Control Method and System for Time-Event-Triggered Binary Consensus in Multi-Agent Systems

Abstract

The present invention discloses a control method and system for time-event-triggered bipartite consensus of a multi-agent system. The method includes: establishing a communication topology graph of the multi-agent system with negative weights; determining the multi-agent system model and control objective, and designing an event-triggered control protocol; defining the measurement errors of each agent in the multi-agent system model, and designing an event-triggering function and triggering conditions; controlling each agent in the multi-agent system model to achieve bipartite consensus at a predetermined time according to the event-triggering function and the triggering conditions. The agent system achieves bipartite consensus within a preset time, and the communication method is event-triggered, effectively reducing the number of communications and saving communication costs.

Description

Technical Field

[0001] The present invention belongs to the technical field of multi-agent systems, and particularly relates to a control method and system for time-event-triggered bipartite consensus of a multi-agent system. Background Technique

[0002] Multi-agent systems (MAS) have been increasingly applied in many fields, such as robotics, networked control, microgrids, etc. In these systems, the consensus problem is the core and foundation of cooperative control. Consensus generally means that in a multi-agent system, the speeds and states of each agent finally asymptotically converge to the same value. With the continuous development of different application scenarios and MAS research, many different consensus laws have emerged, such as the bipartite consensus problem. Bipartite consensus means that the agents in the system need to converge to two states with the same modulus but opposite signs, which undoubtedly makes the multi-agent consensus have more diversified applications.

[0003] However, in these studies, the convergence speed is a very important factor. Most previous studies mainly focused on finite-time convergence and fixed-time convergence. The establishment time of finite-time consensus depends on the initial states of all agents. If the initial states differ greatly, the convergence time is too long to meet the system control requirements. For fixed-time consensus, although the convergence time of fixed-time consensus does not depend on the initial state of the system, it has greater conservatism, and the upper bound of the estimated convergence time is a complex function related to the controller parameters, and its stability is poor in practical applications. The preset-time controller proposed in this invention patent can better overcome the above problems, and this invention patent also adds an event-triggering mechanism, which can further optimize the utilization of resources and bring more value in practical applications. Summary of the Invention

[0004] The present invention provides a control method and system for time-event-triggered bipartite consensus of a multi-agent system, which is used to solve the technical problem of bipartite consensus of a multi-agent system.

[0005] In a first aspect, the present invention provides a control method for time-event-triggered bipartite consensus of a multi-agent system, including:

[0006] Establish a communication topology graph of a multi-agent system with negative weights;

[0007] Determine the multi-agent system model and control objectives, and design an event-triggered control protocol;

[0008] Define the measurement errors of each agent in the multi-agent system model, and design an event-triggering function and triggering conditions, where the expression of the event-triggering function is:

[0009] ,

[0010] ,

[0011] wherein, is an event trigger function, is a measurement error, is a constant, is a control gain, is the error between agents, is the number of agents, is an element of the adjacency matrix, is the state of agent i, is the state of agent j;

[0012] The expression of the triggering condition is:

[0013] ,

[0014] wherein, is the next triggering time, is time, is a lower bound function;

[0015] Control the predetermined-time bipartite consensus of each agent in the multi-agent system model according to the event trigger function and the triggering condition.

[0016] In a second aspect, the present invention provides a control system for time-event-triggered bipartite consensus of a multi-agent system, including:

[0017] A construction module configured to establish a communication topology graph of a multi-agent system with negative weights;

[0018] A determination module configured to determine a multi-agent system model and a control target, and design an event-triggered control protocol;

[0019] A definition module configured to define the measurement error of each agent in the multi-agent system model, and design an event trigger function and a triggering condition, wherein the expression of the event trigger function is:

[0020] ,

[0021] ,

[0022] wherein, is an event trigger function, is a measurement error, is a constant, is a control gain, is the error between agents, is the number of agents, is an adjacency matrix element, is the state of agent i, is the state of agent j;

[0023] The expression of the triggering condition is:

[0024] ,

[0025] In the formula, is the next triggering moment, is the time, is the lower bound function;

[0026] A control module, configured to control the predetermined time bipartite consensus of each agent in the multi-agent system model according to the event triggering function and the triggering condition.

