A multi-agent cooperative control method and device for transmission time lag

Abstract

The application relates to a multi-agent cooperative control method and device for transmission time lag, and belongs to the technical field of multi-agent control. In the method, a directed network topology thought is introduced into information interaction among agents in a multi-agent system, a second-order dynamic system model of the agent is constructed to model the internal state of the agent, a tracking error equation of the multi-agent system containing the transmission time lag is established, the tracking error equation is analyzed by using Lyapunov stability theory and finite time stability theory, and a stability control condition is obtained, so that a control gain coefficient capable of realizing consistency stability of the multi-agent system in a finite time can be obtained by solving the stability control condition.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of multi-agent control, and particularly relates to a multi-agent cooperative control method and device for transmission time lag. BACKGROUND

[0002] With the development of automatic control system technology, the research and application of multi-agent system show a rapid development momentum. The multi-agent system can contain multiple agents, each agent can be controlled and run independently, and there can be information interaction and mutual influence between different agents. The multi-agent system can be a UAV cluster, a multi-agent system, etc.

[0003] In the multi-agent system, the cooperative control of multi-agent is an important research direction in current system control, which can be mainly realized through information interaction between agents in different environments. However, due to the influence of the interaction network, there can be transmission time lag, system delay and other network problems in the information interaction process between agents. Especially when the multi-agent system needs to be dynamically adjusted, the information interaction is delayed, and the multi-agent system is difficult to achieve consistent stability within a limited time, and cannot reach a balanced state in a short time.

[0004] Therefore, the increasingly complex application scenarios and business requirements put higher requirements on the cooperative control of the multi-agent system, and therefore there is an urgent need for a system control scheme of the multi-agent system, so that the multi-agent system can achieve consistent stability within a limited time under the network state of transmission time lag and system delay. SUMMARY

[0005] In order to ensure that the internal multi-agent system reaches consistent stability within a limited time, the embodiments of the present application provide a multi-agent cooperative control method and device for transmission time lag. The technical scheme is as follows:

[0006] In a first aspect, the embodiments of the present application provide a multi-agent cooperative control method for transmission time lag, which comprises: dividing all agents in a multi-agent system into one leader and multiple followers, and generating information interaction relationship of the leader and the followers by using a directed topological network;

[0007] establishing a second-order dynamic system model of each agent, and establishing a tracking error equation between the followers and the leader based on the second-order dynamic system model;

[0008] Based on the tracking error equation and the information interaction relationship, a control input equation u i of each follower containing transmission time lag is constructed, the control input equation u i contains a control gain coefficient to be solved;

[0009] The control input equation u i The tracking error equation is generated by substituting the control input equation u

[0010] The stability control condition of the multi-agent system is generated by analyzing the system tracking error equation through Lyapunov stability theory and finite time stability theory;

[0011] The control input equation u i of each follower is solved to obtain the control gain coefficient corresponding to the follower;

[0012] The control gain coefficient is loaded into the controller of each follower, so that the controller controls the follower according to the control gain coefficient.

[0013] Based on the above technical solution, the agent state model of the multi-agent system is modeled, the cooperative control gain coefficient between agents is obtained through mathematical analysis, the individual controller can be used to accurately control the agent in real time, and therefore the multi-agent system can effectively achieve consistent stability in a limited time.

[0014] Optionally, the information interaction relationship between the leader and the follower is generated by using a directed topological network, including:

[0015] All the agents are set as nodes in the directed topological network by using graph theory knowledge;

[0016] An adjacency matrix A=[a ij ] of the directed topological network is generated, where i and j are adjacent agents, i,j=1,2,...,n+1, and element a ij =1 indicates that there is information interaction between the i th agent and the j th agent, and element a ij =0 indicates that there is no information interaction between the i th agent and the j th agent.

[0017] Based on the above technical solution, the directed network topology idea is introduced into the information interaction of the agents in the multi-agent system by using graph theory knowledge, so that the information interaction between other agents is not affected when an agent is added or deleted in the multi-agent system, which is more in line with the actual needs of the multi-agent system construction.

[0018] Optionally, the second-order dynamic system model of each agent is established, and the tracking error equation between the follower and the leader is established based on the second-order dynamic system model, including:

[0019] based on the internal state x0(t) of the leader, a state change amount and a control input r0(t), a second-order dynamic system model of the leader is established:

[0020] based on the internal state x i (t) of each follower, a state change amount a system disturbance w i (t) and the control input equation u i (t), a second-order dynamic system model of each follower is established: based on the internal state of the leader and the internal state of the i-th follower, a tracking error equation ξ i (t) of the i-th follower and the leader is set i (t) = x0(t) - x i (t) - f i (t), wherein f i (t) is a system vector of the i-th follower, a system formation control signal, C = [1 0],

[0021] Based on the above technical solutions, by establishing a second-order dynamic system model, the complex state model inside the agent can be modeled, and the consistency stability data of the multi-agent system is dataized as the tracking error equation between the follower and the leader, so that the subsequent analysis of the state change and system stability of the agent is fast and effective.

