Heterogeneous uncertain cluster constraint multi-alliance game preset time control method and system

Abstract

The invention discloses a heterogeneous uncertain cluster constraint multi-alliance game preset time control method and system, and relates to the technical field of intelligent cluster collaboration and game decision. According to the method, a constrained multi-alliance game model is constructed, a corresponding Nash equilibrium judgment rule is defined, a complex scene in which cooperation and competition of the agents coexist is adapted, efficient support is provided for information interaction between the agents through structural design of communication topology in the alliance and the whole, and based on a local cost function of the agents, the algorithm is more efficient and efficient. By means of a projection gradient algorithm of an equilibrium search layer, distributed gradient estimation of a global cost function is realized through collaborative updating of an auxiliary variable and an average gradient estimation variable, full-alliance cost information does not need to be acquired by an intelligent agent, and satisfaction of a Nash equilibrium solution to a non-empty convex tight constraint can be strictly guaranteed through a projection operator. The preset time gain operator enforces the equilibrium search process to converge within the preset time through the time-varying gain characteristic, and an efficient equilibrium search scheme is provided for constraining the multi-alliance game scene.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of intelligent cluster cooperation and game decision, in particular to a heterogeneous uncertain cluster constraint multi-alliance game preset time control method and system. BACKGROUND

[0002] With the increasingly wide application of game theory in the field of multi-agent systems, Nash equilibrium, as the core concept of non-cooperative game, provides important theoretical support for the optimal strategy selection of agents. The complexity of practical application scenarios often presents a coexistence of cooperation and competition among multi-agents, forming a multi-alliance game mode. At the same time, agents often face problems such as strategy set constraints, heterogeneous dynamics models and uncertainties, and there is an urgent need for efficient game control methods to meet the actual needs of heterogeneous clusters converging to Nash equilibrium quickly under the constraint conditions.

[0003] The existing technology has many limitations: most algorithms only focus on single competitive relationship, and are difficult to adapt to multi-alliance cooperation-competition coexistence scenarios; some multi-alliance game algorithms do not consider the constraint limitations of agent strategy set, and are not practical enough; and the existing models mostly assume that agents are homogeneous, and have poor adaptability to heterogeneous systems, with most convergence rates being asymptotic convergence, which cannot meet the demand of reaching equilibrium quickly within a preset time; in addition, the suppression scheme for agent dynamics uncertainty is not perfect, which limits the equilibrium tracking accuracy and makes it difficult to support game confrontation applications in complex scenarios.

[0004] In summary, the existing technology has obvious shortcomings in adapting to multi-alliance cooperation-competition mixed scenarios, handling strategy constraints and heterogeneous uncertainties, and achieving preset time fast convergence.

[0005] To solve the above problems, it is necessary to build a hierarchical game control method, which realizes the fast game equilibrium of heterogeneous uncertain clusters under the constraint conditions through accurate equilibrium search and efficient output tracking, and provides more reliable technical support for complex game applications of multi-agent systems. SUMMARY

[0006] The purpose of the present application is to make up for the deficiencies of the prior art, and provide a heterogeneous uncertain cluster constrained multi-alliance game preset time control method and system, which can construct a constrained multi-alliance game model and define the corresponding Nash equilibrium judgment rule, accurately adapt to the complex scene of coexistence of agent cooperation and competition, provide efficient support for information interaction between agents through the structured design of the communication topology of the whole and the alliance, based on the local cost function of the agent, through the projection gradient algorithm of the equilibrium search layer, through the cooperative update of the auxiliary variable and the average gradient estimation variable, realize the distributed gradient estimation of the global cost function, without the need for the agent to obtain the whole alliance cost information, and strictly comply with the non-empty convex constraint of the strategy set through the projection operator, at the same time, the preset time gain operator converges the equilibrium search process within the preset time through the time-varying gain characteristic, solves the technical problems that the traditional algorithm is difficult to balance the local information constraint, the strategy set restriction and the fast convergence, and provides an efficient equilibrium search scheme for the constrained multi-alliance game scene.