[0027] In a third aspect, an electronic device is provided, which includes: at least one processor, and a memory communicatively connected to the at least one processor, wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to execute the steps of the control method for multi-agent system time event-triggered bipartite consensus according to any embodiment of the present invention.

[0028] In a fourth aspect, the present invention further provides a computer-readable storage medium, on which a computer program is stored, and when the program instructions are executed by a processor, the processor is enabled to execute the steps of the control method for multi-agent system time event-triggered bipartite consensus according to any embodiment of the present invention.

[0029] The control method and system for multi-agent system time event-triggered bipartite consensus of the present application combine the event triggering mechanism with the preset time bipartite consensus control, which enables effective reduction of communication resource consumption in the actual application of multi-agent systems, and integrates the knowledge of graph theory into multi-agent control, making the control results more intuitively presented. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the following drawings are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0031] Figure 1 is a flowchart of a control method for multi-agent system time event-triggered bipartite consensus provided by an embodiment of the present invention;

[0032] Figure 2 Schematic diagram of communication topology and corresponding Laplacian matrix among agents provided by an embodiment of the present invention;

[0033] Figure 3 Schematic diagram of the position trajectories of multiple agents provided by an embodiment of the present invention;

[0034] Figure 4 Schematic diagram of the input changes of multiple agents provided by an embodiment of the present invention;

[0035] Figure 5 Schematic diagram of the error changes of each agent provided by an embodiment of the present invention;

[0036] Figure 6 Schematic diagram of the event trigger moments of multiple agents provided by an embodiment of the present invention;

[0037] Figure 7 Block diagram of a control system for time - event - triggered bipartite consensus of a multi - agent system provided by an embodiment of the present invention;

[0038] Figure 8 Schematic diagram of the structure of an electronic device provided by an embodiment of the present invention. Detailed implementation manners

[0039] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0040] Please refer to Figure 1 , which shows a flowchart of a control method for time - event - triggered bipartite consensus of a multi - agent system of the present application.

[0041] As Figure 1 shown, the control method for time - event - triggered bipartite consensus of a multi - agent system specifically includes the following steps:

[0042] Step S101, establish a communication topology graph of a multi - agent system with negative weights.

[0043] As Figure 2 shown, use the weighted signed graph to describe the communication topology relationship of a MAS with agents, where is the node set, is the edge set, is the adjacency matrix;

[0044] When it means that the agent communicates with the agent At this time, and when the agent is in a cooperative relationship with the agent ; when it means that the agent is in a competitive relationship with the agent ; is the i-node, is the j-node;

[0045] The Laplacian matrix of the weighted signed graph is denoted as where ; ; is the total number of agents. For the weighted signed graph if there exists a partition of two node sets that satisfies and then when there is ; when there is which means that the weighted signed graph is structurally balanced, where ; is the node set 1, is the node set 2, is the node set k, is the node set.

[0046] Step S102, determine the multi-agent system model and control objective, and design an event-triggered control protocol.

[0047] In this step, consider a nonlinear multi-agent system model with disturbances composed of N agents. Among them, the dynamic equation of the i-th agent is:

[0048] ;

[0049] In a nonlinear multi-agent system with disturbances, given a set time constant such that under the condition of any initial value of the nonlinear multi-agent system, when the control objective is:

[0050] ;

[0051] In the formula, is the state of agent i at time t, is the state of neighbor j of agent i at time t, is the time at t, is the preset time.

[0052] It should be noted that the expression of the event-triggered control protocol is:

[0053] ,

[0054] In the formula, is the input of agent i, is the control gain, , is the preset convergence time, is the sign function, is defined as , is the element of the adjacency matrix, is the number of agents, is the state of neighbor j of agent i, is the control gain, is a constant, is the latest trigger time, is the gain constant, is the non-zero minimum eigenvalue of the Laplacian matrix.

