Iterative learning control method and system for second-order switching multi-agent system

Abstract

This invention discloses an iterative learning control method and system for second-order switching multi-agent systems. The method includes: constructing a communication topology for the second-order switching multi-agent system with a directed spanning tree rooted at the leader; constructing a dynamic model of the second-order switching nonlinear multi-agent system under disturbance; defining position consistency tracking error and velocity consistency tracking error, and designing a distributed initial state iterative update strategy; superimposing error feedback correction terms and designing a distributed iterative learning control law; and combining the distributed initial state iterative update strategy and the distributed iterative learning control law to achieve robust consistency tracking results for all agents' positions and velocities. This invention can overcome the influence of iteratively dependent switching signals and external disturbances, improving the accuracy of the agents' consistency tracking results. As an iterative learning control method and system for second-order switching multi-agent systems, this invention can be widely applied in the field of multi-agent cooperative control technology.

Description

Technical Field

[0001] This invention relates to the field of multi-agent cooperative control technology, and in particular to an iterative learning control method and system for second-order switching multi-agent systems. Background Technology

[0002] In many practical applications, the dynamic characteristics of agents are often modeled as second-order state-space models, where both position and velocity vectors exist simultaneously (e.g., multi-rotor UAV systems). Since second-order consensus control requires simultaneous consistency between position and velocity states, its technical requirements are more stringent than those of first-order systems. Most current research on consensus control in second-order multi-agent systems is conducted under the assumption of a fixed communication topology. However, for second-order multi-agent systems with multiple operating modes, system switching frequently occurs. This switching behavior typically includes not only communication topology changes but also dynamic system switching. For example, a swarm of quadcopter UAVs carrying suspended loads exhibits two distinctly different dynamic characteristics when performing a series of pick-up and place-down tasks. Currently, the consensus problem of second-order nonlinear multi-agent systems considering both dynamic and topology switching remains an unsolved open problem.

[0003] On the other hand, most existing consensus control algorithms for distributed second-order multi-agent systems are based on the infinite time method. However, in reality, most second-order multi-agent systems (such as multi-robot arm systems and multi-mobile robot systems) perform given repetitive tasks within finite time intervals. For the finite-time consensus problem of multi-agent systems, iterative learning control, as a typical finite-time controller, has been widely used in recent years. However, existing iterative learning control methods for such systems have significant limitations, such as:

[0004] 1) In the traditional iterative learning control framework, it is usually assumed that the multi-agent system is strictly repeatable, that is, the initial state or external disturbance of the system remains unchanged in different iteration batches.

[0005] 2) In complex real-world scenarios, the dynamic model of a multi-agent system may not be accurately replicated. Switching signals and external disturbances in non-repetitive switching second-order nonlinear multi-agent systems typically depend on the number of iterations, rendering traditional iterative learning algorithms inapplicable.

[0006] 3) Traditional iterative learning control methods theoretically require the system to have strictly identical initial conditions in each iteration. This restriction is infeasible for non-repeating switching multi-agent systems because accurately resetting the initial state during iterative learning is extremely difficult. Summary of the Invention

[0007] To address the aforementioned technical problems, the present invention aims to provide an iterative learning control method and system for second-order switched multi-agent systems, which can overcome the influence of switching signals dependent on iteration and external interference, and improve the accuracy of the agents' consistency tracking results.

[0008] The first technical solution adopted in this invention is: an iterative learning control method for second-order switched multi-agent systems, comprising the following steps:

[0009] Based on the interaction relationship of multiple agents, a switching communication topology is constructed, and a second-order switching multi-agent system communication topology containing a directed spanning tree with the leader as the root node is constructed.

[0010] Based on the communication topology of a second-order switched multi-agent system, a dynamic model of a second-order switched nonlinear multi-agent system under disturbance is constructed, and a consensus control objective for the second-order switched multi-agent system is set.

[0011] Based on the dynamic model of a second-order switching nonlinear multi-agent system, position consistency tracking error and velocity consistency tracking error are defined, and a distributed initial state iterative update strategy is designed.