[0007] To solve the above technical problems, the present application provides the following technical solutions: on the one hand, a heterogeneous uncertain cluster constrained multi-alliance game preset time control method, which executes fast game control of the heterogeneous uncertain cluster through hierarchical design, and the specific steps are as follows: S100, a constrained multi-alliance game model is established, the number, numbering rule and cost function definition of the agent and the alliance are clarified, and the judgment condition of the Nash equilibrium of the constrained multi-alliance game is defined; S200, a high-order heterogeneous agent dynamics model containing time-varying uncertain items is established, the physical meaning and constraint relationship of each matrix and variable in the model are clarified, the communication topology between the agents participating in the game in the alliance and the whole is constructed, and the node, edge, weight adjacency matrix and Laplacian matrix related to the topology are defined; S300, the related parameters of the equilibrium search layer are initialized, including the auxiliary variable, the average gradient estimation variable and the virtual Nash equilibrium search vector, and a preset time gain operator containing a rate control parameter and an exponential parameter is designed based on a preset convergence time; S400, an equilibrium search layer algorithm containing the virtual Nash equilibrium search vector update rate, the auxiliary variable update rate and the average gradient estimation variable calculation method is designed, and the Nash equilibrium solution of the constrained multi-alliance game is searched within the preset time through the interaction of the agents in the alliance; S500, based on the Nash equilibrium solution, the high-order heterogeneous agent dynamics model and the preset time gain operator, an output tracking layer control law is designed, and the control input of the agent is generated to drive the actual output of the heterogeneous uncertain cluster to track the Nash equilibrium solution within the preset time.

[0008] Further, in S100, the specific process of establishing a constrained multi-alliance game model and defining a constrained multi-alliance game Nash equilibrium is as follows: S110, based on the total number of agents participating in the game , each agent is divided into a coalition according to the cooperation and competition relationship reflected by the cost function , each coalition has agents, the number of individuals in the coalition and the total number of agents satisfy , the set of coalitions is , the number set of all agents in the coalition is , and the cost function of each agent is , wherein represents the combined vector of the decision variables of all agents participating in the game in the th coalition, that is represents the decision variable of the th agent in the th coalition, and is a dimensional real vector, and the cost function of the coalition is , wherein represents the combined vector of the decision variables of the agents in all coalitions except the th coalition, each agent minimizes the overall cost function of its own coalition by adjusting its own decision state, and each agent can only obtain its own cost function information. The coalition as a virtual entity participates in the upper game, and the strategy decision is realized by the agents in the coalition; S120, when there is an optimal decision state vector , satisfying , the state vector is the Nash equilibrium solution of the constrained multi-coalition game, wherein is the constraint set that the combined vector of the decision variables of all agents participating in the game in the th coalition needs to satisfy, which is a non-empty convex compact set.

[0009] Further, the specific process of establishing a high-order heterogeneous agent dynamics model and constructing a topological communication in S200 is: S210, the agent participating in the constrained multi-coalition game is a heterogeneous uncertain agent, and its dynamics model is: , wherein represents the decision variable of the th agent in the th coalition, represents the control input of the th agent in the th coalition, represents the internal state of the th agent in the th coalition, Indicates the first The first in the alliance The update rate of the internal state of an agent. Indicates the first The first in the alliance The system dynamics matrix of each agent is a real constant matrix. Indicates the first The first in the alliance The system input matrix for each agent is a real constant matrix. Indicates the first The first in the alliance The decision matrix of each agent is a real constant matrix, and the matrix... The condition of full rank for rows is met. It is a time-varying matrix, representing the uncertainty in the agent's policy evolution process, and , All matrices satisfy dimension matching; S220, Building Alliances Internal communication topology ,in This represents the set of all intelligent agents within the alliance. This represents the set of communication edges between intelligent agents within the alliance. Refers to the first The first in the alliance The agent points to the first The first in the alliance The communication edge of an agent, when there exists and If the graph is a directed graph, then the weighted adjacency matrix of the communication topology graph is... For a square matrix, its first... Line number Column elements If and only if Otherwise, it is 0, defining the first The first in the alliance Nodes in-degree is Out-degree is If all nodes have the same out-degree and in-degree, then the graph is a weighted directed graph, and its Laplace matrix is ​​defined as follows: ,in It is a diagonal matrix constructed from the in-degree information of all nodes in the alliance; it constructs the communication topology among the intelligent agents participating in the game as a whole. ,in For a set of intelligent agents For the set of communication edges between intelligent agents, Refers to the first The first in the alliance The agent points to the first The first in the alliance The communication edges of the agents, and the overall communication topology of the game are as follows: .

[0010] Furthermore, in S300, the specific process of initializing the relevant parameters of the equalization search layer and designing the preset time gain operator is as follows: S310, Regarding the first The first in the alliance An intelligent agent initializes auxiliary variables. Average gradient estimated variables All are 0, virtual Nash equilibrium search vector Let be the zero vector, where , ; S320, Select preset time Design a preset time gain operator : ,in, The preset time gain operator rate control parameters, This represents the first auxiliary dynamic function. Represents the first auxiliary dynamic function The derivative, This indicates the preset time gain operator.

