Second-order multi-agent event triggering consistency control method under combined connected topology

Abstract

The invention discloses a second-order multi-agent event triggering consistency control method under a combined connected topology, which comprises the following steps of: firstly, performing type division on multiple agents according to a combined connected topology concept; secondly, a fixed-time event triggering consistency controller is constructed based on formation collaborative errors, and event triggering conditions are given; finally, it is proved through a Lyapunov function method that the method can achieve fixed-time convergence, and an expression of convergence time is given. According to the method, consistency control of the second-order multi-agent system under the combined connected topology is achieved, and a consistency control law with fixed time control and event triggering functions is obtained.

Description

Technical Field

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

[0002] In recent years, cooperative control of second-order multi-agent systems has attracted extensive attention in fields such as control engineering, physics, and biology. Most cooperative control tasks, such as formation flying and swarm control, can be attributed to consensus control, that is, each agent can receive and propagate state information with adjacent agents and update the control input to achieve convergence of the entire system. Consensus plays an important role in cooperative control and has developed into an independent discipline in the field of control, with rich achievements, especially in consensus algorithms and event-triggered control.

[0003] In actual formation applications, the environment in which the second-order multi-agent system is located is not ideal. There may be various external disturbances affecting the second-order multi-agent system, which may interfere with the operation and operation of the system and seriously threaten the normal operation of the system. Among them, one point of widespread concern is the topology transformation. Consistency control requires that the topology is time-invariant and connected. Subsequently, research on switching topology consistency has emerged, but research on time-varying topology still needs to ensure that the topology is still connected before and after the change. However, in practice, due to factors such as limited system communication bandwidth and environmental interference, the time-varying topology cannot guarantee that it is always connected. Therefore, the relevant concepts and research work of combined connected topology are introduced.

[0004] Existing statements of the convergence of combined connected topology consistency all consider that time tends to infinity, or do not give clear limits on the convergence time. However, for many practical applications, the system is often required to achieve consistency in a finite time, especially a fixed time. Therefore, it is particularly important to construct and analyze event-triggered consistency algorithms with fixed time constraints. Although finite time can speed up convergence, the convergence time is related to the initial state of the system. In order to remove this limitation, fixed time control is proposed. Summary of the invention

[0005] In order to overcome the shortcomings of the prior art, the present invention provides a second-order multi-agent event-triggered consistency control method under a combined connected topology. First, the 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 condition is given; finally, the Lyapunov function method is used to prove that the method of the present invention can achieve fixed-time convergence and an expression for the convergence time is given. The present invention solves the consistency control of the second-order multi-agent system under a combined connected topology and derives a consistency control law with fixed-time control and event triggering functions.

[0006] The technical solution adopted by the present invention to solve the technical problem is as follows:

[0007] Step 1: Determine the number of agents N in the second-order multi-agent system and design the combined connectivity topology G1~G m , get the corresponding undirected graph a ij With b i , get the Laplace matrix L and the navigator matrix B;

[0008] Step 1-1: The interaction relationship between agents is described by an undirected graph G, where agent i is represented by node i, the interaction channel between node i and node j is represented by edge (i, j), the interaction channel between nodes is represented by edge, and the value of edge is expressed as a ij ; When there is a communication connection between node i and node j, and the edge (i, j) actually exists, a ij The value is 1, otherwise it is 0; therefore, in a second-order multi-agent system consisting of N agents, a ij The N×N dimensional adjacency matrix A=[a ij ]∈R N×N ;

[0009] Degree matrix D = diag[d1,d2,], d i ,…,d N ] is defined as:

[0010]

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

[0012] For an undirected graph, the matrix L 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 denoted by λ2(L), which is used to characterize the algebraic connectivity of the undirected graph;

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

[0014] In a set of N agents, there exists a set of undirected graphs G1, G2, ..., G m , used to describe undirected graphs at different times, if the union of these undirected graphs G = {G|G1∪G2∪……∪G m} satisfies connectivity, then G1,G2,……,G m Construct a combined connectivity topology;

[0015] The pilot following error expression is ξ i =x i -x0, if the following formula is satisfied, consistency control is implemented:

[0016]

[0017] Among them, x i is the state variable of node i, x0 is the leader state variable; T max is a preset fixed time. When the time t approaches this value, the state variables of each agent are consistent with the navigator. The navigator is an agent with a preset trajectory.