[0012] Based on the position consistency tracking error and velocity consistency tracking error, combined with the consistency control objective of the second-order switching multi-agent system, and with the addition of an error feedback correction term, a compact form of distributed iterative learning control law is designed.

[0013] By combining a distributed initial state iterative update strategy with a compact form of distributed iterative learning control law, robust and consistent tracking results of the velocity of all intelligent body positions are achieved under the constraint that the gain is satisfied.

[0014] Furthermore, the step of constructing a switching communication topology based on multi-agent interaction relationships, specifically constructing a second-order switching multi-agent system communication topology containing a directed spanning tree with the leader as the root node, includes:

[0015] Based on the communication and interaction relationships between agents, a directed topological graph of arbitrary subtopology is defined, which is described by the set of all agents, the adjacency matrix, and the set of edges between all agents.

[0016] Determine the Laplace matrix corresponding to any subtopology based on the directed topological graph of any subtopology;

[0017] A global leader agent is introduced as the tracking target of all followers, and a leader state connection matrix is ​​defined.

[0018] Define a communication topology switching signal to enable the system's communication topology to dynamically switch between a finite number of preset sub-topologies, and use the leader as the root node of a directed spanning tree to construct the communication topology structure of a second-order switching multi-agent system.

[0019] Furthermore, the step of constructing a dynamic model of a second-order switched nonlinear multi-agent system under disturbance based on the communication topology of the second-order switched multi-agent system, and setting a consensus control objective for the second-order switched multi-agent system, specifically includes:

[0020] Based on the communication topology of a second-order switched multi-agent system, construct the first... The agent in the th... The dynamic model at the next iteration includes nonlinear terms, control inputs, and non-repetitive external disturbances;

[0021] Based on the dynamic model, define the dynamic mode switching signal of the agent;

[0022] Set the control objective of the second-order switching multi-agent system. The control objective means that, under the action of non-repetitive interference signals, through iterative learning of the control law, the position and velocity states of all follower agents will eventually track the desired position and velocity states of the leader.

[0023] Furthermore, the second-order switched multi-agent system's... The agent in the th... The expression for the dynamic model at the next iteration is:

[0024]

[0025] In the above formula, Indicates continuous time. Indicates the number of agents. Indicates the number of iterations. Represents the set of positive integers. and These represent the position state and velocity state of the agent, respectively. Represents the set of real numbers. Represents the input vector. Indicates a non-repetitive interference signal. Represents a nonlinear vector-valued function. Represents intelligent agents The mode switching signal.

[0026] Furthermore, the step of defining position consistency tracking error and velocity consistency tracking error based on the dynamic model of the second-order switching nonlinear multi-agent system, and designing a distributed initial state iterative update strategy, specifically includes:

[0027] Based on the adjacency matrix and leader state connection matrix of the directed topological graph in the dynamic model of a second-order switching nonlinear multi-agent system, position consistency tracking error and velocity consistency tracking error are defined.

[0028] Based on the position consistency tracking error and the velocity consistency tracking error, a distributed initial state iterative update strategy is designed.

[0029] Based on a distributed initial state iterative update strategy, the initial position and velocity states of the agent automatically converge to the desired initial state as the number of iterations increases.

[0030] Furthermore, the expressions for the position consistency tracking error and the velocity consistency tracking error are as follows:

[0031]

[0032]

[0033] In the above formula, This indicates position consistency tracking error. Indicates speed consistency tracking error. Adjacency matrix representing the communication topology The Line 1 Column elements, Represents the state connection matrix The Line 1 The elements of the column.

[0034] Furthermore, the step of designing a compact distributed iterative learning control law based on the position consistency tracking error and velocity consistency tracking error, combined with the consistency control objective of the second-order switching multi-agent system, and superimposed with an error feedback correction term, specifically includes:

[0035] Based on the position consistency tracking error and velocity consistency tracking error, combined with the consistency control objective of the second-order switching multi-agent system, and with the addition of an error feedback correction term, a distributed iterative learning control law is designed.

[0036] Define a global tracking error vector;

[0037] The distributed iterative learning control law for a single agent is extended to a compact matrix form for all agents. By integrating the Laplace matrix and the leader connection matrix through the Kronecker product and combining it with the global tracking error vector, a compact form of distributed iterative learning control law is designed.

