Method for controlling bipartite consistency of multi-agent system with external interference
By using a disturbance observation function and a state feedback control protocol, external disturbances can be observed and eliminated in real time, thus solving the control accuracy and stability problems of multi-agent systems and improving system performance.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-07-29
- Publication Date
- 2026-03-13
Smart Images
Figure CN121657501A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of artificial intelligence technology, specifically to a control method for binary consensus of a multi-agent system with external interference, a control device for binary consensus of a multi-agent system with external interference, an electronic device, and a computer-readable storage medium. Background Technology
[0002] The binary consistency problem in leader-follower multi-agent systems is a fundamental problem in the cooperative control of multi-agent systems. Binary consistency refers to the process in which two groups of agents achieve consistency in the state of agents within each group through the action of control protocols, while agents in the two groups reach a state with equal modulus but opposite signs.
[0003] However, interference is an unavoidable problem in the operation of existing multi-agent systems. Systems such as drone swarms, robotic systems, and smart grid systems are all affected by external interference caused by internal factors and environmental factors. Significant interference to one agent can affect other agents and ultimately disrupt the entire system. External interference can introduce errors between the actual and ideal states of a multi-agent system, affecting its control accuracy, stability, and performance. Summary of the Invention
[0004] In view of this, it is necessary to provide a control method for binary consensus of a multi-agent system with external disturbances, a control device for binary consensus of a multi-agent system with external disturbances, an electronic device, and a computer-readable storage medium, so as to achieve the technical effect of improving the control accuracy, stability, and system performance of the multi-agent system.
[0005] To address the aforementioned technical problems, in a first aspect, this application provides a control method for binary consensus in a multi-agent system with external disturbances, applied to controlling a multi-agent system including followers and leaders. The control method for binary consensus in a multi-agent system with external disturbances includes: An interference observation function is provided, which includes a first constant matrix, a second constant matrix, a gain matrix, a first system matrix, and a second system matrix; The feedback gain matrix is determined based on the first constant matrix, the second constant matrix, the gain matrix, the first system matrix, and the second system matrix; A state feedback control protocol is constructed based on the feedback gain matrix, and the state feedback control protocol includes an interference compensation term. The interference signal received by each follower is observed in real time based on the interference observation function. Feedback control inputs for each follower are generated based on the state feedback control protocol and the interference signal. The followers are controlled based on the feedback control inputs, so that the multi-agent system can achieve binary consensus.
[0006] In one possible embodiment, the interference observation function is specifically: ; in, The label of the followers. For followers The corresponding state variables of the disturbance observation function, The gain matrix is... , These are the first constant matrix and the second constant matrix, respectively. For the first system matrix, This is the second system matrix. Followers The observed interference signal, The status of the external support system that generated the observed interference signal. Let be the set of all real numbers. for of A dimensional real vector space.
[0007] In one possible embodiment, determining the feedback gain matrix based on the first constant matrix, the second constant matrix, the gain matrix, the first system matrix, and the second system matrix includes: Obtain the first constant matrix, the second constant matrix, the gain matrix, the first system matrix, and the second system matrix that satisfy preset constraints, including: It's by Hurwitz, and ; in, For positive integers, , For matrix The smallest eigenvalue, , Symbolic diagram of all the followers The corresponding Laplace matrix, , I n for n 1-dimensional unit vector; Based on formula K=B TP The feedback gain matrix is calculated. K .
[0008] In one possible embodiment, the symbol diagram For N The followers are symbolic graphs composed of nodes. ; in, , for N The set of nodes consisting of the aforementioned followers, nodes For the first The aforementioned followers, set To be based on the node set V The constructed edge set is currently only valid if the node... and nodes When they can communicate with each other, there are , Symbol diagram The corresponding adjacency matrix, , for The weight on the follower and followers If a cooperative relationship exists, then , If followers and followers If there is no cooperative relationship between them, then , If followers and followers If there is no interaction between them, then , If symbol diagram If there are no self-loops, then , .