[0018] Step 1-3: Based on the concept of combined connectivity topology, the second-order 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 the subgraph can obtain the navigator information. Such subgraphs are numbered with l, and the number is q, where l = 1~q; is the number of subgraph nodes with type c feature number l;

[0020] (2) Type s: Several agents form a local connected subgraph but no agent inside can obtain the navigator information. Such subgraphs are numbered with l, and the number is m, where l = q+1 to q+m. is the number of subgraph nodes with type s feature number l;

[0021] (3) Type r: Each agent cannot obtain neighbor node information and navigator information. Such agents are numbered using l, where l = q + m + 1 to N. is the number of nodes with type r feature number l;

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

[0023] B=diag(b i )

[0024] Among them, b iIt 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 by linear modeling method:

[0026]

[0027] Among them, x i is the follower state variable, v i is the follower velocity variable, u i is the control quantity of the second-order multi-agent system. The dynamic model of the navigator is described as follows by the linear modeling method:

[0028]

[0029] Among them, x0 is the navigator state variable, v0 is the navigator speed variable, and u0 is the navigator control variable.

[0030] Step 3: Design a fixed-time event-triggered consistency controller u i , the expression is:

[0031]

[0032] Among them, x i (t k ) is the time when agent i triggers itself k The state variable, v i (t k ) is the time when agent i triggers itself k The speed variable x j (t k' ) is the time when agent j triggers itself k' The state variable, v j (t k' ) is the time when agent j triggers itself k' The speed variable x0(t k ) indicates that the leader agent is at t k The state information at the moment, v0(t k ) indicates that the leader agent is at t k Speed ​​information at the moment; K1 and K2 are design parameters.

[0033] Step 4: Perform stability analysis on the second-order multi-agent system controlled by the fixed-time event-triggered consistency controller, and derive the corresponding event triggering condition, expressed as;

[0034] ξ i =x i-x0,e ξ,i =ξ i (t k )-ξ i

[0035] η i =v i -v0,e η,i =η i (t k )-η i

[0036]

[0037]

[0038] Among them, ξ i represents the pilot-following state error of agent i, ξ i (t k ) represents the triggering time t k The corresponding ξ i Variable, e ξ,i represents the event triggering error of the state variable of agent i; η i represents the pilot following speed error of agent i, η i (t k ) represents the triggering time t k The corresponding η i Variable, e η,i represents the event triggering error of the velocity variable of agent i; and represents the Laplacian matrix and leader-follower matrix formed by the multi-agent set with c features and numbered l; min (.) represents the minimum eigenvalue of the matrix; The variable ξ represents the agent numbered i in the multi-agent set numbered l with feature c; The variable η represents the agent with sequence number i in the multi-agent set with feature c and sequence number l; It is represented by the number of subgraph nodes with type s feature number l; The variable η represents the agent with sequence number i in the multi-agent set with sequence number l and with characteristics s; The variable ξ represents the agent numbered i in the multi-agent set numbered l with characteristics s; The Laplacian matrix formed by the multi-agent local connected subgraph with feature s and numbered l. According to the definition of type s in steps 1-3, since there is no agent in this type of local connected subgraph that can obtain the leader information, its leader-follower matrix does not exist;

[0039] ρ and μ are design parameters, and α is a design parameter that must satisfy the following constraints:

[0040]

[0041]

[0042] Step 5: Verify the formation control effect. Use a fixed-time event to trigger a consistency controller to conduct a control simulation experiment on the second-order multi-agent system to verify the formation effect of the second-order multi-agent system.