[0038] Furthermore, the step of combining a distributed initial state iterative update strategy with a compact form of distributed iterative learning control law to achieve robust and consistent tracking results for all intelligent body positions under the constraint of gain satisfaction specifically includes:

[0039] Based on a second-order switching multi-agent system, a distributed iterative learning control law and a distributed initial state iterative update strategy are applied to clarify the gain constraints of the system.

[0040] When the gain constraint of the system is satisfied, the position consistency tracking error and velocity consistency tracking error of the second-order switched multi-agent system increase with the number of iterations and converge to within the preset limit.

[0041] When the external disturbance is a repetitive signal, the position consistency tracking error and velocity consistency tracking error of the second-order switching multi-agent system increase with the number of iterations and converge to zero, achieving robust consistency tracking results of position and velocity for all agents.

[0042] Furthermore, the expression for the gain constraint condition of the system is as follows:

[0043]

[0044] In the above formula, Represents the gain matrix. and They represent peacekeeping An identity matrix of dimension 1 Indicates taking the supremum. The Laplace matrix represents the switching. The leader state connection matrix represents the switching process. It represents a constant less than 1.

[0045] The second technical solution adopted in this invention is: an iterative learning control system for second-order switched multi-agent systems, comprising:

[0046] The first module is used to construct a switching communication topology based on the interaction relationship of multiple agents, and to construct a second-order switching multi-agent system communication topology containing a directed spanning tree with the leader as the root node.

[0047] The second module is used to construct a dynamic model of a second-order switched nonlinear multi-agent system under disturbance based on the communication topology of the second-order switched multi-agent system, and to set the consistency control target of the second-order switched multi-agent system.

[0048] The third module is used to define the position consistency tracking error and velocity consistency tracking error based on the dynamic model of the second-order switching nonlinear multi-agent system, and to design a distributed initial state iterative update strategy.

[0049] The fourth module is used to design a compact form of distributed iterative learning control law based on the position consistency tracking error and the velocity consistency tracking error, combined with the consistency control objective of the second-order switching multi-agent system, and superimposed with an error feedback correction term.

[0050] The fifth module combines a distributed initial state iterative update strategy with a compact form of distributed iterative learning control law to achieve robust and consistent tracking results for all intelligent body position velocities under the constraint that the gain is satisfied.

[0051] The beneficial effects of the method and system of this invention are as follows: This invention constructs a switching communication topology based on the interaction relationship of multiple agents, and builds a second-order switching multi-agent system communication topology containing a directed spanning tree with the leader as the root node; then, based on the second-order switching multi-agent system communication topology, it constructs a dynamic model of a second-order switching nonlinear multi-agent system under disturbance, and sets a consistency control objective for the second-order switching multi-agent system; further, based on the dynamic model of the second-order switching nonlinear multi-agent system, it defines position consistency tracking error and velocity consistency tracking error, designs a distributed initial state iterative update strategy, introduces an initial state learning mechanism, and acquires and utilizes the local tracking error information of the multi-agent system at the initial moment of each iteration to learn and update the initial state of the agents, thereby relaxing the restriction that the system must meet the same initial conditions in each iteration. For the aforementioned second-order switching multi-agent system, a distributed state learning mechanism is designed for both position and velocity states, enabling the initial state of the agent to converge to the desired initial state with increasing iterations. Based on the position consistency tracking error and velocity consistency tracking error, combined with the consistency control objective of the second-order switching multi-agent system and an error feedback correction term, a compact distributed iterative learning control law is designed. This allows the agent system to gradually converge to the desired initial state with increasing iterations without needing to reset the initial state during iterative learning. Finally, by combining the distributed initial state iterative update strategy with the compact distributed iterative learning control law, robust consistency tracking results for the position and velocity states of all agents are achieved under the constraint of gain satisfaction. Attached Figure Description

[0052] Figure 1 This is a flowchart of the iterative learning control method for second-order switched multi-agent systems according to the present invention.