[0009] In one possible embodiment, the symbol diagram It has a directed spanning tree and a symbolic graph. It is structurally balanced, and the leader is a symbolic diagram. The root node of a directed spanning tree, a matrix It is a positive definite matrix.
[0010] In one possible embodiment, constructing the state feedback control protocol based on the feedback gain matrix includes: Based on formula Construct the state feedback control protocol; in, The label of the followers. It is a symbolic function, and If followers Able to receive information from the leader If followers Unable to receive information from the leader , For followers The state function, Let the leader be the state function, when the followers... When in the same group as the leader When followers When the leader belongs to a different group , This refers to the interference compensation term.
[0011] In one possible embodiment, controlling the follower based on the feedback control input includes: Substituting the feedback control input into the motion equation of the multi-agent system, we obtain the motion function of the multi-agent system; The equation of motion for the multi-agent system is: ; in, For followers The state function, Let be the state function of the leader. For followers The motion function, The motion function of the leader. It is a nonlinear function, and for ,inequality Established, , , The set of followers whose state is consistent with the leader's. The set of followers whose state is the opposite of the leader's. , These are the first constant matrix and the second constant matrix, respectively. For followers The corresponding feedback control input, Followers The corresponding interference signal.
[0012] Secondly, this application provides a control device for binary consensus in a multi-agent system with external disturbances, applied to controlling a multi-agent system including followers and leaders. The control device for binary consensus in a multi-agent system with external disturbances includes: An interference observation module is used to run an interference observation function, which includes a first constant matrix, a second constant matrix, a gain matrix, a first system matrix, and a second system matrix. A protocol construction module is configured to determine a feedback gain matrix based on the first constant matrix, the second constant matrix, the gain matrix, the first system matrix, and the second system matrix, and to construct a state feedback control protocol based on the feedback gain matrix, wherein the state feedback control protocol includes an interference compensation term. The interference observation module is also used to observe the interference signals received by each follower in real time based on the interference observation function. A feedback control module is provided, which generates feedback control inputs for each follower based on the state feedback control protocol and the observed interference signal, and controls the followers based on the feedback control inputs, so that the multi-agent system can achieve binary consensus.
[0013] Thirdly, this application also provides an electronic device, including a memory and a processor, wherein, The memory is used to store programs; The processor, coupled to the memory, is used to execute the program stored in the memory to implement the steps in the control method for binary consensus of a multi-agent system with external interference as described in any of the above implementations.
[0014] Fourthly, this application also provides a computer-readable storage medium for storing a computer-readable program or instructions, which, when executed by a processor, can implement the steps in the control method for binary consensus of a multi-agent system with external interference described in any of the above implementations.
[0015] The beneficial effects of this application are as follows: In the binary consensus control method for multi-agent systems with external disturbances provided in this application, the disturbance signals received by each follower are first observed in real time based on the disturbance observation function to obtain the observed disturbance signals. Then, the feedback control inputs of each follower are generated according to the state feedback control protocol and the observed disturbance signals. Since the state feedback control protocol includes a disturbance compensation term, the disturbance compensation term can eliminate the influence of the disturbance signals received by the followers on the control inputs of the followers, so that the generated feedback control inputs are not affected by the disturbance signals received by the followers. This improves the anti-interference performance of the multi-agent system, reduces the impact of external disturbances on the control accuracy, stability and system performance of the multi-agent system, and achieves the technical effect of improving the control accuracy, stability and system performance of the multi-agent system. Attached Figure Description
[0016] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0017] Figure 1 This is a flowchart illustrating a control method for binary consensus in a multi-agent system with external interference, provided in one embodiment of this application. Figure 2 This is a schematic diagram of the structure of a control device for a multi-agent system with external interference, provided in one embodiment of this application; Figure 3 This is a schematic diagram of the structure of an electronic device provided in one embodiment of this application. Detailed Implementation
[0018] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.