[0011] Furthermore, in S400, the specific process of designing the equilibrium search layer algorithm is as follows: Regarding the first The first alliance An intelligent agent utilizes a preset time gain operator in S320. The algorithm for designing the equilibrium search layer is as follows: in, For vectors To the The first in the alliance The set of constraints satisfied by an intelligent agent The projection on the surface is calculated as follows: That is, to traverse the constraint set and find the one that minimizes the value. , The gain parameter is positive; additionally, the average gradient estimate variable... It is an alliance The Middle Individuals for the coalition cost function Regarding the Decision-Making Alliance The Middle Individual decision variables The estimation of the partial derivative, and its calculation method, Indicates the first The first in the alliance The cost function for each agent; Indicates the first The cost function of a coalition is the sum of the cost functions of all agents in that coalition. , Indicates the first The first in the alliance The agent for the first Cost function of a coalition about The estimated vector of the partial derivatives, Indicates the first The first in the alliance The agent for the first Cost function of a coalition about The estimated vector of the partial derivatives; Execute the equilibrium search layer algorithm, the first... The first alliance An intelligent agent at a preset time Internal control virtual Nash equilibrium search vector The search found the Nash equilibrium in a constrained multi-alliance game.

[0012] Furthermore, in S500, the specific process of initializing the relevant constant parameters of the output tracking layer and converging the Nash equilibrium solution is as follows: S510, Initialization For positive numbers, select satisfy ; S520, Design of the first gain matrix based on the dynamic model Second gain matrix Regarding the first The first in the alliance An intelligent agent designs the first gain matrix. Second gain matrix ,in ; S530, based on the preset time gain operator in S320 Regarding the first The first alliance An intelligent agent designs time-varying exponential parameters. update rate ,in Let be the initial gain of the time-varying exponential parameter, and ; S540, based on the preset time gain operator in S320 The update rate of time-varying exponential parameters designed for S530 Regarding the first The first alliance An intelligent agent is designed to withstand uncertain parameter update rates. ; S550, Virtual Nash Equilibrium Search Vector Obtained from S400 The preset time gain operator in S320 The control input is designed based on the gain matrix in S520, the time-varying exponential parameter in S530, and the uncertainty resistance parameter in S540: ,in, For constant gain, its selection satisfies The tracking layer algorithm is executed to drive the heterogeneous uncertain cluster to a preset time. It converges inward to the Nash equilibrium solution of the constrained multi-alliance game.

[0013] On the other hand, a pre-set time control system for heterogeneous uncertain cluster-constrained multi-alliance game, the system comprising: The game model construction module establishes a constrained multi-alliance game model, clarifies the number of agents and alliances, numbering rules, and cost function definitions, and defines the conditions for determining the Nash equilibrium of the constrained multi-alliance game. The Dynamics and Topology Construction Module is used to build a high-order heterogeneous agent dynamics model containing time-varying uncertainties, clarify the physical meaning and constraint relationship of each matrix and variable in the model, construct the communication topology between agents participating in the game within the alliance and the whole, and define the topology-related nodes, edges, weighted adjacency matrices and Laplace matrices. The equilibrium search layer initialization module is used to initialize the relevant parameters of the equilibrium search layer, including auxiliary variables, average gradient estimation variables and virtual Nash equilibrium search vectors. It designs a preset time gain operator with rate control parameters and exponential parameters based on the preset convergence time. The equilibrium search module is used to design an equilibrium search layer algorithm that includes methods for calculating the virtual Nash equilibrium search vector update rate, auxiliary variable update rate, and average gradient estimation variable. Through the interaction of agents within the alliance, it searches for the Nash equilibrium solution of the constrained multi-alliance game within a preset time. The output tracking module, based on the Nash equilibrium solution, the high-order heterogeneous agent dynamics model, and the preset time gain operator, designs the output tracking layer control law and generates the control input of the agent to drive the actual output of the heterogeneous uncertain cluster to track to the Nash equilibrium solution within a preset time.

[0014] Furthermore, the game model construction module includes: The agent decision state dynamics model construction unit is used to construct a constrained multi-alliance game agent decision state dynamics model, clarify the number and numbering rules of agents and alliances, and define the cost functions of agents and alliances, where the alliance cost function is the sum of the cost functions of all agents in the alliance; The Nash equilibrium definition unit is used to define the Nash equilibrium in constrained multi-alliance games, and to clarify the conditions that the optimal decision state vector must satisfy and the property that the constraint set is a non-empty convex compact set.