[0043] 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.

[0044] Preferably, the stability analysis adopts Lyapunov direct method, that is, constructing a Lyapunov function and judging the stability of the second-order multi-agent system.

[0045] Preferably, the Lyapunov function V is defined as:

[0046]

[0047] Where y = [ξ T ,η T ] T ,ξ=[ξ1,……,ξ N ] T represents the column vector consisting of the pilot-follower state errors of N agents, η=[η1,……,η N ] T . Positive judgment needs to satisfy λ min (K1(L T +L)+2K2B-I N )>0, according to the prior condition λ min (K1L+K2B)>1, we can see that the positive definiteness of the function holds.

[0048] Preferably, the Lyapunov function has positive definiteness if its derivative satisfies the following format:

[0049]

[0050]

[0051]

[0052] According to the function properties, it is determined that the derivative function has negative definiteness. Combined with the positive definiteness of the Lyapunov function described in claim 5 and the negative definiteness of the derivative function of the Lyapunov function described in this requirement, it can be concluded that the closed-loop system is stable.

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

[0054] (1) The present invention takes into account the combined connectivity topology and relaxes the requirement of consistency control for the undirected graph to be fixed and connected or switched 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 working in complex scenarios.

[0055] (2) The present invention adopts an event triggering mechanism, and 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.

[0056] (3) The present invention takes into account second-order multi-agents. In addition to research objects such as wheeled unmanned vehicles that can directly control the wheel speed, research objects such as drones, unmanned vehicles, and four-wheeled unmanned vehicles all conform to second-order dynamic behavior. This choice of the present invention makes the control algorithm more in line with the actual research object. 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 is the controlled second-order multi-agent system of the present invention. ξ,i Curves changing over time;

[0060] Figure 4 is the controlled second-order multi-agent system of the present invention. η,i Curves changing over time;

[0061] Figure 5 Schematic diagram of event triggering of the controlled second-order multi-agent system of the present invention. DETAILED DESCRIPTION

[0062] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0063] The present invention provides a second-order multi-agent event-triggered consistency control method under a combined connected topology, aiming to solve the following technical problem: how to ensure that the second-order multi-agent system can achieve fixed-time consistency control and reduce the communication volume through an event triggering mechanism under a combined connected topology.

[0064] A second-order multi-agent event-triggered consistency control method under a combined connected topology comprises the following steps:

[0065] Step 1: Determine the number of agents N in the second-order multi-agent system and design the combined connectivity topology G1~G m , get the corresponding undirected graph a ij With b i , get the Laplace matrix L and the navigator matrix B;

[0066] Step 1-1: The interaction relationship between agents is described by an undirected graph G, where agent i is represented by node i, the interaction channel between node i and node j is represented by edge (i, j), the interaction channel between nodes is represented by edge, and the value of edge is expressed as a ij ; When there is a communication connection between node i and node j, and the edge (i, j) actually exists, a ij The value is 1, otherwise it is 0; therefore, in a second-order multi-agent system consisting of N agents, a ij The N×N dimensional adjacency matrix A=[a ij ]∈R N×N ;

[0067] Degree matrix D = diag[d1, d2, ..., d i ,…,d N ] is defined as:

[0068]

[0069] The Laplacian matrix of an undirected graph L = [l ij ]∈R N×N Defined as L = DA; l ij If it is a diagonal element, then l ii , whose value represents the number of nodes connected to node i; l ij If at other positions in the same row of the matrix, l ij Its value indicates that there is a communication connection between node i and node j;

[0070] For an undirected graph, the matrix L 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 denoted by λ2(L), which is used to characterize the algebraic connectivity of the undirected graph;