[0055] Step S103, define the measurement error of each agent in the multi-agent system model, and design the event-trigger function and trigger condition.

[0056] In this step, the expression of the measurement error is:

[0057] ,

[0058] In the formula, is the control gain, , is the preset convergence time, is the sign function, is defined as , is the element of the adjacency matrix, is the number of agents, is the state of neighbor j of agent i, is the control gain, is a constant, is the latest trigger time, is the gain constant, is the non-zero minimum eigenvalue of the Laplacian matrix.

[0059] The expression of the event-trigger function is:

[0060] ,

[0061] ,

[0062] wherein, is an event trigger function, is a measurement error, is a constant, is a control gain, is the error between agents, is the number of agents, is an element of the adjacency matrix, is the state of agent i, is the state of agent j;

[0063] The expression of the trigger condition is:

[0064] ,

[0065] wherein, is the next trigger time, is time, is a lower bound function;

[0066] Step S104, control the predetermined time bipartite consensus of each agent in the multi-agent system model according to the event trigger function and the trigger condition.

[0067] From Figure 3 The position trajectories of the multi-agents show that the 6 agents are finally divided into two groups and reach consensus before the preset time T.

[0068] From Figure 4 The input changes of the multi-agents show that the inputs of each agent finally tend to zero, and the inputs of each agent are not continuous, but have obvious trigger intervals, so the goal of reducing communication consumption is achieved.

[0069] From Figure 5 The error changes of each agent show that the errors between each agent are continuously decreasing and finally tend to zero, achieving consensus.

[0070] From Figure 6 The event trigger times of the multi-agents show that each agent receives communication data intermittently, and the event trigger method can effectively reduce the number of communications, thereby achieving the saving of control costs.

[0071] In summary, for the binary consensus of the preset time in the method of this application, after adding the event-triggered mechanism, the multi-agent system successfully achieves binary consensus within the preset time, and the communication method is event-triggered, effectively reducing the number of communications and saving communication costs.

[0072] Please refer to Figure 7 , which shows a structural block diagram of a control system for time event-triggered binary consensus of a multi-agent system in this application.

[0073] As Figure 7 shown, the control system 200 for time event-triggered binary consensus of a multi-agent system includes a construction module 210, a determination module 220, a definition module 230, and a control module 240.

[0074] Among them, the construction module 210 is configured to establish a communication topology graph of a multi-agent system with negative weights;

[0075] The determination module 220 is configured to determine a multi-agent system model and a control target, and design an event-triggered control protocol;

[0076] The definition module 230 is configured to define the measurement error of each agent in the multi-agent system model, and design an event-triggered function and a trigger condition. Among them, the expression of the event-triggered function is:

[0077] ,

[0078] ,

[0079] In the formula, is the event-triggered function, is the measurement error, is a constant, is the control gain, is the error between agents, is the number of agents, is the element of the adjacency matrix, is the state of agent i, is the state of agent j;

[0080] The expression of the trigger condition is:

[0081] ,

[0082] In the formula, is the next trigger time, is the time, is the lower bound function;

[0083] The control module 240 is configured to control the predetermined-time bipartite consensus of each agent in the multi-agent system model according to the event triggering function and the triggering condition.

[0084] In some other embodiments, the embodiment of the present invention further provides a computer-readable storage medium, on which a computer program is stored. When the program instructions are executed by a processor, the processor is enabled to execute the control method for the multi-agent system time event-triggered bipartite consensus in any of the above method embodiments;

[0085] As an implementation manner, the computer-readable storage medium of the present invention stores computer-executable instructions, and the computer-executable instructions are set as:

[0086] Establish a communication topology graph of the multi-agent system with negative weights;

[0087] Determine the multi-agent system model and the control objective, and design an event-triggered control protocol;

[0088] Define the measurement error of each agent in the multi-agent system model, and design an event triggering function and a triggering condition. Among them, the expression of the event triggering function is:

[0089] ,

[0090] ,

[0091] In the formula, is the event triggering function, is the measurement error, is a constant, is the control gain, is the error between agents, is the number of agents, is the element of the adjacency matrix, is the state of agent i, is the state of agent j;

[0092] The expression of the triggering condition is:

[0093] ,

[0094] In the formula, is the next triggering moment, is the time, is the lower bound function;

[0095] Control the predetermined-time bipartite consensus of each agent in the multi-agent system model according to the event triggering function and the triggering condition.