[0022] Optionally, the control input equation u i of each follower containing a transmission time delay is constructed based on the tracking error equation and the information interaction relationship, comprising:

[0023] The tracking error equation is set to approach zero, and a control auxiliary term of the i-th follower is generated by analyzing the tracking error equation

[0024] The control auxiliary term and the control input r0(t) of the leader, and the system formation control signal are used to construct the control input equation of the i-th follower Wherein, K1, K2, K3 are control gain coefficients to be solved.

[0025] Based on the above technical solutions, the tracking error equation is analyzed, and the control input equation of the follower is established in combination with the control input of the leader and the system formation control signal, so that the control input equation can match the real needs of the follower.

[0026] Optionally, the control input equation u i is substituted into the tracking error equation, and a system tracking error equation of the multi-agent system is generated by an augmentation process, including:

[0027] the control input equation u i is substituted into the tracking error equation, and K2 and K3 are set as identity matrices, to obtain a tracking error dynamic equation

[0028] The tracking error dynamic equation is augmented to construct a system tracking error equation in the multi-agent system wherein, ξ = col{ξ1, ξ2,..., ξ n}, w = col{w1, w2,..., w n}, I N is an N-dimensional identity matrix, represents a Kronecker product, and L is a Laplacian matrix corresponding to the adjacency matrix.

[0029] Optionally, the stability control condition is: if there exist constants γ>0, d>0, a suitable dimension matrix K, and positive definite matrices P, Q, and Z, which satisfy

[0030]

[0031] Ω 11 = A T P+PA+2P+Q+3A T ZA-d -1 e -γd Z-γP+I

[0032] Ω 22 =-(1-d)Q-d -1 e -γd Z

[0033] is established, and the then when the transmission time delay d(t) satisfies 0 the element * in the element R T , are inverse matrices of P and Z respectively, α = λ max (L T L), t0 is an arbitrary time, t is an arbitrary time greater than t0, c2>c1>0 and λ2, λ3, and λ4 are maximum eigenvalues of P, Q, and Z respectively, and the suitable dimension matrix K is a control gain coefficient in the form of a matrix.

[0034] Optionally, the method further comprises:

[0035] for the tracking error equation ξ i (t) and system disturbance w i (t), a performance index function H ∞ is introduced, wherein s is an integral variable;

[0036] The performance index function is analyzed by Lyapunov stability theory to generate a disturbance suppression condition, and if there exists a disturbance suppression parameter 0 < γ < 1 and a positive definite matrix P, Q, Z, which satisfies Ω < 0, then all agents in the multi-agent system have disturbance suppression performance;

[0037] The control input equation of each follower is solved by using the stability condition of the multi-agent system to obtain the corresponding control gain coefficient of the follower, comprising:

[0038] The control input equation of each follower is solved by using the stability condition of the multi-agent system and the disturbance suppression condition to obtain the corresponding control gain coefficient of the follower.

[0039] Based on the above technical solutions, in addition to the stability control condition, a H ∞ method is introduced to set the disturbance suppression condition of the agent, and the stability control condition and the disturbance suppression condition are combined to solve the corresponding control gain coefficient of the follower, so that the solved control gain coefficient can meet the stability requirement of the multi-agent system and effectively suppress the noise disturbance.

[0040] In a second aspect, the embodiments of the present application also provide a multi-agent cooperative control device for transmission time delay, comprising:

[0041] A topological structure analysis module is configured to divide all agents in a multi-agent system into one leader and multiple followers, and generate information interaction relationships of the leader and the followers by using a directed topological network;

[0042] A system equation building module is configured to establish a second-order dynamic system model of each agent, and establish a tracking error equation between the followers and the leader based on the second-order dynamic system model;

[0043] A control input analysis module is configured to construct a control input equation u i of each follower containing transmission time delay based on the tracking error equation and the information interaction relationship, wherein the control input equation u i contains a control gain coefficient to be solved.​

[0044] The system equation building module is further configured to substitute the control input equation u i into the tracking error equation, and generate a system tracking error equation of the multi-agent system through an augmentation process;

[0045] a stability analysis module configured to analyze the system tracking error equation through Lyapunov stability theory and finite time stability theory, and generate a stability control condition of the multi-agent system;

[0046] a control gain solving module configured to solve the control input equation u i of each follower by using the stability control condition of the multi-agent system, and obtain a control gain coefficient corresponding to the follower;

[0047] a control gain loading module configured to load the control gain coefficient into a controller of each follower, so that the controller controls the follower according to the control gain coefficient.

[0048] In a third aspect, a central controller is provided, which includes a processor and a memory, and the memory stores at least one instruction, at least one program, a code set or an instruction set, which are loaded and executed by the processor to implement the multi-agent cooperative control method for transmission time lag as described in the first aspect.

[0049] In a fourth aspect, a computer readable storage medium is provided, which stores at least one instruction, at least one program, a code set or an instruction set, which are loaded and executed by a processor to implement the multi-agent cooperative control method for transmission time lag as described in the first aspect.

