Multi-agent event-triggered consensus control method under combined communication topology

Abstract

The application discloses a kind of multi-agent event-triggered consistency control methods under combination connected topology.First, according to the type division of multi-agent to combination connected topology concept;Second, based on formation coordination error, a fixed time event-triggered consistency controller is constructed and the event-triggered condition is given;Finally, it is proved by Lyapunov function method that the method of the application can realize fixed time convergence and the expression of convergence time is given.The application solves the consistency control of multi-agent system under combination connected topology and obtains the consistency control law with fixed time control and event-triggered function.

Description

Technical Field

[0001] The present invention belongs to the field of intelligent agent control technology, and specifically relates to a multi-agent event-triggered consistency control method under a combined connected topology. Background Art

[0002] In recent years, the cooperative control of multi-agent systems has attracted widespread attention in fields such as control engineering, physics, and biology. Most cooperative control tasks, such as formation flying and swarm control, can be reduced to consensus control, where each agent can receive and communicate state information with its neighbors and update control inputs to achieve convergence for the entire system. Consensus plays a crucial role in cooperative control and has developed into an independent discipline within the control field, with rich research achievements, particularly in consensus algorithms and event-triggered control.

[0003] In practical platooning applications, the environment in which multi-agent systems operate is far from ideal. Various external disturbances may affect the multi-agent system, disrupting its operations and seriously threatening its normal functioning. Topology transformations have received widespread attention. Consistency control requires that the topology remain constant and connected. Subsequently, research on switching topology consistency has emerged, but research on time-varying topologies still requires ensuring that the topology remains connected before and after the change. However, in practice, due to factors such as limited system communication bandwidth and environmental interference, time-varying topologies cannot guarantee constant connectivity. This has led to the concept and research of combined connected topologies.

[0004] Existing formulations of the convergence of composite connected topology consistency all consider time tending to infinity or do not explicitly limit the convergence time. However, many practical applications often require that the system achieve consistency within a finite time, especially a fixed time. Therefore, constructing and analyzing event-triggered consistency algorithms with fixed-time constraints is particularly important. While finite time can accelerate convergence, the convergence time is related to the initial state of the system. To overcome this limitation, fixed-time control is proposed. Summary of the Invention

[0005] To overcome the shortcomings of the existing technology, the present invention provides a method for event-triggered consistency control of multi-agent systems under a combined connected topology. First, multi-agents are classified according to the concept of combined connected topology. Second, a fixed-time event-triggered consistency controller is constructed based on the formation coordination error, and the event triggering conditions are given. Finally, the Lyapunov function method is used to prove that the method can achieve fixed-time convergence and an expression for the convergence time is given. This invention solves the problem of consistency control of multi-agent systems under a combined connected topology and derives a consistency control law with fixed-time control and event triggering functions.

[0006] The technical solutions adopted by the present invention to solve the technical problems are as follows:

[0007] Step 1: Determine the number of agents N in the multi-agent system and design the combined connectivity topology ~ , get the corresponding undirected graph and , and get the Laplace matrix and the navigator matrix B;

[0008] Step 1-1: The interaction relationship between agents is described by an undirected graph G, where agents use Nodes are represented, the action channel between node i and node j is represented by edge (i, j), the action channel between nodes is represented by edge, and the value of the edge is expressed as ; When there is a communication connection between node i and node j, and the edge (i, j) actually exists, The value is 1, otherwise it is 0; therefore, in a multi-agent system composed of N agents, a composed of Adjacency matrix of dimension ;

[0009] Degree Matrix Defined as:

[0010]

[0011] Laplacian matrix of an undirected graph Defined as ; If it is a diagonal element, then , whose value represents the number of nodes connected to node i; If at other positions in the same row of the matrix, Its value indicates that there is a communication connection between node i and node j;

[0012] For an undirected graph, the matrix is a semi-positive symmetric matrix with one zero eigenvalue and all other non-zero eigenvalues ​​are positive real numbers; all eigenvalues ​​are arranged from small to large, and the second eigenvalue is recorded as , used to characterize the algebraic connectivity of undirected graphs;

[0013] Step 1-2: For an undirected graph, if there is an edge between any two nodes, the graph is connected. The graph is connected in time series. Such an undirected graph constitutes a composite connected topology, which is defined as:

[0014] In a set of N agents, there exists a set of undirected graphs , ,……, , used to describe undirected graphs at different times, if the union of these undirected graphs If connectivity is satisfied, then , ,……, Construct a combined connectivity topology;

[0015] The expression of pilot following error is: , the consistency control is achieved if the following formula is satisfied:

[0016]

[0017] in, is the state variable of node i, is the navigator state variable; is a preset fixed time. When time t approaches this value, the state variables of each agent remain consistent with the leader. The leader is the agent with the preset trajectory.