[0053] Figure 2 This is a structural block diagram of the iterative learning control system for second-order switching multi-agent systems according to the present invention;

[0054] Figure 3This is a schematic diagram of the switching directed topology of a second-order switching multi-agent system provided in a specific embodiment of the present invention;

[0055] Figure 4 This is a schematic diagram of a switching signal for a second-order switched multi-agent system provided in a specific embodiment of the present invention;

[0056] Figure 5 This is a schematic diagram illustrating the position-state consistency convergence of a second-order switching multi-agent system after 1, 10, 20, and 60 iterations of learning, according to a specific embodiment of the present invention.

[0057] Figure 6 This is a schematic diagram illustrating the speed-state consistency convergence of a second-order switching multi-agent system after 1, 10, 20, and 60 iterations of learning, according to a specific embodiment of the present invention. Detailed Implementation

[0058] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments. The step numbers in the following embodiments are only for ease of explanation and do not limit the order of the steps. The execution order of each step in the embodiments can be adapted according to the understanding of those skilled in the art.

[0059] Reference Figure 1 This invention provides an iterative learning control method for second-order switched multi-agent systems, which includes the following steps:

[0060] S100. Based on the multi-agent interaction relationship, construct a switching communication topology structure, and construct a second-order switching multi-agent system communication topology containing a directed spanning tree with the leader as the root node.

[0061] Specifically, based on the communication interaction relationships between agents, a directed topological graph of arbitrary sub-topologies is defined, which is described by the set of all agents, the adjacency matrix, and the set of edges between all agents. Based on the directed topological graph of arbitrary sub-topologies, the Laplace matrix corresponding to the arbitrary sub-topology is determined. A global leader agent is introduced as the tracking target of all followers, and a leader state connection matrix is ​​defined. A communication topology switching signal is defined to enable the system communication topology to dynamically switch between a finite number of preset sub-topologies, and the leader is used as the root node of the directed spanning tree to construct the communication topology structure of the second-order switching multi-agent system.

[0062] In this embodiment, a communication topology for a second-order switching multi-agent system is constructed, and the communication topology of the system is switched in a finite number of sub-topologies, wherein each sub-topology contains at least one directed spanning tree and the leader agent is the root node of this directed spanning tree.

[0063] like Figure 3As shown, the communication and interaction relationships between agents can be represented by a directed topology graph, where 0 represents the leader agent, and 1, 2, and 3 represent the follower agents. ,in This is a signal indicating a switching of the communication topology, which means that the communication topology between agents is based on a finite number of sub-topologies. ,…, Switching between the two repeatedly.

[0064] For any subtopology ,in For the set of all intelligent agents, It is an adjacency matrix. For the set of real numbers, Let edge sets be used to describe the communication relationships between agents, if , representing intelligent agents Able to transmit information .

[0065] The Laplace matrix corresponding to any one of the sub-topologies is: ,in The element in the j-th row and l-th column of the Laplacian matrix is ​​defined as:

[0066]

[0067] For the aforementioned multi-agent system, there exists a leader agent. All agents must follow the leader agent. However, only some agents can obtain information from the leader agent, defining the leader's state connection matrix. ,in Indicates diagonalization, Representation matrix The j-th element on the diagonal is defined as: when the j-th agent can obtain information from the leader agent, then... ,otherwise .

[0068] For any subtopology It contains at least one directed spanning tree and the leader agent is the root node of this directed spanning tree.

[0069] S200. Based on the communication topology of a second-order switched multi-agent system, a dynamic model of a second-order switched nonlinear multi-agent system under disturbance is constructed, and a consensus control objective for the second-order switched multi-agent system is set.

[0070] Specifically, based on the communication topology of the second-order switched multi-agent system, the first... The agent in the th... The dynamic model for the next iteration includes nonlinear terms, control inputs, and non-repetitive external disturbances. Based on the dynamic model, a dynamic mode switching signal for the agents is defined. A control objective for the second-order switching multi-agent system is set, which means that under the action of non-repetitive disturbance signals, the position and velocity states of all follower agents are made to eventually track the desired position and velocity states of the leader by iteratively learning the control law.

[0071] In this embodiment, a dynamic model of a second-order switching nonlinear multi-agent system under disturbance is constructed. The multi-agent system has M sub-modes, and its dynamic model switches between the M sub-modes.