[0050] In summary, the present application has the following beneficial effects:

[0051] This application employs a multi-agent cooperative control method for transmission delays, introducing the concept of directed network topology into the information interaction between agents in a multi-agent system. A second-order dynamic system model of the agents is constructed to model their states under transmission delays, thereby establishing the system tracking error equation. Lyapunov stability theory and finite-time stability theory are then used to analyze the tracking error equation, deriving stability conditions. These stability conditions can then be used to solve for the control gain coefficients that enable consistent stability of the multi-agent system. By modeling the agent states of the multi-agent system and obtaining the cooperative control gain coefficients between agents through mathematical analysis, the controller can perform real-time and precise control of the agents. Even when the transmission delay is unknown and varies with the state at different times, tracking control of the multi-agent system can still be achieved, effectively realizing consistent stability of the multi-agent system under transmission delays. Attached Figure Description

[0052] Figure 1 This is a schematic diagram of a scenario architecture for a multi-agent system in an embodiment of this application;

[0053] Figure 2 This is a flowchart of an intelligent agent cooperative control method in an embodiment of this application;

[0054] Figure 3 This is a schematic diagram of the structure of an intelligent agent collaborative control device in an embodiment of this application. Detailed Implementation

[0055] To make the purpose, technical solution, and advantages of this application clearer, the following description is provided in conjunction with the appendix. Figures 1-3 The present application will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the application.

[0056] This application provides a multi-agent cooperative control method for transmission delay, which can be applied to applications such as... Figure 1 In the multi-agent system shown, execution can be performed by a central controller. The multi-agent system can include a central controller and multiple agents, each agent corresponding to one controller. The central controller can interact with the controllers of each agent in the multi-agent system (hereinafter referred to as individual controllers), such as obtaining the agent's internal state data from the individual controllers and sending control gain coefficients to them. The central controller can also have data processing and analysis functions, that is, it can process and analyze the agent's internal state data and state changes to obtain the control gain coefficients loaded into the individual controllers.

[0057] The following will be described in detail in conjunction with specific embodiments, and the content can be as follows: step 201, all agents in the multi-agent system are divided into a leader and multiple followers, and the information interaction relationship of the leader and the followers is generated by using a directed topological network. Figure 2

[0058] In implementation, the central controller can record all online agents in the multi-agent system, and select one agent as the leader from all agents, and determine the remaining agents as followers. In other words, let there be n+1 agents in the multi-agent system, and set one of them as the leader, and the remaining n agents as followers. Then, the central controller can introduce a directed topological network, take an undirected graph G to describe the communication network topological relationship between the leader and the followers in the multi-agent system, thereby generating the information interaction relationship between any two agents.

[0059] Optionally, the information interaction relationship can be expressed by using an adjacency matrix, and correspondingly, the processing of step 201 can be as follows: all agents are set as nodes in the directed topological network by using graph theory knowledge; the adjacency matrix A=[a ij ] of the directed topological network is generated.

[0060] Wherein, i and j are adjacent agents, i, j = 1, 2,..., n, and the element a ij =1 indicates that there is information interaction between the i th agent and the j th agent, and the element a ij =0 indicates that there is no information interaction between the i th agent and the j th agent.

[0061] In implementation, the central controller can introduce graph theory knowledge, and use the directed topological network to identify the information interaction relationship between the agents in the multi-agent system. Specifically, the agents can be first set as nodes in the directed topological network, and then the adjacency matrix A=[a ij ] of the directed topological network is generated, wherein i and j are adjacent agents, i, j = 1, 2,..., n, and the element a ij is the information interaction weight between the i th agent and the j th agent, when the element a ij =1 indicates that there is information interaction between the i th agent and the j th agent, and the element a ij =0 indicates that there is no information interaction between the i th agent and the j th agent, for example, a 12 =0, which means that there is no information interaction between the first agent and the second agent. In addition, a ii =0, which means that the information interaction weight of each agent with itself is 0. It is worth mentioning that the leader is set as the 0 th agent by default in this embodiment, and a ij ​The information interaction weight value between the followers can be established.

[0062] In step 202, a second-order dynamic system model of each agent is established, and a tracking error equation between the follower and the leader is established based on the second-order dynamic system model.

[0063] In implementation, the internal state value and change of the agent in the multi-agent system during running can be fitted by the second-order dynamic system model, and further, the consistency stability between the plurality of agents can be reflected by the error between the follower and the leader. Therefore, for each agent, the central controller can establish the second-order dynamic system model of the agent, and construct the tracking error equation between the leader and the follower through the second-order dynamic system model, so as to dataize the state deviation between the leader and the follower existing in the influence of the consistency stability.