[0018] Step 1-3: Based on the concept of combined connectivity topology, the multi-agent system composed of N agents at the current moment is divided into three types:

[0019] (1) Type c: Several agents form a local connected subgraph and at least one agent inside it can obtain the navigator information. Such a subgraph adopts Number them, the quantity is , ;remember For a c-type feature number The number of subgraph nodes;

[0020] (2) Type s: Several agents form a local connected subgraph but no agent inside can obtain the leader information. Such a subgraph adopts Number them, the quantity is , ;remember For the s type feature number The number of subgraph nodes;

[0021] (3) Type :Each agent cannot obtain neighboring node information and navigator information, such agents use Numbering, ;remember To have The type feature number is The number of nodes;

[0022] Step 1-4: Define the expression of the navigator matrix B as:

[0023]

[0024] in, It is the diagonal element of the navigator matrix B, which is used to describe whether agent i can obtain the navigator information. If it can be obtained, the value is 1, and if it cannot be obtained, the value is 0;

[0025] Step 2: The dynamic model of agent i is described as follows using the linear modeling method:

[0026]

[0027] in, is the follower state variable, is the control quantity of the multi-agent system, It is a nonlinear dynamic term of the multi-agent system and has the following characteristics:

[0028]

[0029] in, is the state variable of node j, is an uncertain constant;

[0030] The dynamic model of the navigator is described as follows using the linear modeling method:

[0031]

[0032] Step 3: Design a fixed-time event-triggered consistency controller , the expression is:

[0033]

[0034]

[0035] in, is the agent i at its own triggering moment The state variables, is the agent j at its own triggering moment The state variables, represents the formation coordination error of node i, represents the symbolic function, Indicates that the leader agent is Status information at all times, 、 、 and All are design parameters;

[0036] Step 4: Perform stability analysis on the multi-agent system controlled by the fixed-time event-triggered consistency controller and derive the corresponding event triggering condition, which is expressed as follows:

[0037]

[0038]

[0039]

[0040] in, Indicates the event triggering error, Indicates the time when the event is triggered The obtained formation coordination error of node i is, Indicates the current time The calculated node i formation coordination error, is the event triggering error of the qth agent in the lth agent set of type c, is the formation coordination error of the qth agent in the lth agent set of type c, is the event triggering error of the qth agent in the lth agent set of type s, is the formation coordination error of the qth agent in the lth agent set of type s, Expressed as design parameters, express The second eigenvalue of the matrix, where the superscripts c and s correspond to the type of the multi-agent system, the superscript l corresponds to the lth set of agents with this characteristic, and the subscript q corresponds to the qth agent in the set of agents;

[0041] Step 5: Verify the formation control effect. Use a fixed-time event to trigger the consistency controller to conduct a control simulation experiment on the multi-agent system to verify the formation effect of the multi-agent system.

[0042] Preferably, in step 4, when the event triggering condition is met, the agent obtains its own state information and broadcasts its own state information to the undirected graph, and other agents connected to it can update their own control laws.

[0043] Preferably, the stability analysis adopts Lyapunov direct method, that is, constructing Lyapunov function and judging the stability of the multi-agent system.

[0044] Preferably, the Lyapunov function is defined as:

[0045]

[0046] in, represents a column vector consisting of the pilot-following errors of N agents.

[0047] Preferably, the Lyapunov function is positive definite if its derivative satisfies the following format:

[0048]

[0049]

[0050]

[0051]

[0052] in, and These are design parameters. and is the calculated coefficient, The maximum convergence time of the system, Indicates the actual convergence time of the system, This indicates that the actual convergence time of the system has a clear upper bound, which conforms to fixed-time control; therefore, the multi-agent system is ultimately determined to be fixed-time stable.

[0053] The beneficial effects of the present invention are as follows:

[0054] (1) The present invention considers the combined connectivity topology and relaxes the consistency control requirement for the undirected graph to be fixed and connected or switch connected. It only requires the undirected graph to be temporally connected. This setting makes the control algorithm more in line with actual needs and more suitable for the undirected graph changes faced by multiple agents when operating in complex scenarios.