[0072] like Figure 4 As shown, each agent has two subsystems. When the switching signal value is 1, the first subsystem is activated; when the switching signal value is 2, the second subsystem is activated. The j-th agent in the second-order switched multi-agent system is in the... The dynamic model at the next iteration is expressed as follows:

[0073]

[0074] in For continuous time, Indicates the number of agents. Indicates the number of iterations. It is a set of positive integers. and These represent the position state and velocity state of the agent, respectively. It represents the set of real numbers. Represents the input vector. Indicates a non-repetitive interference signal. This represents a nonlinear vector-valued function. The mode switching signal for agent j is defined as:

[0075]

[0076] in , Indicates the switching time, when At that time, that is Then the agent's kth subsystem is activated.

[0077] The control objective of the second-order switching multi-agent system is to achieve robust and consistent tracking as the number of iterations increases under non-repetitive interference signals, meaning that the velocity and position states of all follower agents can eventually track the position state of the leader agent. and .

[0078] S300. Based on the dynamic model of the second-order switching nonlinear multi-agent system, define the position consistency tracking error and the velocity consistency tracking error, and design a distributed initial state iterative update strategy.

[0079] Specifically, based on the adjacency matrix of the directed topological graph and the leader state connection matrix in the dynamic model of a second-order switching nonlinear multi-agent system, position consistency tracking error and velocity consistency tracking error are defined; based on position consistency tracking error and velocity consistency tracking error, a distributed initial state iterative update strategy is designed; based on the distributed initial state iterative update strategy, the initial position and velocity state of the agent automatically converge to the desired initial state as the number of iterations increases.

[0080] In this embodiment, an initial state learning mechanism is introduced. At the initial moment of each iteration, the local tracking error information of the multi-agent system is acquired and used to learn and update the initial state of the agent, thereby relaxing the restriction that the system must meet the same strict initial conditions in each iteration. For the aforementioned second-order switching multi-agent, distributed state learning mechanisms are designed for the position state and velocity state respectively, so that the initial state of the agent can continuously converge to the desired initial state as the number of iterations increases.

[0081] For the initial position and velocity states of the aforementioned second-order switched multi-agent system, to achieve the goal of consistent tracking, the following two position consistency tracking errors are defined. and speed consistency tracking error for:

[0082]

[0083]

[0084] in Adjacency matrix representing the communication topology The element in the j-th row and l-th column. Represents the state connection matrix The element in the j-th row and j-th column. Based on the aforementioned position consistency tracking error and speed consistency tracking error The following iterative initial state learning is designed (i.e., for any number of iterations) initial moment ,and If the first communication sub-topology is activated, the strategy is:

[0085]

[0086]

[0087] in The first Subsequent The initial position at the next iteration. Let be the gain matrix at the initial time. The first Subsequent The initial velocity state at the next iteration Let be the gain matrix at the initial time.

[0088] S400. Based on the position consistency tracking error and velocity consistency tracking error, combined with the consistency control objective of the second-order switching multi-agent system, and with the addition of an error feedback correction term, a compact form of distributed iterative learning control law is designed.

[0089] Specifically, based on the position consistency tracking error and velocity consistency tracking error, combined with the consistency control objective of the second-order switching multi-agent system, and with the addition of error feedback correction terms, a distributed iterative learning control law is designed; a global tracking error vector is defined; the distributed iterative learning control law of a single agent is extended to a compact matrix form for all agents, and the Laplace matrix and the leader connection matrix are integrated through the Kronecker product, combined with the global tracking error vector, to design a compact form of distributed iterative learning control law.

[0090] In this embodiment, for the aforementioned second-order switching nonlinear multi-agent system, consistency tracking errors are defined for both position and velocity states, and a distributed iterative learning controller is constructed based on the consistency error feedback.