[0064] Optionally, the second-order dynamic system model of the agent in step 202 can be divided into a second-order dynamic system model of the leader and a second-order dynamic model of the follower, and the corresponding construction process can be as follows: based on the internal state x0(t) of the leader, the state change amount and the control input r0(t) of the individual controller, the second-order dynamic system model of the leader is established as follows: Based on the internal state x i of each follower, the state change amount system disturbance w i (t) and control input equation u i (t) of the power supply controller, the second-order dynamic system model of each follower is established as follows:

[0065] In implementation, when constructing the second-order dynamic system model of the leader, the internal state and the state change amount of the leader, and the control input of the individual controller to the leader can be considered, and therefore, the second-order dynamic system model of the leader can be established based on the internal state x0(t) of the leader, the state change amount and the control input r0(t) of the individual controller. As for the follower, the internal state and the state change amount of the follower, and the control input of the power supply controller to the follower also need to be considered, in addition to the influence of external disturbance on the follower, and therefore, the second-order dynamic system model of the follower can be established based on the internal state x i of each follower, the state change amount system disturbance w i (t) and control input equation u i (t) of the power supply controller. The internal state is a multi-dimensional state vector of each follower, and each dimension corresponds to a state parameter of the follower, x i(t) represents the internal state of the i-th follower at time t, and the state change amount can be understood as the internal state at the next moment. It can be understood that when the leader shares its own state with the follower, in order to achieve the output consistency goal, the leader itself can be regarded as an intelligent agent with anti-interference performance, so when constructing the second-order dynamic system model of the leader, the noise interference can not be considered.

[0066] Further, based on the above-mentioned constructed second-order dynamic system model of the leader and the follower, the establishment process of the tracking error equation can be as follows: based on the internal state of the leader and the internal state of the i-th follower, the tracking error equation ξ i (t) = x0(t) - x i (t) - f i (t).

[0067] Wherein, f i (t) is the system vector of the i-th follower, is the system formation control signal, C = [1 0],

[0068] In implementation, in a stable multi-agent system, a specific formation form needs to be ensured between agents, such as when the agent is a UAV and the multi-agent system is a UAV formation, in the flight process of the UAV formation, a fixed distance needs to be maintained between each UAV, and the relative position with other UAVs remains unchanged. Therefore, for such a formation form, the system vector f i (t) can be used to reflect, and there is is the system formation control signal. It is not difficult to understand that the formation form is dynamically changing, and the change amount is influenced by both the current formation form and the system formation control input. In summary, when constructing the tracking error equation of the follower and the leader, not only the internal state x i (t) of the follower and the internal state x0(t) of the leader need to be considered, but also the above-mentioned system vector f i (t) needs to be introduced to ensure the formation stability of the multi-agent system, so that the tracking error equation ξ i (t) = x0(t) - x i (t) - f i (t) can be obtained.

[0069] Step 203, based on the tracking error equation and the information interaction relationship, constructing a control input equation u i of each follower containing transmission time delay.

[0070] Wherein, the control input equation u iThe control gain coefficients to be solved include K1, K2, and K3.

[0071] In implementation, the central controller constructs a tracking error equation between the follower and the leader, analyzes the tracking error equation from the perspective of ensuring that the states of the two satisfy consistency stability, and determines the control signal suitable for each follower. Meanwhile, considering the mutual interference between agents in the multi-agent system, the control input equation u i of each follower with transmission time delay can be further constructed in combination with the information interaction relationship.

[0072] Optionally, the construction process of the control input equation u i may be as follows: set the tracking error equation to approach zero, analyze the tracking error equation to generate the control auxiliary item of the ith follower , and construct the control input equation of the ith follower using the control auxiliary item, the control input r0(t) of the leader, and the system formation control signal

[0073] wherein K1, K2, and K3 are control gain coefficients to be solved.

[0074] In implementation, when the multi-agent system tends to be consistent and stable, the value of the tracking error equation between any follower and the leader will tend to zero, so the tracking error equation can be set to approach zero, and the tracking error equation is analyzed. That is, take i (t) = x0(t) - x i (t) - f i (t) → 0, and considering that there is transmission time delay in information interaction between agents, the internal state quantity x i (t-d(t)) of each follower with transmission time delay needs to be introduced when setting the control input of the follower controller. Then the control auxiliary item of the ith follower under the condition of existing transmission time delay can be reversely solved. In this way, when constructing the control input equation u i of the ith follower, the control auxiliary item and the control input r0(t) of the leader, and the system formation control signal of the agent system can be introduced at the same time, and the following equation can be obtained. It is not difficult to understand that the consistency stability of the multi-agent system is mainly affected by two aspects: one is the synchronization of the internal states of different agents, and the other is the consistency of the external inputs of different agents, so the control input equation u i(t) can be composed of the control auxiliary term and the external control input term (including the control input of the leader and the control input of the system formation).

[0075] Step 204, substituting the control input equation u i into the tracking error equation, the system tracking error equation of the multi-agent system is generated through the augmentation process.

[0076] In implementation, the central controller constructs the control input equation u i of the i-th follower with the transmission time delay. i Then, u i is substituted into the tracking error equation between the follower and the leader, and then the system tracking error equation of the multi-agent system can be generated from the tracking error equation through the augmentation process.

[0077] Optionally, after the form of the control input equation u i is determined, the generation process of the system tracking error equation can be as follows: substituting the control input equation u i into the tracking error equation, and setting K2 and K3 as unit matrices to obtain the tracking error dynamic equation Augmenting the tracking error dynamic equation , the system tracking error equation in the multi-agent system is constructed.