[0055] (2) The present invention adopts a fixed-time consistency control algorithm, which avoids the situation in which the time of asymptotic convergence approaches infinity to ensure that the error approaches zero. Compared with finite-time convergence, the method adopted by the present invention avoids the limitation of the convergence time being associated with the initial state, and the convergence time is only related to the controller design parameters;

[0056] (3) The present invention adopts an event triggering mechanism. The controller is updated only when it is triggered by itself or a neighboring node, which greatly reduces the communication volume and computing resource consumption of the undirected graph. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 is a flow chart of the present invention;

[0058] Figure 2 This is a schematic diagram of the combined connectivity topology of the present invention;

[0059] Figure 3 The state of the multi-agent of the present invention Graph of changes over time;

[0060] Figure 4 Schematic diagram of event triggering of the multi-agent system of the present invention. DETAILED DESCRIPTION

[0061] The present invention will be further described below with reference to the accompanying drawings and examples.

[0062] The present invention provides a multi-agent event-triggered consistency control method under a combined connected topology, aiming to solve the following technical problem: how to ensure that the multi-agent system can achieve fixed-time consistency control under a combined connected topology and reduce the communication volume through an event triggering mechanism.

[0063] A multi-agent event-triggered consistency control method under a combined connected topology includes the following steps:

[0064] Step 1: Determine the number of agents N in the multi-agent system and design the combined connectivity topology ~ , get the corresponding undirected graph and , and get the Laplace matrix and the navigator matrix B;

[0065] Step 1-1: The interaction relationship between agents is described by an undirected graph G, where agents use Nodes are represented, the action channel between node i and node j is represented by edge (i, j), the action channel between nodes is represented by edge, and the value of the edge is expressed as ; When there is a communication connection between node i and node j, and the edge (i, j) actually exists, The value is 1, otherwise it is 0; therefore, in a multi-agent system composed of N agents, a composed of Adjacency matrix of dimension ;

[0066] Degree Matrix Defined as:

[0067]

[0068] Laplacian matrix of an undirected graph Defined as ; If it is a diagonal element, then , whose value represents the number of nodes connected to node i; If at other positions in the same row of the matrix, Its value indicates that there is a communication connection between node i and node j;

[0069] For an undirected graph, the matrix is a semi-positive symmetric matrix with one zero eigenvalue and all other non-zero eigenvalues ​​are positive real numbers; all eigenvalues ​​are arranged from small to large, and the second eigenvalue is recorded as , used to characterize the algebraic connectivity of undirected graphs;

[0070] Step 1-2: For an undirected graph, if there is an edge between any two nodes, the graph is connected. However, in practical problems, it is difficult to guarantee connectivity at all times or switch connectivity. As a result, undirected graphs appear connected in time series superposition. Such undirected graphs constitute a composite connectivity topology, which is defined as:

[0071] In a set of N agents, there exists a set of undirected graphs , ,……, , used to describe undirected graphs at different times, if the union of these undirected graphs If connectivity is satisfied, then , ,……, Construct a combined connectivity topology;

[0072] The expression of pilot following error is: , the consistency control is achieved if the following formula is satisfied:

[0073]

[0074] in, is the state variable of node i, is the navigator state variable; is a preset fixed time. When time t approaches this value, the state variables of each agent remain consistent with the leader. The leader is the agent with the preset trajectory.

[0075] Step 1-3: Based on the concept of combined connectivity topology, the multi-agent system composed of N agents at the current moment is divided into three types:

[0076] (1) Type c: Several agents form a local connected subgraph and at least one agent inside it can obtain the navigator information. Such a subgraph adopts Number them, the number is , ;remember For a c-type feature number The number of subgraph nodes;

[0077] (2) Type s: Several agents form a local connected subgraph but no agent inside can obtain the leader information. Such a subgraph adopts Number them, the number is , ;remember For the s type feature number The number of subgraph nodes;

[0078] (3) Type :Each agent cannot obtain neighboring node information and navigator information, such agents use Numbering, ;remember To have The type feature number is The number of nodes;

[0079] Step 1-4: Define the expression of the navigator matrix B as:

[0080]

[0081] in, It is the diagonal element of the navigator matrix B, which is used to describe whether agent i can obtain the navigator information. If it can be obtained, the value is 1, and if it cannot be obtained, the value is 0;

[0082] Step 2: The dynamic model of agent i is described as follows using the linear modeling method:

[0083]

[0084] in, is the follower state variable, is the control quantity of the multi-agent system, It is a nonlinear dynamic term of the multi-agent system and has the following characteristics:

[0085]

[0086] in, is the state variable of node j, is an uncertain constant;

[0087] The dynamic model of the navigator is described as follows using the linear modeling method:

[0088]

[0089] Step 3: Design a fixed-time event-triggered consistency controller , the expression is:

[0090]

[0091]

[0092] Step 4: Perform stability analysis on the multi-agent system controlled by the fixed-time event-triggered consistency controller and derive the corresponding event triggering condition, which is expressed as follows:

[0093]

[0094]

[0095]

[0096] Step 5: Verify the formation control effect. Use a fixed-time event to trigger the consistency controller to conduct a control simulation experiment on the multi-agent system to verify the formation effect of the multi-agent system.

[0097] Preferably, in step 4, when the event triggering condition is met, the agent obtains its own state information and broadcasts its own state information to the undirected graph, and other agents connected to it can update their own control laws.

[0098] Preferably, the stability analysis adopts Lyapunov direct method, that is, constructing Lyapunov function and judging the stability of the multi-agent system.

[0099] Preferably, the Lyapunov function Defined as:

[0100]

[0101] in, represents a column vector consisting of the pilot-following errors of N agents.

[0102] Preferably, the Lyapunov function is positive definite if its derivative satisfies the following format:

[0103]

[0104]

[0105]

[0106]

[0107] in, and These are design parameters. and is the calculated coefficient, The maximum convergence time of the system, Indicates the actual convergence time of the system, This indicates that the actual convergence time of the system has a clear upper bound, which conforms to fixed-time control; therefore, the multi-agent system is ultimately determined to be fixed-time stable.

[0108] Example:

[0109] The control parameters are shown in the following table. Based on the design parameters and the fixed time theory, the total simulation time is set to 4.13s and the switching interval between different undirected graphs is set to 0.05s. Table 1 is a table of simulation experiment parameters.

[0110] Table 1 Simulation experiment parameters

[0111]

[0112] The initial state of the navigator is:

[0113]

[0114] The number of follower agents is 6, and the initial state is:

[0115]

[0116]

[0117] The combined connectivity topology used in the simulation experiment is as follows: Figure 1 As shown, follow Figure 2 The simulation process is shown in Figure 2, and the calculation results are as follows: Figure 3~Figure 4 shown.

[0118] like Figure 3 As shown in the figure, the states of the agents initially differ. However, under the control algorithm, the states of the agents gradually converge, achieving state consistency. At approximately 4 seconds, the states of the agents converge, meeting the fixed control time (4.13 seconds) calculated before the simulation.

[0119] like Figure 4 As shown in the figure, from the perspective of the undirected graph design, since agents 1, 2, 3 and agents 5, 6 always remain connected and can communicate with the navigator throughout the undirected graph transformation, their event triggering errors converge faster. Figure 4 In the example, the trigger interval is longer and the number of triggers is less. On the contrary, Agent 4 cannot obtain the information of the leader and is completely independent in some undirected graphs. Therefore, its event triggering error converges slowly. Figure 4 The performance is shorter trigger interval and more trigger times.