[0019] In the description of the embodiments of this application, unless otherwise stated, "multiple" means two or more. "And / or" describes the relationship between related objects, indicating that there can be three relationships. For example, A and / or B can represent three situations: A exists alone, A and B exist simultaneously, and B exists alone.
[0020] The terms "first," "second," etc., used in the embodiments of this application are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a technical feature defined with "first" or "second" may explicitly or implicitly include at least one of that feature.
[0021] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.
[0022] This application provides a control method for binary consensus of a multi-agent system with external disturbances, a control device for binary consensus of a multi-agent system with external disturbances, an electronic device, and a computer-readable storage medium, which are described below.
[0023] The following definitions and lemmas are followed during the computation of this application. These include: Definition 1: In control protocols Under the influence of the law, if the following conditions are met
[0024] Then system (1) can achieve leader-follower binary consistency, where When followers and leaders belong to the same group ,otherwise .
[0025] Lemma 1: , , If a matrix has appropriate dimensions, then the following three conditions are equivalent: ; and ; and .
[0026] Lemma 2: For any and The following inequalities hold: ; Denotes the set of all real numbers. express A dimensional real vector space.
[0027] Please refer to Figure 1 The binary consensus control method for multi-agent systems with external interference provided in this application embodiment is used to control multi-agent systems including followers and leaders. For multi-agent systems, symbolic diagrams can be used to describe the communication relationships between the agents, i.e., using... Symbolic diagram composed of nodes To describe a containing The information interaction methods among agents in a multi-agent system with one agent. Among them, the set... It is a set of nodes composed of each intelligent agent. Representing the An intelligent agent. .gather Denotes an edge set if and only if the node and nodes When they can communicate with each other, there are Symbol diagram Corresponding adjacency matrix , represent The weights on the agent. If the agent... and intelligent agents If a cooperative relationship exists, then... In this embodiment, it can be taken ,otherwise In this embodiment, it can be taken If the intelligent agent and intelligent agents There is no interaction between them, meaning they cannot communicate with each other. ,but Furthermore, if the diagram There are no self-loops in the array, meaning there are no edges pointing from a node to itself. .
[0028] In the embodiments of this application, the symbol diagram It has a directed spanning tree and a symbolic graph. It is structurally balanced, with the leader represented by a symbolic diagram. The root node of a directed spanning tree, a matrix It is a positive definite matrix.
[0029] The control method for binary consensus in a multi-agent system with external disturbances provided in this embodiment may specifically include the following steps: Step S101: Observe the observation interference signal received by each follower in real time based on the interference observation function. The interference observation function includes a first constant matrix, a second constant matrix, a gain matrix, a first system matrix, and a second system matrix.
[0030] In this step, the interference observation function is specifically: ; in, As a label for followers, For followers The corresponding state variables of the disturbance observation function, Here is the gain matrix. , These are the first constant matrix and the second constant matrix, respectively. For the first system matrix, For the second system matrix, Followers The observed interference signal, The status of the external support system that generates the observation interference signal. Let be the set of all real numbers. for of A real vector space of dimension, for followers The state function, The state function of the leader.
[0031] In this step, the real-time observation of the observation interference signal received by each follower based on the interference observation function can specifically be achieved by measuring the state function of each follower during operation. Measuring the leader's state function during operation The measured state function and state function Substituting the above interference observation function, we obtain the observation interference signals experienced by each follower. .
[0032] Step S102: Determine the feedback gain matrix based on the first constant matrix, the second constant matrix, the gain matrix, the first system matrix, and the second system matrix. Construct a state feedback control protocol based on the feedback gain matrix. The state feedback control protocol includes an interference compensation term.
[0033] In step S102, determining the feedback gain matrix may specifically include: obtaining a first constant matrix, a second constant matrix, a gain matrix, a first system matrix, and a second system matrix that satisfy preset constraints; substituting the first constant matrix, the second constant matrix, the gain matrix, the first system matrix, and the second system matrix that satisfy preset constraints into the calculation formula of the feedback gain matrix to obtain the feedback gain matrix.