[0091] The aforementioned position consistency tracking error and speed consistency tracking error To achieve convergence of the consistent tracking error with respect to the iteration direction, the following iterative learning strategy is designed:

[0092]

[0093] in The first Subsequent Control input signals during the next iteration. and Let be the learning gain matrix of appropriate dimensions. For ease of subsequent analysis, the above control policy is given in compact form for all agents as follows:

[0094]

[0095] in , , Represents a diagonal matrix. This represents the Kronecker product. and They are defined as follows:

[0096]

[0097]

[0098] S500, combining a distributed initial state iterative update strategy with a compact distributed iterative learning control law, achieves robust and consistent tracking results for the velocity of all intelligent body positions under the constraint that the gain is satisfied.

[0099] Specifically, based on a second-order switching multi-agent system, a distributed iterative learning control law and a distributed initial state iterative update strategy are applied to clarify the gain constraints of the system. When the gain constraints of the system are met, the position consistency tracking error and velocity consistency tracking error of the second-order switching multi-agent system increase with the number of iterations and converge to within a preset limit. When the external disturbance is a repetitive signal, the position consistency tracking error and velocity consistency tracking error of the second-order switching multi-agent system increase with the number of iterations and converge to zero, thus achieving robust and consistent position and velocity tracking results for all agents.

[0100] In this embodiment, the distributed initial state learning mechanism and distributed iterative learning controller constructed above are applied to a second-order switching nonlinear multi-agent system. When the control gain matrix meets a certain selection range, it can be guaranteed that the position state and velocity state of all agents can achieve robust consistency.

[0101] For the aforementioned second-order switching multi-agent system, applying the initial state iterative learning strategy and the iterative learning strategy, if the gain matrix... The following conditions must be met:

[0102]

[0103] The aforementioned position consistency tracking error and speed consistency tracking error It can converge to a finite bound as the number of iterations increases, that is:

[0104]

[0105]

[0106] in:

[0107]

[0108]

[0109] , For the upper bound of the two non-repetitive interference signals ( This relates to [the previous point]. Furthermore, if the non-repetitive signal is a repetitive signal, then position consistency tracking error can be achieved. and speed consistency tracking error It can converge to zero with increasing iterations, that is:

[0110]

[0111]

[0112] Therefore, the embodiments of the present invention have the following advantages compared with the prior art:

[0113] 1) Considering a class of second-order nonlinear multi-agent systems under simultaneous dynamic model switching and communication topology switching, an iterative learning control strategy was designed to achieve consistent tracking of position and velocity states within a finite time interval. The effectiveness of the iterative learning control method described in this invention was verified by numerical simulation.

[0114] 2) A learning strategy for initial position and velocity states is proposed, which eliminates the need to reset the initial state during iterative learning. Instead, the system gradually converges to the desired initial state with increasing iterations. Compared to traditional iterative learning control strategies that rely on the same initial state assumption, this greatly simplifies the initial state setting process. It only needs to be set once during the first iteration, instead of resetting the initial state in each iteration, making the design process much simpler.

[0115] Finally, as Figure 5 The figure shows a schematic diagram of the position state consistency convergence of a second-order switching multi-agent system after 1, 10, 20, and 60 iterations of learning, as provided in a specific embodiment of the present invention. As can be seen from the figure, as the number of iterations increases, the position states of the three following agents in the second-order switching multi-agent system can gradually track the expected position state of the leader agent 0.

[0116] Figure 6 This diagram illustrates the convergence of velocity state consistency in a second-order switching multi-agent system after 1, 10, 20, and 60 iterations of learning, according to a specific embodiment of the present invention. As shown in the diagram, with the increase in the number of learning iterations, the velocity states of the three following agents in the second-order switching multi-agent system gradually track the desired velocity state of the leader agent 0.

[0117] Reference Figure 2 An iterative learning control system for second-order switching multi-agent systems includes:

[0118] The first module 201 is used to construct a switching communication topology based on the multi-agent interaction relationship, and to construct a second-order switching multi-agent system communication topology containing a directed spanning tree with the leader as the root node.

[0119] The second module 202 is used to construct a dynamic model of a second-order switched nonlinear multi-agent system under disturbance based on the communication topology of the second-order switched multi-agent system, and to set the consistency control target of the second-order switched multi-agent system.

[0120] The third module 203 is used to define the position consistency tracking error and velocity consistency tracking error based on the dynamic model of the second-order switching nonlinear multi-agent system, and to design a distributed initial state iterative update strategy.