Claims

1. A multi-agent event-triggered consistency control method under a combined connected topology, characterized in that: The steps include: Step 1: Determine the number of agents N in the multi-agent system and design the combined connectivity topology ~ , get the corresponding undirected graph and , and get the Laplace matrix and the navigator matrix B; Step 1-1: The interaction relationship between agents is described by an undirected graph G, where agents use Nodes are represented, the action channel between node i and node j is represented by edge (i, j), the action channel between nodes is represented by edge, and the value of the edge is expressed as ; When there is a communication connection between node i and node j, and the edge (i, j) actually exists, The value is 1, otherwise it is 0; Therefore, in a multi-agent system consisting of N agents, a composed of Adjacency matrix of dimension ; Degree Matrix Defined as: ； Laplacian matrix of an undirected graph Defined as ; If it is a diagonal element, then , whose value represents the number of nodes connected to node i; If at other positions in the same row of the matrix, Its value indicates that there is a communication connection between node i and node j; For an undirected graph, the matrix is a semi-positive symmetric matrix with one zero eigenvalue and all other non-zero eigenvalues ​​are positive real numbers; all eigenvalues ​​are arranged from small to large, and the second eigenvalue is recorded as , used to characterize the algebraic connectivity of undirected graphs; Step 1-2: For an undirected graph, if there is an edge between any two nodes, the graph is connected. The graph is connected in time series. Such an undirected graph constitutes a composite connected topology, which is defined as: In a set of N agents, there exists a set of undirected graphs , ,……, , used to describe undirected graphs at different times, if the union of these undirected graphs If connectivity is satisfied, then , ,……, Construct a combined connectivity topology; The expression of pilot following error is: , the consistency control is achieved if the following formula is satisfied: ； in, is the state variable of node i, is the navigator state variable; is a preset fixed time. When time t approaches this value, the state variables of each agent remain consistent with the leader. The leader is the agent with the preset trajectory. Step 1-3: Based on the concept of combined connectivity topology, the multi-agent system composed of N agents at the current moment is divided into three types: (1) Type c: Several agents form a local connected subgraph and at least one agent inside it can obtain the navigator information. Such a subgraph adopts Number them, the quantity is , ;remember For a c-type feature number The number of subgraph nodes; (2) Type s: Several agents form a local connected subgraph but no agent inside can obtain the leader information. Such a subgraph adopts Number them, the number is , ;remember For the s type feature number The number of subgraph nodes; (3) Type :Each agent cannot obtain neighboring node information and navigator information, such agents use Numbering, ;remember To have The type feature number is The number of nodes; Step 1-4: Define the expression of the navigator matrix B as: ； in, It is the diagonal element of the navigator matrix B, which is used to describe whether agent i can obtain the navigator information. If it can be obtained, the value is 1, and if it cannot be obtained, the value is 0; Step 2: The dynamic model of agent i is described as follows using the linear modeling method: ； in, is the follower state variable, is the control quantity of the multi-agent system, It is a nonlinear dynamic term of the multi-agent system and has the following characteristics: ； in, is the state variable of node j, is an uncertain constant; The dynamic model of the navigator is described as follows using the linear modeling method: ； Step 3: Design a fixed-time event-triggered consistency controller , the expression is: ； ； in, is the agent i at its own triggering moment The state variables, is the agent j at its own triggering moment The state variables, represents the formation coordination error of node i, represents the symbolic function, Indicates that the leader agent is Status information at all times, 、 、 and All are design parameters; Step 4: Perform stability analysis on the multi-agent system controlled by the fixed-time event-triggered consistency controller and derive the corresponding event triggering condition, which is expressed as follows: ； ； ； in, Indicates the event triggering error, Indicates the time when the event is triggered The obtained formation coordination error of node i is, Indicates the current time The calculated node i formation coordination error, is the event triggering error of the qth agent in the lth agent set of type c, is the formation coordination error of the qth agent in the lth agent set of type c, is the event triggering error of the qth agent in the lth agent set of type s, is the formation coordination error of the qth agent in the lth agent set of type s, Expressed as design parameters, express The second eigenvalue of the matrix, where the superscripts c and s correspond to the type of the multi-agent system, the superscript l corresponds to the lth set of agents with this characteristic, and the subscript q corresponds to the qth agent in the set of agents; Step 5: Verify the formation control effect. Use a fixed-time event to trigger the consistency controller to conduct a control simulation experiment on the multi-agent system to verify the formation effect of the multi-agent system.

2. The method for controlling consistency of multi-agent event triggering in a combined connected topology according to claim 1, characterized in that: In step 4, when the event triggering condition is met, the agent obtains its own state information and broadcasts its own state information to the undirected graph, and other agents connected to it can update their own control laws.

3. The method for controlling consistency of multi-agent event triggering in a combined connected topology according to claim 1, characterized in that: The stability analysis adopts the Lyapunov direct method, that is, constructing a Lyapunov function and judging the stability of the multi-agent system.

4. The method for controlling consistency of multi-agent event triggering in a combined connected topology according to claim 3, characterized in that: The Lyapunov function is defined as: ； in, represents a column vector consisting of the pilot-following errors of N agents.

5. The method for controlling consistency of multi-agent event triggering under a combined connected topology according to claim 4, characterized in that: The Lyapunov function is positive definite if its derivative satisfies the following format: ； ； ； ； in, and These are design parameters. and is the calculated coefficient, The maximum convergence time of the system, Indicates the actual convergence time of the system, This indicates that the actual convergence time of the system has a clear upper bound, which conforms to fixed-time control; therefore, the multi-agent system is ultimately determined to be fixed-time stable.

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