[0096] A computer-readable storage medium may include a program storage area and a data storage area. Among them, the program storage area may store an operating system and application programs required for at least one function; the data storage area may store data created according to the use of a control system that triggers bipartite consensus based on multi-agent system time events, etc. In addition, the computer-readable storage medium may include high-speed random access memory, and may also include memories, such as at least one magnetic disk storage device, a flash memory device, or other non-volatile solid-state storage devices. In some embodiments, the computer-readable storage medium may optionally include a memory remotely provided with respect to the processor, and these remote memories may be connected to the control system that triggers bipartite consensus based on multi-agent system time events through a network. Examples of the above-mentioned network include but are not limited to the Internet, an intranet, a local area network, a mobile communication network, and combinations thereof.

[0097] Figure 8 is a schematic structural diagram of an electronic device provided by an embodiment of the present invention. As Figure 8 shown, the device includes: a processor 310 and a memory 320. The electronic device may further include: an input device 330 and an output device 340. The processor 310, the memory 320, the input device 330, and the output device 340 may be connected through a bus or other means, Figure 8 and here, the connection through the bus is taken as an example. The memory 320 is the above-mentioned computer-readable storage medium. The processor 310 executes various functional applications and data processing of the server by running non-volatile software programs, instructions, and modules stored in the memory 320, that is, implements the control method for triggering bipartite consensus based on multi-agent system time events in the above method embodiments. The input device 330 may receive input digital or character information, and generate key signal inputs related to user settings and function controls of the control system that triggers bipartite consensus based on multi-agent system time events. The output device 340 may include a display device such as a display screen.

[0098] The above-mentioned electronic device may execute the method provided by the embodiment of the present invention, and has corresponding functional modules and beneficial effects for executing the method. For technical details not described in detail in this embodiment, reference may be made to the method provided by the embodiment of the present invention.

[0099] As an implementation manner, the above-mentioned electronic device is applied to a control system that triggers bipartite consensus based on multi-agent system time events and is used for a client, including: at least one processor; and a memory communicatively connected to the at least one processor; wherein, the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to:

[0100] Establish a communication topology graph of a multi-agent system with negative weights;

[0101] Determine the multi-agent system model and control objectives, and design an event-triggered control protocol;

[0102] Define the measurement error of each agent in the multi-agent system model, and design an event-triggering function and a triggering condition. Among them, the expression of the event-triggering function is:

[0103] ,

[0104] ,

[0105] In the formula, is the event-triggering function, is the measurement error, is a constant, is the control gain, is the error between agents, is the number of agents, is the element of the adjacency matrix, is the state of agent i, is the state of agent j;

[0106] The expression of the triggering condition is:

[0107] ,

[0108] In the formula, is the next triggering moment, is the time, is the lower bound function;

[0109] Control the predetermined-time bipartite consensus of each agent in the multi-agent system model according to the event-triggering function and the triggering condition.

[0110] Through the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a necessary general hardware platform, and of course also by hardware. Based on such an understanding, the essence of the above technical solution or the part that contributes to the prior art can be embodied in the form of a software product, and this computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., including several instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods of each embodiment or some parts of the embodiments.