[0121] The fourth module 204 is used to design a compact form of distributed iterative learning control law based on the position consistency tracking error and the velocity consistency tracking error, combined with the consistency control objective of the second-order switching multi-agent system, and superimposed with an error feedback correction term.

[0122] The fifth module 205 is used to combine a distributed initial state iterative update strategy with a compact form of distributed iterative learning control law to achieve robust and consistent tracking results of all intelligent body position velocities under the constraint that the gain is satisfied.

[0123] The content of the above method embodiments is applicable to this system embodiment. The specific functions implemented in this system embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments.

[0124] The preferred embodiments of the present application have been described above with reference to the accompanying drawings, but this does not limit the scope of the claims of the present application. Any modifications, equivalent substitutions, and improvements made by those skilled in the art without departing from the scope and substance of the embodiments of the present application shall be within the scope of the claims of the present application.

Claims

1. An iterative learning control method for second-order switched multi-agent systems, characterized in that, Includes the following steps: Based on the interaction relationship of multiple agents, a switching communication topology is constructed, and a second-order switching multi-agent system communication topology containing a directed spanning tree with the leader as the root node is constructed. Based on the communication topology of a second-order switched multi-agent system, a dynamic model of a second-order switched nonlinear multi-agent system under disturbance is constructed, and a consensus control objective for the second-order switched multi-agent system is set. Based on the dynamic model of a second-order switching nonlinear multi-agent system, position consistency tracking error and velocity consistency tracking error are defined, and a distributed initial state iterative update strategy is designed. Based on the position consistency tracking error and velocity consistency tracking error, combined with the consistency control objective of the second-order switching multi-agent system, and with the addition of an error feedback correction term, a compact form of distributed iterative learning control law is designed. By combining a distributed initial state iterative update strategy with a compact form of distributed iterative learning control law, robust and consistent tracking results of the velocity of all intelligent body positions are achieved under the constraint that the gain is satisfied.

2. The iterative learning control method for second-order switched multi-agent systems according to claim 1, characterized in that, The step of constructing a switching communication topology based on multi-agent interaction relationships, specifically constructing a second-order switching multi-agent system communication topology containing a directed spanning tree with the leader as the root node, includes: Based on the communication and interaction relationships between agents, a directed topological graph of arbitrary subtopology is defined, which is described by the set of all agents, the adjacency matrix, and the set of edges between all agents. Determine the Laplace matrix corresponding to any subtopology based on the directed topological graph of any subtopology; A global leader agent is introduced as the tracking target of all followers, and a leader state connection matrix is ​​defined. Define a communication topology switching signal to enable the system's communication topology to dynamically switch between a finite number of preset sub-topologies, and use the leader as the root node of a directed spanning tree to construct the communication topology structure of a second-order switching multi-agent system.

3. The iterative learning control method for second-order switched multi-agent systems according to claim 2, characterized in that, The step of constructing a dynamic model of a second-order switched nonlinear multi-agent system under disturbance based on the communication topology of the second-order switched multi-agent system, and setting a consensus control objective for the second-order switched multi-agent system, specifically includes: Based on the communication topology of a second-order switched multi-agent system, construct the first... The agent in the th... The dynamic model at the next iteration includes nonlinear terms, control inputs, and non-repetitive external disturbances; Based on the dynamic model, define the dynamic mode switching signal of the agent; Set the control objective of the second-order switching multi-agent system. The control objective means that, under the action of non-repetitive interference signals, through iterative learning of the control law, the position and velocity states of all follower agents will eventually track the desired position and velocity states of the leader.

4. The iterative learning control method for second-order switched multi-agent systems according to claim 3, characterized in that, The second-order switching multi-agent system The agent in the th... The expression for the dynamic model at the next iteration is: In the above formula, Indicates continuous time. Indicates the number of agents. Indicates the number of iterations. Represents the set of positive integers. and These represent the position state and velocity state of the agent, respectively. Represents the set of real numbers. Represents the input vector. Indicates a non-repetitive interference signal. Represents a nonlinear vector-valued function. Represents intelligent agents The mode switching signal.