[0071] Step 1-2: For an undirected graph, when there is an edge between any two nodes, the undirected graph is connected. However, in practical problems, it is difficult to ensure connectivity or switch connectivity at all times. As a result, the undirected graph appears connected in time series superposition. Such an undirected graph constitutes a combined connectivity topology, which is defined as:

[0072] In a set of N agents, there exists a set of undirected graphs G1, G2, ..., G m , used to describe undirected graphs at different times, if the union of these undirected graphs G = {G|G1∪G2∪……∪G m} satisfies connectivity, then G1,G2,……,G m Construct a combined connectivity topology;

[0073] The pilot following error expression is ξ i =x i -x0, if the following formula is satisfied, consistency control is implemented:

[0074]

[0075] Among them, x i is the state variable of node i, x0 is the leader state variable; T max is a preset fixed time. When the time t approaches this value, the state variables of each agent are consistent with the navigator. The navigator is an agent with a preset trajectory.

[0076] Step 1-3: Based on the concept of combined connectivity topology, the second-order multi-agent system composed of N agents at the current moment is divided into three types:

[0077] (1) Type c: Several agents form a local connected subgraph and at least one agent inside the subgraph can obtain the navigator information. Such subgraphs are numbered with l, and the number is q, where l = 1~q; is the number of subgraph nodes with type c feature number l;

[0078] (2) Type s: Several agents form a local connected subgraph but no agent inside can obtain the navigator information. Such subgraphs are numbered with l, and the number is m, where l = q+1 to q+m. is the number of subgraph nodes with type s feature number l;

[0079] (3) Type r: Each agent cannot obtain neighbor node information and navigator information. Such agents are numbered using l, where l = q + m + 1 to N. is the number of nodes with type r feature number l;

[0080] Step 1-4: Define the expression of the navigator matrix B as:

[0081] B=diag(b i )

[0082] Among them, b iIt 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;

[0083] Step 2: The dynamic model of agent i is described as follows by linear modeling method:

[0084]

[0085] Among them, x i is the follower state variable, v i is the follower velocity variable, u i is the control quantity of the second-order multi-agent system:. The dynamic model of the navigator is described as follows by the linear modeling method:

[0086]

[0087] Among them, x0 is the navigator state variable, v0 is the navigator speed variable, and u0 is the navigator control variable.

[0088] Step 3: Design a fixed-time event-triggered consistency controller u i , the expression is:

[0089]

[0090] Step 4: Perform stability analysis on the second-order multi-agent system controlled by the fixed-time event-triggered consistency controller and derive the corresponding event triggering condition, expressed as;

[0091] ξ i =x i -x0,e ξ,i =ξ i (t k )-ξ i

[0092] η i =v i -v0,e η,i =η i (t k )-η i

[0093]

[0094]

[0095] 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 second-order multi-agent system to verify the formation effect of the second-order multi-agent system.

[0096] 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.

[0097] Preferably, the stability analysis adopts Lyapunov direct method, that is, constructing a Lyapunov function and judging the stability of the second-order multi-agent system.

[0098] Preferably, the Lyapunov function V is defined as:

[0099]

[0100] Where y = [ξ T ,η T ] T ,ξ=[ξ1,……,ξ N ] T represents the column vector consisting of the pilot-follower state errors of N agents, η=[η1,……,η N ] T . Positive judgment needs to satisfy λ min (K1(L T +L)+2K2B-I N )>0, according to the prior condition λ min (K1L+K2B)>1, we can see that the positive definiteness of the function holds.

[0101] Preferably, the Lyapunov function has positive definiteness if its derivative satisfies the following format:

[0102]

[0103]

[0104]

[0105] According to the properties of the function, it can be determined that the derivative function has negative definiteness. Combined with the positive definiteness of the Lyapunov function described in claim 5 and the negative definiteness of the derivative function of the Lyapunov function described in this requirement, it can be concluded that the closed-loop system is stable.