[0078] wherein, ξ = col{ξ1, ξ2,..., ξ n N}, w = col{w1, w2,..., w n N}, I N is an N-dimensional unit matrix, denotes the Kronecker product, and L is the Laplacian matrix corresponding to the adjacency matrix.

[0079] In implementation, the central controller can substitute the constructed control input equation of the i-th follower into the corresponding tracking error equation, and in order to simplify the operation process, set K2 and K3 as unit matrices, so as to obtain the tracking error dynamic equation of the i-th follower Next, by using the idea of individual analysis transformation into system analysis, the tracking error dynamic equations of all followers are augmented, so as to obtain the system tracking error equation in the multi-agent system

[0080] Step 205, the system tracking error equation is analyzed by using the Lyapunov stability theory and the finite time stability theory, and the stability control condition of the multi-agent system is generated.

[0081] In implementation, Lyapunov stability theory is a theory for studying stability of a system, i.e. to explore an equilibrium state of the system, when the system is in the equilibrium state, no matter what external disturbance exists, the system will eventually tend to return to the equilibrium state. Finite time stability theory is a theory for studying whether a state of a system can always be kept within a certain limit within a specific time interval under given initial conditions. Therefore, the system tracking error equation can be analyzed based on Lyapunov stability theory and finite time stability theory to calculate the control condition required to be met by the multi-agent system when reaching the equilibrium state within a finite time, i.e. to generate the stability control condition of the multi-agent system.

[0082] Based on the above system tracking error equation If the multi-agent system is to reach group consensus within a finite time, it is required that tends to 0. Therefore, by analyzing the system tracking error equation based on Lyapunov stability theory and finite time stability theory, the following stability control condition can be obtained: if there exist constants γ>0, d>0, a suitable dimensional matrix K and positive definite matrices P, Q, Z, which satisfy

[0083]

[0084] Ω 11 = A T P+PA+2P+Q+3A T ZA-d -1 e -γd Z-γP+IΩ 22 =-(1-d)Q-d -1 e -γd Z

[0085] , and then when the transmission time delay d(t) satisfies 0

[0086] wherein, the element * in the element R in denotes an element R symmetric to the element R T , are inverse matrices of P and Z respectively, α=λ max (L T L), t0 is an arbitrary time, t is an arbitrary time greater than t0, c2>c1>0 and λ2, λ3, λ4 are maximum eigenvalues of P, Q and Z respectively, and the suitable dimensional matrix K is a control gain coefficient in the form of a matrix.

[0087] It is worth mentioning that denotes the inequality The inequality can be derived That is, when t0 satisfies the inequality , the right side of the inequality is replaced by And any t is selected to substitute into the inequality, which can satisfy the inequality

[0088] Step 206, the control input equation u i of each follower is solved by using the stability control condition of the multi-agent system, to obtain the control gain coefficient corresponding to the follower.

[0089] In implementation, after analyzing the stability control condition of the multi-agent system, the central controller can inversely solve the control gain coefficient of each agent in the multi-agent system by using the stability control condition. Specifically, the central controller can uniformly solve the control input equation of each follower based on the above stability control condition, so as to obtain the control gain coefficient corresponding to the follower.

[0090] Step 207, the control gain coefficient is loaded into the controller of each follower, so that the controller controls the follower according to the control gain coefficient.

[0091] In implementation, after determining the control gain coefficient of the follower, the central controller can send the control gain coefficient to the individual controller of each follower. The individual controller receives and loads the control gain coefficient, and substitutes the control gain coefficient into the control input equation of the follower to obtain the specific control input of each follower, so that the individual controller can control the follower through the specific control input.

[0092] Optionally, the H ∞ performance index can be introduced to suppress the system disturbance, and accordingly, the following processing can exist: for the tracking error equation ξ i (t) and the system disturbance w i (t), the H ∞ performance index function The performance index function is analyzed by using Lyapunov stability theory to generate a disturbance suppression condition, that is, if there exists a disturbance suppression parameter 0 < γ < 1 and a positive definite matrix P, Q, Z, which satisfies Ω < 0, then all agents in the multi-agent system have disturbance suppression performance.

[0093] In implementation, the central controller can introduce the H i performance index function for the tracking error equation ξ i (t) and the system disturbance w ∞ (t). So that the bias between the internal states of each agent in the multi-agent system is always kept within a bound, so that the internal state of the agent can be guaranteed not to exceed the instantaneous range, so as to meet the safety performance requirements of the multi-agent system. Wherein, s is the integral variable, and ξ i (s) is the integral operation of ξ i (t), w i (s) is the integral operation of w i (t). Then, the Lyapunov stability theory can also be used to analyze the performance index function, and the disturbance suppression condition can be obtained, which can be specifically: if there exists a disturbance suppression parameter 0 < γ < 1 and a positive definite matrix P, Q, Z, which satisfies Ω < 0, then all agents in the multi-agent system have disturbance suppression performance.