[0034] The preset restrictions include: Restriction 1: It's by Hurwitz; Restriction 2: ; in, For positive integers, , For matrix The smallest eigenvalue, , Symbolic diagram composed of all followers The corresponding Laplace matrix, , I n It is an n-dimensional unit vector.
[0035] The gain matrix is determined based on the aforementioned preset constraints. First constant matrix and second constant matrix , The first system matrix Second system matrix .
[0036] Then, based on the calculation formula of the feedback gain matrix... K=B T P The feedback gain matrix is calculated. K .
[0037] In this embodiment, constructing a state feedback control protocol based on the feedback gain matrix specifically involves calculating the feedback gain matrix. K Substitute into the formula In this process, the state feedback control protocol is obtained.
[0038] in, As a label for followers, It is a symbolic function, and If followers Able to receive information from leaders If followers Unable to receive messages from the leader , For followers The state function, For the leader's state function, when the followers When in the same group as the leader When followers When the leader belongs to a different group , This is an interference compensation item.
[0039] Step S103: Generate feedback control inputs for each follower based on the state feedback control protocol and observed interference signals, and control the followers based on the feedback control inputs, so that the multi-agent system can achieve binary consensus.
[0040] In this step S103, the feedback control input can be specifically... Substituting the equations of motion of the multi-agent system, we obtain the motion function of the multi-agent system. and Then, based on the motion function and By controlling the followers and the leader separately, the multi-agent system can achieve binary consistency.
[0041] The motion equations of a multi-agent system can be specifically described as follows: ; in, For followers The state function, For the leader's state function For followers The motion function, For the leader's motion function, It is a nonlinear function, and for ,inequality Established, , , The set of followers whose state is consistent with that of the leader. For the set of followers whose state is the opposite of the leader's, , These are the first constant matrix and the second constant matrix, respectively. For followers The corresponding feedback control input, Followers The corresponding interference signal.
[0042] Compared with related technologies, the binary consensus control method for multi-agent systems with external interference provided in this embodiment first observes the interference signals received by each follower in real time based on the interference observation function to obtain the observed interference signals. Then, feedback control inputs for each follower are generated according to the state feedback control protocol and the observed interference signals. Since the state feedback control protocol includes an interference compensation term, the interference compensation term can eliminate the influence of the interference signals received by the followers on the control inputs of the followers, so that the generated feedback control inputs are not affected by the interference signals received by the followers. This improves the anti-interference performance of the multi-agent system, reduces the impact of external interference on the control accuracy, stability and system performance of the multi-agent system, and achieves the technical effect of improving the control accuracy, stability and system performance of the multi-agent system.
[0043] The following proves that the feedback control protocol provided in the above embodiments enables the multi-agent system to achieve binary consensus, specifically including the following proof steps: A linear model of external interference can be constructed, which can be specifically described by the following formula: (1) Based on the interference observation function: (2) definition for and The interference estimation error, i.e. (3) The equations of motion for a multi-agent system are described as follows: (4) Substituting equations (1), (2), and (3) into equation (4), we obtain the disturbance estimation error system: (5) make Then equation (5) can be written as (6) Representation matrix and Kronecker product; Define the binary consistency state error as: (7) make .because Combining formula (7), we can calculate: (8) in It is a symbolic function that satisfies ,Right now Equation (8) above can be transformed into:
[0044] If written in a compact form, then... (9) in , .
[0045] Feedback control protocol Substituting into formula (4), we get: (10) Substituting equation (10) into equation (7), we obtain the differential equation for the state error: (11) According to equations (5), (6), and (7), we have (12) According to equations (8), (12), and the state error (11), we have (13) in .
[0046] Constructing Lyapunov functions: (14) in .