[0106] Example:

[0107] The control parameters are shown in the following table. According to the design parameters and the fixed time theory, the total simulation time is selected as 8s and the switching interval of different undirected graphs is selected as 0.2s in this embodiment. Table 1 is a table of simulation experiment parameters.

[0108] Table 1 Simulation experiment parameters

[0109]

[0110] The initial state of the navigator is

[0111] x0=0

[0112] v0=0

[0113] The number of follower agents is 6, and the initial state is

[0114] x i (t=0)=[-1,-2,-2,-3,-2,-1]

[0115] v i (t=0)=[1,1,0,0,-1,-1]

[0116] 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. The calculation results are as follows: Figure 3 to Figure 5 shown.

[0117] like Figure 3 As shown in the figure, the states of multiple agents are different at the initial moment, but under the control algorithm, the states of each agent gradually converge and achieve state consistency. At about 5s, the states of each agent converge.

[0118] like Figure 4 As shown in Figure 2, combined with the topology design, since agents 1, 2, 3 and agents 5, 6 remain connected throughout the entire topology transformation and can communicate with the navigator, 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 topologies. Therefore, its event triggering error converges slowly. Figure 4 The performance is shorter trigger interval and more trigger times.

Claims

1. A second-order 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 second-order multi-agent system and design the combined connectivity topology G1~G m , get the corresponding undirected graph a ij With b i , get the Laplace matrix L and the navigator matrix B; Step 1-1: The interaction relationship between agents is described by an undirected graph G, where agent i is represented by node i, the interaction channel between node i and node j is represented by edge (i, j), the interaction channel between nodes is represented by edge, and the value of edge is expressed as a ij ; When there is a communication connection between node i and node j, and the edge (i, j) actually exists, a ij The value is 1, otherwise it is 0; Therefore, in a second-order multi-agent system consisting of N agents, a ij The N×N dimensional adjacency matrix A=[a ij ]∈R N×N ; Degree matrix D = diag[d1, d2, ..., d i ,…,d N ] is defined as: The Laplacian matrix of an undirected graph L = [l ij ]∈R N×N Defined as L = DA; l ij If it is a diagonal element, then l ii , whose value represents the number of nodes connected to node i; l ij If at other positions in the same row of the matrix, l ij Its value indicates that there is a communication connection between node i and node j; For undirected graphs, the matrix L 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 denoted as λ2(L), which is used to characterize the algebraic connectivity of the undirected graph; Step 1-2: For an undirected graph, when there is an edge between any two nodes, the undirected graph is connected. The undirected graph is connected in time series superposition. Such an undirected graph constitutes a combined connected topology, which is defined as: In a set of N agents, there exists a set of undirected graphs G1, G2, ..., G m , used to describe undirected graphs at different times, if the union of these undirected graphs G = {G|G1∪G2∪……∪G m } satisfies connectivity, then G1,G2,……,G m Construct a combined connectivity topology; The pilot following error expression is ξ i =x i -x0, if the following formula is satisfied, consistency control is implemented: Among them, x i is the state variable of node i, x0 is the leader state variable; T max is a preset fixed time. When the time t approaches this value, the state variables of each agent are consistent with the navigator. The navigator is an agent with a preset trajectory. Step 1-3: Based on the concept of combined connectivity topology, the second-order 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 the subgraph can obtain the navigator information. Such subgraphs are numbered with l, and the number is q, where l = 1~q; is the number of subgraph nodes with type c feature number l; (2) Type s: Several agents form a local connected subgraph but no agent inside can obtain the navigator information. Such subgraphs are numbered with l, and the number is m, where l = q+1 to q+m. is the number of subgraph nodes with type s feature number l; (3) Type r: Each agent cannot obtain neighbor node information and navigator information. Such agents are numbered using l, where l = q + m + 1 to N. is the number of nodes with type r feature number l; Step 1-4: Define the expression of the navigator matrix B as: B=diag(b i ) Among them, b i 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 by linear modeling method: Among them, x i is the follower state variable, v i is the follower velocity variable, u i is the control quantity of the second-order multi-agent system; the dynamic model of the navigator is described as follows through the linear modeling method: Among them, x0 is the navigator state variable, v0 is the navigator speed variable, and u0 is the navigator control variable; Step 3: Design a fixed-time event-triggered consistency controller u i , the expression is: Among them, x i (t k ) is the time when agent i triggers itself k The state variable, v i (t k ) is the time when agent i triggers itself k The speed variable x j (t k' ) is the time when agent j triggers itself k' The state variable, v j (t k' ) is the time when agent j triggers itself k 'Speed ​​variable; x0(t k ) indicates that the leader agent is at t k The state information at the moment, v0(t k ) indicates that the leader agent is at t k Speed ​​information at the moment; K1 and K2 are both design parameters; Step 4: Perform stability analysis on the second-order multi-agent system controlled by the fixed-time event-triggered consistency controller, and derive the corresponding event triggering condition, expressed as; x i =x i -x0,e ξ,i =ξ i (t k )-ξ i η i =v i -v0,e η,i =η i (t k )-η i Among them, ξ i represents the pilot-following state error of agent i, ξ i (t k ) represents the triggering time t k The corresponding ξ i Variable, e ξ,i represents the event triggering error of the state variable of agent i; η i represents the pilot following speed error of agent i, η i (t k ) represents the triggering time t k The corresponding η i Variable, e η,i represents the event triggering error of the velocity variable of agent i; and represents the Laplacian matrix and leader-follower matrix formed by the multi-agent set with c features and numbered l; min (.) represents the minimum eigenvalue of the matrix; The variable ξ represents the agent numbered i in the multi-agent set numbered l with feature c; The variable η represents the agent with sequence number i in the multi-agent set with feature c and sequence number l; It is represented by the number of subgraph nodes with type s feature number l; The variable η represents the agent with sequence number i in the multi-agent set with sequence number l and with characteristics s; The variable ξ represents the agent numbered i in the multi-agent set numbered l with characteristics s; The Laplacian matrix formed by the multi-agent local connected subgraph with feature s and numbered l. According to the definition of type s in steps 1-3, since there is no agent in this type of local connected subgraph that can obtain the leader information, its leader-follower matrix does not exist; ρ and μ are design parameters, and α is a design parameter that must satisfy the following constraints: Step 5: Verify the formation control effect. Use a fixed-time event to trigger a consistency controller to conduct a control simulation experiment on the second-order multi-agent system to verify the formation effect of the second-order multi-agent system.