[0094] Further, the disturbance suppression condition can be used to solve the control gain coefficient, and correspondingly, the processing of step 206 can be as follows: the stability condition and the disturbance suppression condition of the multi-agent system are used to solve the control input equation of each follower, and the corresponding control gain coefficient of the follower is obtained.

[0095] In implementation, after the stability control condition and the disturbance suppression condition of the multi-agent system are analyzed, the central controller can simultaneously use the stability control condition and the disturbance suppression condition to solve the control gain coefficient of each agent in the multi-agent system. Specifically, the central controller can solve the control input equation u i of each follower based on the stability control condition and the disturbance suppression condition, so as to obtain the corresponding control gain coefficient of the follower, so that the solved control gain coefficient can meet the stability requirements of the multi-agent system and effectively suppress the noise disturbance.

[0096] By using the multi-agent cooperative control method for transmission time delay disclosed in the present application, the directed network topology idea is introduced into the information interaction of the agents in the multi-agent system, a second-order dynamic system model of the agent is constructed, the state model of the agent under the transmission time delay is modeled, and then the system tracking error equation of the multi-agent system is established. The Lyapunov stability theory and the finite time stability theory are used to analyze the tracking error equation, and the stability condition is obtained, so that the control gain coefficient that can realize the consistency stability of the multi-agent system can be solved. In this way, the state of the agent in the multi-agent system is modeled, the cooperative control gain coefficient between the agents is obtained through mathematical analysis, the agent can be accurately controlled in real time by using the controller, and the tracking control of the multi-agent system can still be realized when the transmission time delay is unknown and the transmission time delay of the state at different times changes, so that the consistency stability of the multi-agent system under the transmission time delay can be effectively realized.

[0097] The embodiment of the application further provides a multi-agent cooperative control device for transmission time lag, as shown in the figure, the device comprises: Figure 3

[0098] A topology analysis module 301 is configured to divide all agents in a multi-agent system into one leader and multiple followers, and generate information interaction relationship of the leader and the followers by using a directed topology network;

[0099] A system equation building module 302 is configured to build a second-order dynamic system model of each agent, and build a tracking error equation between the followers and the leader based on the second-order dynamic system model;

[0100] A control input analysis module 303 is configured to build a control input equation u i of each follower with transmission time lag based on the tracking error equation and the information interaction relationship, wherein the control input equation u i contains to-be-solved control gain coefficients; and the system equation building module 302 is further configured to substitute the control input equation u i into the tracking error equation, and generate a system tracking error equation of the multi-agent system through augmentation processing;

[0101] A stability analysis module 304 is configured to analyze the system tracking error equation by using Lyapunov stability theory and finite time stability theory, and generate a stability control condition of the multi-agent system;

[0102] A control gain solving module 305 is configured to solve the control input equation u i of each follower by using the stability control condition of the multi-agent system, and obtain the control gain coefficients corresponding to the followers;

[0103] A control gain loading module 306 is configured to load the control gain coefficients into a controller of each follower, so that the controller controls the follower according to the control gain coefficients.

[0104] Optionally, the topology analysis module 301 is specifically configured to:

[0105] set all agents as nodes in a directed topology network by using graph theory knowledge;

[0106] generate an adjacency matrix A=[a ij ] of the directed topology network, wherein i and j are adjacent agents, i,j=1,2,...,n+1, and element a ij ​= 1 indicates that there is information interaction between the ith agent and the jth agent, and element a ij = 0 indicates that there is no information interaction between the ith agent and the jth agent.

[0107] Optionally, the system equation building module 302 is specifically configured to:

[0108] Based on the internal state x0(t) of the leader, the state change amount and the control input r0(t), a second-order dynamic system model of the leader is established:

[0109] Based on the internal state x i (t) of each follower, the state change amount system disturbance w i (t) and the control input equation u i (t), a second-order dynamic system model of each follower is established: Based on the internal state of the leader and the internal state of the ith follower, a tracking error equation of the ith follower and the leader is set as follows: ξ i (t) = x0(t) - x i (t) - f i (t), where f i (t) is a system vector of the ith follower, is a system formation control signal, C = [1 0],

[0110] Optionally, the control input analysis module 303 is specifically configured to:

[0111] The tracking error equation is set to approach zero, and a control auxiliary term of the ith follower is generated by analyzing the tracking error equation

[0112] The control auxiliary term and the control input r0(t) of the leader, and the system formation control signal are used to construct a control input equation of the ith follower Where K1, K2, K3 are control gain coefficients to be solved.

[0113] Optionally, the system equation building module 302 is specifically configured to:

[0114] The control input equation u i is substituted into the tracking error equation, and K2 and K3 are set to unit matrices to obtain a tracking error dynamic equation

[0115] augmenting the tracking error dynamic equation to construct a system tracking error equation in the multi-agent system wherein, ξ = col{ξ1, ξ2,..., ξ n}, w = col{w1, w2,..., w n}, I N is an N-dimensional unit matrix, denotes a Kronecker product, and L is a Laplace matrix corresponding to the adjacency matrix.