[0047] According to equations (6) and (14), we can obtain Regarding time derivative (15) According to Lemma 2, and in conjunction with nonlinear functions It satisfies the Lipschitz condition, that is, there exists a positive constant. This makes for The following inequalities hold true for all of them. , According to structural equilibrium, it can be known that , ,in and These are two subsets of a multi-agent system, satisfying This characteristic can be obtained as follows: (16) Substituting equation (16) into equation (15), we have (17) Furthermore, by rearranging equation (17), we obtain:
[0048] in
[0049] It is a matrix The smallest eigenvalue. According to condition (2) of Theorem 1, based on Schur's supplementary lemma 1, we know .because It's from Hurwitz, that's possible. ,therefore It is a constant matrix. When α is chosen to be sufficiently large, according to Lemma 1, we can conclude that:
[0050] Right now Therefore, when Sometimes, and It can be seen that the state feedback control protocol provided in the embodiments of this application is effective for multi-agent systems affected by external interference. This allows for leader-follower binary consistency.
[0051] To better implement the control method for binary consensus in a multi-agent system with external interference in the embodiments of this application, based on the control method for binary consensus in a multi-agent system with external interference, correspondingly, as follows: Figure 2As shown in the figure, this application embodiment also provides a control device for binary consensus of a multi-agent system with external interference. The control device for binary consensus of a multi-agent system with external interference includes: The interference observation module 201 is used to run the interference observation function, which includes a first constant matrix, a second constant matrix, a gain matrix, a first system matrix, and a second system matrix. The protocol construction module 202 is used to determine the feedback gain matrix based on the first constant matrix, the second constant matrix, the gain matrix, the first system matrix and the second system matrix, and to construct a state feedback control protocol based on the feedback gain matrix. The state feedback control protocol includes an interference compensation term. The interference observation module 201 is also used to observe the observation interference signal received by each follower in real time based on the interference observation function; Feedback control module 203 is used to generate feedback control inputs for each follower based on the state feedback control protocol and observed interference signals, and to control the followers based on the feedback control inputs, so that the multi-agent system can achieve binary consensus.
[0052] The control device for binary consensus of a multi-agent system with external interference provided in the above embodiments can realize the technical solutions described in the above embodiments of the control method for binary consensus of a multi-agent system with external interference. The specific implementation principles of each module or unit can be found in the corresponding content in the above embodiments of the control method for binary consensus of a multi-agent system with external interference, and will not be repeated here.
[0053] Please refer to Figure 3 This application also provides an electronic device 300. The electronic device 300 includes a processor 301, a memory 302, and a display 303. Figure 3 Only some components of the electronic device 300 are shown, but it should be understood that it is not required to implement all of the components shown, and more or fewer components may be implemented instead.
[0054] In some embodiments, processor 301 may be a central processing unit (CPU), microprocessor, or other data processing chip, used to run program code stored in memory 302 or process data, such as the binary consensus control method for multi-agent systems with external interference in this application.
[0055] In some embodiments, processor 301 may be a single server or a group of servers. The server group may be centralized or distributed. In some embodiments, processor 301 may be local or remote. In some embodiments, processor 301 may be implemented on a cloud platform. In one embodiment, the cloud platform may include a private cloud, public cloud, hybrid cloud, community cloud, distributed cloud, intranet, multi-cloud, etc., or any combination thereof.
[0056] In some embodiments, memory 302 may be an internal storage unit of electronic device 300, such as a hard disk or memory of electronic device 300. In other embodiments, memory 302 may also be an external storage device of electronic device 300, such as a plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, etc. equipped on electronic device 300.
[0057] Furthermore, the memory 302 may include both internal storage units of the electronic device 300 and external storage devices. The memory 302 is used to store application software and various types of data installed on the electronic device 300.
[0058] In some embodiments, display 303 may be an LED display, a liquid crystal display, a touch-sensitive liquid crystal display, or an OLED (Organic Light-Emitting Diode) touchscreen. Display 303 is used to display information from electronic device 300 and to display a visual user interface. Components 301-303 of electronic device 300 communicate with each other via a system bus.
