconds. Under the designed adaptive algorithm, the neural network weights w estimate the upper bound of the error. Once a stable state is reached, the difference between the observed state value and the state value of each agent during normal operation decreases to zero within 5 seconds. This indicates that by utilizing the disturbed signal in the multi-agent system, the control protocol and adaptive state observer designed in this embodiment can restore the correct signal.

[0149] The above-described embodiments are merely preferred embodiments provided to fully illustrate the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are all within the scope of protection of the present invention. The scope of protection of the present invention is defined by the claims.

Claims

1. A group consensus control method for a leader-follower nonlinear multi-agent system, characterized in that: include: Step 1: Set the convergence objective of the agents. Divide the agents with the same convergence objective in the group multi-agent system into a subsystem to obtain several subsystems. In each subsystem, select an agent as the leader agent and the other agents as follower agents. Step 2: Establish a global coordinate system in the activity space of the agents, treat each agent as a point mass that follows a single integrator motion model, and establish a nonlinear dynamic model for each agent in the group multi-agent system; Step 3: Establish a communication network between intelligent agents; Step 4: Design the control protocol and initialize the state values ​​and state observations of each agent; Step 5: Calculate the corresponding control protocol based on the current state value of each agent and the convergence target, and each agent executes the next action; Step 6: Calculate the adaptive law using the agent's current state and observations, and design an adaptive state observer; Step 7: Use the state observer to obtain the state value of each agent after executing the action; In step two, the nonlinear dynamic model of the leader agent is as follows: in, Indicates the first The state of the leader agent in each subsystem; express The first derivative with respect to time; Indicates a time step; Indicates the first A collection of intelligent agents in a subsystem; The nonlinear dynamics model of the follower agent is as follows: in, Indicates the first The state of each agent; express The first derivative with respect to time; Indicates the first The nonlinear component of an agent; Represents the control input matrix; Indicates the first The control parameters of each agent; and = ：= in, Represents intelligent agents The state of item; Indicates the first The nonlinear part of the agent's first... item; , Indicates the first The number of agents in each subsystem; Represents a real number of dimension n; The dimension is real numbers; In step four, the control protocol is as follows: The definition is as follows: in The definition is as follows: Represents a matrix with design dimensions; Represents intelligent agents Poor condition; Represents intelligent agents No. The state difference of the item; Represents a constant that is greater than or equal to 1; and Representing vectors respectively sum vector The One element; Yes The estimated value, This represents the state difference of agent i in the k-th term within the s-th subsystem; It represents a constant greater than zero; and satisfies: vector sum vector They are represented as follows: ：= ， in, This represents the communication weights between agents i and j in a communication network; This represents the total number of agents in the system. The derivative is defined as: The error equation is defined as: , in, Indicates the first The first subsystem The state difference between an agent and its neighboring agents; Represents the followers in the s group subsystem The weight of the connection with the leader; The leader; This represents the set of agents in the s-th subsystem; In step six, the designed adaptive state observer is as follows: in, express The estimated value; express The derivative; It is a positive number greater than zero; This represents an estimate of the signal attenuation rate. Represents the control input matrix; Indicates the first Control parameters for each agent; , representing the adaptive observation gain; and: when hour: when hour: in, Represents the adaptive observation matrix The item; This indicates that the k-th term of agent j is affected by signal attenuation; Indicates to The estimated value; This represents the estimated values ​​of the neural network weights; This represents an estimate of the upper bound of the neural network error. Represents the basis functions of a neural network; This indicates the state value after being affected; Indicates to The estimate; This indicates that agent j is affected by signal attenuation; Indicates to The estimated value; This represents the k-th state term of agent j; and Represents a very small positive number; Indicates to Estimated value.

2. The group consensus control method for a leader-follower nonlinear multi-agent system according to claim 1, characterized in that: In step seven, the method for obtaining the state value of each agent using a state observer is as follows: 71) Construct an adaptive neural network and determine its parameters. , and ;in, This represents the width of the Gaussian function in a neural network; Indicates the center value; Indicates the number of nodes in the neural network; 72) Initialization , and ; Represents the weights of a neural network; Indicates the upper bound of the neural network error; This represents the signal attenuation value received by the agent; 73) Using the agent's state value as input, an adaptive neural network is used to approximate the unknown nonlinear equation: in, It is an unknown positive constant; Indicates a statement about An unknown function; This represents the optimal weight vector for the neural network. Indicates the first The weights of neural network nodes, , This represents the number of nodes in the neural network. Represents a fuzzy basis function vector; The Gaussian equation was chosen, and it takes the following form: in, Indicates about intelligent agents The first basis function of the neural network in the state observer item; Indicates the first Width in the term basis function; Indicates the first The central value in the term basis function; Obtaining unknown nonlinear equations An approximate solution; 74) Utilizing interference signals from communication connection networks (t), calculate the observation matrix 75) will Approximate solution and observation matrix Substituting these values ​​into the state observer yields the recovered state value estimate. ; 76) Judgment Is it equal to zero? If so, then... As the current state value of the agent If not, proceed to step 77). 77) Using state value estimates and state value renew , and : in, , , , All are constants greater than zero; This represents the k-th element of the observation matrix; This represents the k-th term of the state value of agent j; Indicates to Estimated value; 78) Repeat step 73).

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