[0116] Optionally, the stability control condition is: if there exist constants γ>0, d>0, a suitable dimensional matrix K and positive definite matrices P, Q, Z, satisfying

[0117]

[0118] Ω 11 = A T P + PA + 2P + Q + 3A T ZA - d -1 e -γd Z - γP + IΩ 22 = -(1 - d)Q - d -1 e -γd Z

[0119] is established, and the then when the transmission time delay d(t) satisfies 0 the element * in the element R T , are inverse matrices of P and Z respectively, α = λ max (L T L), t0 is an arbitrary time, t is an arbitrary time greater than t0, c2> c1> 0 and λ2, λ3, λ4 are maximum eigenvalues of P, Q and Z respectively, and the suitable dimensional matrix K is a control gain coefficient in the form of a matrix.

[0120] Optionally, the stability analysis module 304 is further configured to:

[0121] for the tracking error equation ξ i (t) and the system disturbance w i (t), a performance index function H ∞ is introduced, wherein s is an integral variable.

[0122] ​The performance index function is analyzed by using Lyapunov stability theory to generate a disturbance suppression condition, wherein if there exists an interference suppression parameter 0 < γ < 1 and a positive definite matrix P, Q, Z, which satisfy Ω < 0, then all agents in the multi-agent system have disturbance suppression performance;

[0123] The control gain solving module 305 is specifically configured to:

[0124] The control input equation of each follower is solved by using the stability condition of the multi-agent system and the disturbance suppression condition, to obtain the corresponding control gain coefficient of the follower.

[0125] The embodiment of the present application also provides a central controller, which comprises a processor and a memory, wherein the memory stores at least one instruction, at least one program, a code set or an instruction set, and the at least one instruction, the at least one program, the code set or the instruction set are loaded and executed by the processor to implement the multi-agent cooperative control method for transmission time delay as described in steps 201-207.

[0126] Those skilled in the art can understand that all or part of the steps of the above-mentioned embodiments can be completed by hardware, or by programs instructing relevant hardware to complete, and the programs can be stored in a computer readable storage medium, and the storage medium mentioned above can be a read-only memory, a magnetic disk or an optical disk.

[0127] The above are preferred embodiments of the present application, and are not intended to limit the protection scope of the present application, and any feature disclosed in the specification (including the abstract and the drawings) can be replaced by other equivalent or similar features unless specifically described. That is, each feature is only an example of a series of equivalent or similar features unless specifically described.

Claims

1. A multi-agent cooperative control method for transmission time delay, characterized in that, The method comprises: All agents in a multi-agent system are divided into one leader and multiple followers, and the information interaction relationship of the leader and the followers is generated by using a directed topological network, including: using graph theory knowledge to set all the agents as nodes in a directed topological network; generating an adjacency matrix A=[a ij ] of the directed topological network, wherein i and j are adjacent agents, i,j=1,2,...,n+1, element a ij =1 indicates that there is information interaction between the i-th agent and the j-th agent, and element a ij =0 indicates that there is no information interaction between the i-th agent and the j-th agent. establishing a second-order dynamic system model of each of the agents, and establishing a tracking error equation between the followers and the leader based on the second-order dynamic system model; Based on the tracking error equation and the information interaction relationship, a control input equation u of each follower containing a transmission time delay is constructed i The control input equation u i contains a control gain coefficient to be solved. The control input equation u i The tracking error equation is substituted into the augmented system, and the system tracking error equation of the multi-agent system is generated; the system tracking error equation is analyzed by Lyapunov stability theory and finite time stability theory, and the stability control condition of the multi-agent system is generated; using the stability control condition of the multi-agent system to solve the control input equation u i of each of the followers to obtain the corresponding control gain coefficient of the follower; loading the control gain coefficient into a controller of each of the followers, so that the controller controls the follower according to the control gain coefficient; The establishment of the second-order dynamic system model of each of the agents and the establishment of the tracking error equation between the followers and the leader based on the second-order dynamic system model comprise: Based on the internal state x0(t) of the leader, the state change amount and the control input r0(t), a second-order dynamic system model of the leader is established: based on an internal state x of each of the followers i (t), a state change amount a system disturbance w i (t) and the control input equation u i (t), a second-order dynamic system model of each follower is established: setting a tracking error equation ξ of the i-th follower and the leader based on an internal state of the leader and an internal state of the i-th follower i (t) = x0(t) - x i (t) - f i (t), wherein f i (t) is a system vector of the i-th follower, is a system formation control signal, C = [1 0], constructing a control input equation u of each of the followers containing a transmission time delay based on the tracking error equation and the information interaction relationship i , comprising: setting the tracking error equation to approach zero, analyzing the tracking error equation to generate a control auxiliary term for the i-th follower using the control auxiliary term and the leader's control input r0(t), and the system formation control signal constructing the ith follower's control input equation where K1, K2, K3 are control gain coefficients to be solved, and d(t) is the transmission time delay.