[0059] In one embodiment, when processor 301 executes the control program for binary consensus of a multi-agent system with external interference stored in memory 302, the following steps can be implemented: Provides an interference observation function, which includes a first constant matrix, a second constant matrix, a gain matrix, a first system matrix, and a second system matrix; The feedback gain matrix is determined based on the first constant matrix, the second constant matrix, the gain matrix, the first system matrix, and the second system matrix. A state feedback control protocol is constructed based on the feedback gain matrix. The state feedback control protocol includes an interference compensation term. The system observes the interference signals received by each follower in real time based on the interference observation function, generates feedback control inputs for each follower based on the state feedback control protocol and the observed interference signals, and controls the followers based on the feedback control inputs, enabling the multi-agent system to achieve binary consistency.
[0060] It should be understood that when the processor 301 executes the control program for the binary consensus of the multi-agent system with external interference in the memory 302, in addition to the functions mentioned above, it can also implement other functions, as can be found in the description of the corresponding method embodiments above.
[0061] Furthermore, this application does not specifically limit the type of electronic device 300 mentioned in the embodiments. Electronic device 300 can be a mobile phone, tablet computer, personal digital assistant (PDA), wearable device, laptop computer, or other portable electronic device. Exemplary embodiments of portable electronic devices include, but are not limited to, portable electronic devices running iOS, Android, Microsoft, or other operating systems. The aforementioned portable electronic device can also be other portable electronic devices, such as a laptop computer with a touch-sensitive surface (e.g., a touch panel). It should also be understood that in some other embodiments of this application, electronic device 300 may not be a portable electronic device, but rather a desktop computer with a touch-sensitive surface (e.g., a touch panel).
[0062] Accordingly, this application also provides a computer-readable storage medium for storing computer-readable programs or instructions. When the programs or instructions are executed by a processor, they can implement the steps or functions of the control method for binary consensus of a multi-agent system with external interference provided in the above-described method embodiments.
[0063] Those skilled in the art will understand that all or part of the processes of the methods described in the above embodiments can be implemented by a computer program instructing related hardware (such as a processor, controller, etc.), and the computer program can be stored in a computer-readable storage medium. The computer-readable storage medium may be a disk, optical disk, read-only memory, or random access memory, etc.
[0064] The foregoing has provided a detailed description of the control method, apparatus, electronic device, and storage medium for binary consensus in a multi-agent system with external interference provided in this application. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of this application. At the same time, those skilled in the art will recognize that there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.
Claims
1. A control method for binary consensus in a multi-agent system with external disturbances, characterized in that, The binary consensus control method for multi-agent systems including followers and leaders, with external disturbances, includes: An interference observation function is provided, which includes a first constant matrix, a second constant matrix, a gain matrix, a first system matrix, and a second system matrix; The feedback gain matrix is determined based on the first constant matrix, the second constant matrix, the gain matrix, the first system matrix, and the second system matrix; A state feedback control protocol is constructed based on the feedback gain matrix, and the state feedback control protocol includes an interference compensation term. The interference signal received by each follower is observed in real time based on the interference observation function. Feedback control inputs for each follower are generated based on the state feedback control protocol and the interference signal. The followers are controlled based on the feedback control inputs, so that the multi-agent system can achieve binary consensus.
2. The control method for binary consensus in a multi-agent system with external disturbances according to claim 1, characterized in that, The interference observation function is specifically: ； in, The label of the followers. For followers The corresponding state variables of the disturbance observation function, The gain matrix is... These are the first constant matrix and the second constant matrix, respectively. For the first system matrix, This is the second system matrix. Followers The observed interference signal, The status of the external support system that generated the observed interference signal. Let be the set of all real numbers. for of 3D real vector space, For followers The state function, Let be the state function of the leader.