[0111] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A control method for time event-triggered binary consistency in a multi-agent system, characterized in that: include: Establish the communication topology of multi-agent systems with negative weights; Determine the multi-agent system model and control objectives, and design an event-triggered control protocol, where the expression of the event-triggered control protocol is: ， In the formula, is the input of agent i, To control the gain, , is the preset convergence time, is the symbolic function, Defined as, is the adjacency matrix element, is the number of agents, is the state of neighbor j of agent i, To control the gain, is a constant, is the latest triggering moment, is the gain constant, is the smallest non-zero eigenvalue of the Laplacian matrix; Define the measurement error of each agent in the multi-agent system model, design the event trigger function and trigger conditions, where the expression of the event trigger function is: ， ， In the formula, is the event trigger function, is the measurement error, is a constant, To control the gain, is the error between agents, is the number of agents, is the adjacency matrix element, is the state of agent i, is the state of agent j; The expression of the trigger condition is: ， In the formula, For the next trigger moment, For time, is the lower bound function; The predetermined time binary consistency of each agent in the multi-agent system model is controlled according to the event trigger function and the trigger condition.

2. A control method for multi-agent system time event triggered binary consistency according to claim 1, characterized in that: The communication topology diagram of the multi-agent system with negative weights is established as follows: Weighted symbol map Used to describe The communication topology of the MAS of the agents is: is a node set, For edge sets, is the adjacency matrix; when , indicating that the agent With Agent Communicate with each other, at this time, and Time Agent With Agent A cooperative relationship, When the agent With Agent In a competitive relationship, is the i-node, is the j node; Weighted symbol map The Laplace matrix of ,in, , , is the total number of agents, for the weighted symbolic graph , if there exists a partition between two sets of nodes that satisfies and , then when ,have ;when , if yes, it represents a weighted symbolic graph is structurally balanced, where , For node set 1, For node set 2, is the node set k, A collection of nodes.

3. A control method for multi-agent system time event triggered binary consistency according to claim 1, characterized in that: Determining the multi-agent system model and control objectives includes: Consider a nonlinear multi-agent system model with N agents under disturbance conditions, where the dynamic equation of the i-th agent is: ， In a nonlinear multi-agent system with perturbations, given a set time constant , so that the nonlinear multi-agent system is under any initial value condition, when When , the control target is: ， In the formula, is the state of agent i at time t, is the state of the neighbor j of agent i at time t, is time t, The preset time.

4. A control method for multi-agent system time event triggered binary consistency according to claim 1, characterized in that: The expression of the measurement error is: ， In the formula, To control the gain, , is the preset convergence time, is the symbolic function, Defined as, is the adjacency matrix element, is the number of agents, is the state of neighbor j of agent i, To control the gain, is a constant, is the latest triggering moment, is the gain constant, is the smallest nonzero eigenvalue of the Laplacian matrix.

5. A control system for multi-agent system time event triggered binary consistency, characterized in that: include: A building module configured to build a communication topology graph of a multi-agent system including negative weights; The determination module is configured to determine the multi-agent system model and control objectives, and design an event-triggered control protocol, wherein the expression of the event-triggered control protocol is: ， In the formula, is the input of agent i, To control the gain, , is the preset convergence time, is the symbolic function, Defined as, is the adjacency matrix element, is the number of agents, is the state of neighbor j of agent i, To control the gain, is a constant, is the latest triggering moment, is the gain constant, is the smallest non-zero eigenvalue of the Laplacian matrix; A definition module is configured to define the measurement error of each agent in the multi-agent system model, design an event trigger function and a trigger condition, wherein the expression of the event trigger function is: ， ， In the formula, is the event trigger function, is the measurement error, is a constant, To control the gain, is the error between agents, is the number of agents, is the adjacency matrix element, The expression of the trigger condition for the state of agent i is: ， In the formula, For the next trigger moment, For time, is the lower bound function; The control module is configured to control the predetermined time binary consistency of each agent in the multi-agent system model according to the event trigger function and the trigger condition.

6. An electronic device, characterized in that: include: At least one processor, and a memory communicatively connected to the at least one processor, wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to perform the method described in any one of claims 1 to 4.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the method according to any one of claims 1 to 4 is implemented.

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