5. The iterative learning control method for second-order switched multi-agent systems according to claim 4, characterized in that, The step of defining position consistency tracking error and velocity consistency tracking error based on the dynamic model of the second-order switching nonlinear multi-agent system, and designing a distributed initial state iterative update strategy, specifically includes: Based on the adjacency matrix and leader state connection matrix of the directed topological graph in the dynamic model of a second-order switching nonlinear multi-agent system, position consistency tracking error and velocity consistency tracking error are defined. Based on the position consistency tracking error and the velocity consistency tracking error, a distributed initial state iterative update strategy is designed. Based on a distributed initial state iterative update strategy, the initial position and velocity states of the agent automatically converge to the desired initial state as the number of iterations increases.

6. The iterative learning control method for second-order switched multi-agent systems according to claim 5, characterized in that, The specific expressions for the position consistency tracking error and the velocity consistency tracking error are as follows: In the above formula, This indicates position consistency tracking error. Indicates speed consistency tracking error. Adjacency matrix representing the communication topology The Line 1 Column elements, Represents the state connection matrix The Line 1 The elements of the column.

7. The iterative learning control method for second-order switched multi-agent systems according to claim 6, characterized in that, The step of designing a compact distributed iterative learning control law based on the position consistency tracking error and velocity consistency tracking error, combined with the consistency control objective of the second-order switching multi-agent system, and superimposed with an error feedback correction term, specifically includes: Based on the position consistency tracking error and velocity consistency tracking error, combined with the consistency control objective of the second-order switching multi-agent system, and with the addition of an error feedback correction term, a distributed iterative learning control law is designed. Define a global tracking error vector; The distributed iterative learning control law for a single agent is extended to a compact matrix form for all agents. By integrating the Laplace matrix and the leader connection matrix through the Kronecker product and combining it with the global tracking error vector, a compact form of distributed iterative learning control law is designed.

8. The iterative learning control method for second-order switched multi-agent systems according to claim 7, characterized in that, The step of achieving robust and consistent tracking results for all intelligent body posture velocities under the constraint of combining a distributed initial state iterative update strategy with a compact form of distributed iterative learning control law includes the following specific steps: Based on a second-order switching multi-agent system, a distributed iterative learning control law and a distributed initial state iterative update strategy are applied to clarify the gain constraints of the system. When the gain constraint of the system is satisfied, the position consistency tracking error and velocity consistency tracking error of the second-order switched multi-agent system increase with the number of iterations and converge to within the preset limit. When the external disturbance is a repetitive signal, the position consistency tracking error and velocity consistency tracking error of the second-order switching multi-agent system increase with the number of iterations and converge to zero, achieving robust consistency tracking results of position and velocity for all agents.

9. The iterative learning control method for second-order switched multi-agent systems according to claim 8, characterized in that, The expression for the gain constraint of the system is: In the above formula, Represents the gain matrix. and They represent peacekeeping An identity matrix of dimension 1 Indicates taking the supremum. The Laplace matrix represents the switching. The leader state connection matrix represents the switching process. It represents a constant less than 1.

10. An iterative learning control system for second-order switched multi-agent systems, characterized in that, Includes the following modules: The first module is used to construct a switching communication topology based on the interaction relationship of multiple agents, and to construct a second-order switching multi-agent system communication topology containing a directed spanning tree with the leader as the root node. The second module is used to construct a dynamic model of a second-order switched nonlinear multi-agent system under disturbance based on the communication topology of the second-order switched multi-agent system, and to set the consistency control target of the second-order switched multi-agent system. The third module is used to define the position consistency tracking error and velocity consistency tracking error based on the dynamic model of the second-order switching nonlinear multi-agent system, and to design a distributed initial state iterative update strategy. The fourth module is used to design a compact form of distributed iterative learning control law based on the position consistency tracking error and the velocity consistency tracking error, combined with the consistency control objective of the second-order switching multi-agent system, and superimposed with an error feedback correction term. The fifth module combines a distributed initial state iterative update strategy with a compact form of distributed iterative learning control law to achieve robust and consistent tracking results for all intelligent body position velocities under the constraint that the gain is satisfied.

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