2. According to the second-order multi-agent event-triggered consistency control method under combined connected topology according to claim 1, it is 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. According to the second-order multi-agent event-triggered consistency control method under a combined connected topology according to claim 1, it is characterized in that: The stability analysis adopts Lyapunov direct method, that is, constructing Lyapunov function and judging the stability of the second-order multi-agent system.

4. According to the second-order multi-agent event-triggered consistency control method under combined connected topology according to claim 3, it is characterized in that: The Lyapunov function is defined as: Where y = [ξ T ,η T ] T ,ξ=[ξ1,……,ξ N ] T represents the column vector consisting of the pilot-follower state errors of N agents, η=[η1,……,η N ] T ; Positive judgment needs to satisfy λ min (K1(L T +L)+2K2B-I N )>0, according to the prior condition λ min (K1L+K2B)>1, we can see that the positive definiteness of the function holds.

5. According to the second-order multi-agent event-triggered consistency control method under combined connected topology according to claim 4, it is characterized in that: The Lyapunov function is positive definite if its derivative satisfies the following format: According to the function properties, it is determined that the derivative function has negative definiteness. Combined with the positive definiteness of the Lyapunov function described in claim 5 and the negative definiteness of the derivative function of the Lyapunov function described in this requirement, it can be concluded that the closed-loop system is stable.

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