2. The method of claim 1, wherein, The control input equation u i Substituting the tracking error equation, a system tracking error equation of the multi-agent system is generated by an augmentation process, comprising: The control input equation u i Substituting into the tracking error equation and setting K2, K3 to be identity matrices, the tracking error dynamics equation is obtained to the tracking error dynamic equation augmented processing, constructing a system tracking error equation in the multi-agent system wherein ξ = col{ξ1, ξ2,..., ξ n}, w = col{w1, w2,..., w n}, I N is an N-dimensional unit matrix, denotes a Kronecker product, and L is a Laplace matrix corresponding to the adjacency matrix.

3. The method of claim 2, wherein, The stability control condition is: if there exist constants γ>0, d>0, a suitable dimensional matrix K and positive definite matrices P, Q and Z, which satisfy Ω 11 = A T P + PA + 2P + Q + 3A T ZA - d -1 e -γd Z - γP + I Ω 22 = -(1 - d)Q - d -1 e -γd Z established, and then when the transmission time delay d(t) satisfies 0 < d(t) < d, the multi-agent system can achieve consistent stability in a finite time, wherein, the element * in R represents an element R which is symmetrical to the element R T , are respectively inverse matrices of P and Z, and α = λ max (L T L), t0 is an arbitrary time, t is an arbitrary time greater than t0, c2 > c1 > 0 and λ2, λ3, λ4 are respectively maximum eigenvalues of P, Q and Z, and the suitable dimension matrix K is a control gain coefficient in the form of a matrix.

4. The method of claim 3, wherein, The method further comprises: for the tracking error equation ζ i (t) and system disturbance w i (t), a performance index function H ∞ of the system where s is the integral variable; analyzing the performance index function by Lyapunov stability theory to generate a disturbance suppression condition, wherein the disturbance suppression condition is: if there exist disturbance suppression parameters 0<γ<1 and positive definite matrices P, Q and Z, which satisfy Ω<0, then all agents in the multi-agent system have disturbance suppression performance; The solving of the control input equation of each of the followers by using the stability condition of the multi-agent system to obtain the corresponding control gain coefficient of the follower comprises: The solving of the control input equation of each of the followers by using the stability condition of the multi-agent system and the disturbance suppression condition to obtain the corresponding control gain coefficient of the follower.

5. A multi-agent collaborative control device for transmission time lag, characterized by, The device comprises: a topology analysis module, configured to divide all agents in a multi-agent system into one leader and multiple followers, and generate information interaction relationship of the leader and the followers by using a directed topology network, comprising: setting all the agents as nodes in a directed topology network by using graph theory knowledge; generating an adjacency matrix A=[a ij ] of the directed topology network, wherein i and j are adjacent agents, i,j=1,2,...,n+1, element a ij =1 indicates that there is information interaction between the i th agent and the j th agent, and element a ij =0 indicates that there is no information interaction between the i th agent and the j th agent; a control input analysis module for constructing a control input equation u i of each of the followers based on the leader's control input r0(t), the internal state variable x i of each of the followers containing a transmission time delay and the information interaction relationship; and i containing a control gain coefficient to be solved. a system equation building module configured to establish a second-order dynamic system model of each of the agents, and establish a tracking error equation of the multi-agent system based on the second-order dynamic system model; a stability analysis module configured to analyze the tracking error equation by Lyapunov stability theory and finite time stability theory to generate a stability control condition of the multi-agent system; a control gain solving module configured to solve the control input equation u i for each of the followers using the stability control condition of the multi-agent system to obtain the control gain coefficient corresponding to the follower; a control gain loading module configured to load the control gain coefficient into a controller of each of the followers, so that the controller controls the follower according to the control gain coefficient; The establishment of the second-order dynamic system model of each of the agents and the establishment of the tracking error equation between the followers and the leader based on the second-order dynamic system model comprise: Based on the internal state x0(t) of the leader, the state change amount and the control input r0(t), a second-order dynamic system model of the leader is established: based on an internal state x of each of the followers i (t), a state change amount system disturbance w i (t) and the control input equation u i (t), a second-order dynamic system model of each follower is established: setting a tracking error equation ξ of the i-th follower and the leader based on the internal state of the leader and the internal state of the i-th follower i (t) = x0(t) - x i (t) - f i (t), where f i (t) is a system vector of the i-th follower, is a system formation control signal, constructing a control input equation u of each of the followers containing a transmission time delay based on the tracking error equation and the information interaction relationship i comprising: setting the tracking error equation to approach zero, analyzing the tracking error equation to generate a control auxiliary term for the i-th follower using the control auxiliary term and the leader's control input r0(t), and the system platoon control signal constructing the ith follower's control input equation where K1, K2, K3 are control gain coefficients to be solved, and d(t) is the transmission time delay.

6. A central controller, characterized by The central controller comprises a processor and a memory, and the memory stores at least one instruction, at least one program, a code set or an instruction set, which are loaded and executed by the processor to implement the multi-agent cooperative control method for transmission time delay according to any one of claims 1-4.

7. A computer-readable storage medium, characterized in that, The storage medium stores at least one instruction, at least one program, a code set or an instruction set, which are loaded and executed by the processor to implement the multi-agent cooperative control method for transmission time delay according to any one of claims 1-4.

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