3. The control method for binary consensus in a multi-agent system with external disturbances according to claim 2, characterized in that, The step of determining the feedback gain matrix based on the first constant matrix, the second constant matrix, the gain matrix, the first system matrix, and the second system matrix includes: Obtain the first constant matrix, the second constant matrix, the gain matrix, the first system matrix, and the second system matrix that satisfy preset constraints, including: It's by Hurwitz, and ; in, For positive integers, , For matrix The smallest eigenvalue, , Symbolic diagram of all the followers The corresponding Laplace matrix, , I n for n 1D unit vector; based on formula K=B T P The feedback gain matrix is calculated. K .
4. The control method for binary consensus in a multi-agent system with external disturbances according to claim 3, characterized in that, The symbol diagram For N The followers are symbolic graphs composed of nodes. ; in, , for N The set of nodes consisting of the aforementioned followers, nodes For the first The aforementioned followers, set For the edge set constructed based on the node set V, currently only if the node and nodes When they can communicate with each other, there are , Symbol diagram The corresponding adjacency matrix, , for The weight on the follower and followers If a cooperative relationship exists, then , If followers and followers If there is no cooperative relationship between them, then , If followers and followers If there is no interaction between them, then , If symbol diagram If there are no self-loops, then , .
5. The control method for binary consensus in a multi-agent system with external disturbances according to claim 4, characterized in that, The symbol diagram It has a directed spanning tree and a symbolic graph. It is structurally balanced, and the leader is a symbolic diagram. The root node of a directed spanning tree, a matrix It is a positive definite matrix.
6. The control method for binary consensus in a multi-agent system with external disturbances according to claim 4, characterized in that, The step of constructing a state feedback control protocol based on the feedback gain matrix includes: Based on formula Construct the state feedback control protocol; in, The label of the followers. It is a symbolic function, and If followers Able to receive information from the leader If followers Unable to receive information from the leader , For followers The state function, Let the leader be the state function, when the followers... When in the same group as the leader When followers When the leader belongs to a different group , This refers to the interference compensation term.
7. The control method for binary consensus in a multi-agent system with external disturbances according to claim 1, characterized in that, The control of the follower based on the feedback control input includes: Substituting the feedback control input into the motion equation of the multi-agent system, we obtain the motion function of the multi-agent system; The equation of motion for the multi-agent system is: ； in, For followers The state function, Let be the state function of the leader. For followers The motion function, The motion function of the leader. It is a nonlinear function, and for ,inequality Established, , , The set of followers whose state is consistent with the leader's. The set of followers whose state is the opposite of the leader's. , These are the first constant matrix and the second constant matrix, respectively. For followers The corresponding feedback control input, Followers The corresponding interference signal.
8. A control device for binary consensus in a multi-agent system with external disturbances, characterized in that, A control device for controlling a multi-agent system including followers and leaders, wherein the multi-agent system with external disturbances exhibits binary consensus includes: An interference observation module is used to run an interference observation function, which includes a first constant matrix, a second constant matrix, a gain matrix, a first system matrix, and a second system matrix. A protocol construction module is configured to determine a feedback gain matrix based on the first constant matrix, the second constant matrix, the gain matrix, the first system matrix, and the second system matrix, and to construct a state feedback control protocol based on the feedback gain matrix, wherein the state feedback control protocol includes an interference compensation term. The interference observation module is also used to observe the interference signals received by each follower in real time based on the interference observation function. A feedback control module is provided, which generates feedback control inputs for each follower based on the state feedback control protocol and the observed interference signal, and controls the followers based on the feedback control inputs, so that the multi-agent system can achieve binary consensus.
9. An electronic device, characterized in that, Including memory and processor, among which, The memory is used to store programs; The processor, coupled to the memory, is used to execute the program stored in the memory to implement the steps in the control method for binary consensus of a multi-agent system with external interference as described in any one of claims 1 to 7.
10. A computer-readable storage medium, characterized in that, Used to store computer-readable programs or instructions, which, when executed by a processor, can implement the steps in the control method for binary consensus of a multi-agent system with external interference as described in any one of claims 1 to 7.