[0015] Furthermore, the dynamics and topology building module includes: The heterogeneous uncertain dynamics model building unit is used to establish a high-order heterogeneous agent dynamics model containing time-varying uncertain terms. It clarifies that the system dynamics matrix, system input matrix, and decision matrix in the model are all real constant matrices, the product of the decision matrix and the system input matrix satisfies the full-rank condition, and the time-varying uncertain term matrix and the system input matrix satisfy a linear relationship of dimension matching. The topology communication construction unit is used to construct communication topologies within the alliance and between agents as a whole. It clarifies that the nodes of the communication topology graph are agents and the edges are communication links between agents. The elements of the weighted adjacency matrix are assigned values ​​according to the existence of the communication edges. The Laplace matrix is ​​composed of the difference between the in-degree diagonal matrix and the weighted adjacency matrix.

[0016] Furthermore, the balanced search module includes: The search algorithm design unit is used to design the virtual Nash equilibrium search vector update rate, auxiliary variable update rate and average gradient estimation variable calculation method based on the preset time gain operator. The average gradient estimation variable is calculated by the partial derivative of the cost function of the agents in the alliance and the mean of the auxiliary variables. The equilibrium search execution unit is used to execute the equilibrium search layer algorithm and control the virtual Nash equilibrium search vector to search for the Nash equilibrium solution of the constrained multi-alliance game within a preset time. The output tracking module includes: The tracking parameter design unit is used to design the update rate of the output tracking layer's gain matrix, time-varying exponential parameters, and anti-uncertainty parameters, where the gain matrix is ​​constructed based on the gain matrix of the dynamic model parameters. The control input design and execution unit is used to design the control input of the intelligent agent based on the virtual Nash equilibrium search vector, the preset time gain operator and the tracking parameters, so as to drive the heterogeneous uncertain cluster to track and converge to the Nash equilibrium solution.

[0017] Compared with existing technologies, this pre-set time control method for heterogeneous uncertain cluster-constrained multi-alliance games has the following advantages: This invention constructs a constrained multi-alliance game model and defines corresponding Nash equilibrium determination rules, accurately adapting to complex scenarios where cooperation and competition coexist among agents. Through the structured design of the communication topology within the alliance and the overall system, it provides efficient support for information interaction between agents. Based on the agent's local cost function, and with the help of the projection gradient algorithm of the equilibrium search layer, it achieves distributed gradient estimation of the global cost function through the collaborative updating of auxiliary variables and average gradient estimation variables. This eliminates the need for agents to obtain the cost information of the entire alliance, and strictly adheres to the non-empty convex and tight constraints of the policy set through the projection operator. At the same time, the preset time gain operator forces the equilibrium search process to converge within a preset time through time-varying gain characteristics, solving the technical problem that traditional algorithms struggle to balance local information constraints, policy set limitations, and fast convergence. This provides an efficient equilibrium search scheme for constrained multi-alliance game scenarios.

[0018] Other advantages, objectives and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination or study, or may be learned from the practice of the invention. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0020] Figure 1 A flowchart illustrating the steps of a pre-defined time control method for heterogeneous uncertain cluster-constrained multi-alliance games; Figure 2 The communication topology diagram for the preset time control method of heterogeneous uncertain cluster constrained multi-alliance game provided by the present invention; Figure 3 The heterogeneous uncertain cluster interference countermeasure trajectory diagram based on constrained multi-alliance Nash equilibrium provided by this invention; Figure 4 The agent outputs a decision error diagram for the preset time control method of heterogeneous uncertain cluster constrained multi-alliance game provided by the present invention. Detailed Implementation

[0021] To better understand the above technical solutions, a detailed description of the solutions will be provided below in conjunction with the accompanying drawings and specific embodiments. Obviously, the described embodiments are merely some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0022] The terminology used in the embodiments of this invention is for the purpose of describing particular embodiments only and is not intended to limit the invention. The singular forms “heterogeneous uncertain cluster constrained multi-alliance game preset time control method”, “the,” and “the” as used in the embodiments of this invention and the appended claims are also intended to include the plural forms, and “multiple” generally includes at least two unless the context clearly indicates otherwise.

[0023] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that an article or device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such an article or device. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the article or device that includes said element.

[0024] To address the shortcomings of existing technologies, this invention first describes the heterogeneous uncertain cluster-constrained multi-alliance game scenario. This invention is primarily applied to scenarios such as unmanned system interference countermeasures and multi-agent collaborative decision-making. In these scenarios, agents often exhibit a relationship of both cooperation and competition, and there are issues such as policy set constraints, heterogeneous dynamic models, and uncertainties. There is an urgent need for rapid cluster convergence to Nash equilibrium. Existing technologies struggle to adapt to mixed multi-alliance relationships, handle complex constraints and heterogeneous uncertainties, and their convergence rates fail to meet preset time requirements. This invention, through a hierarchical game control method combined with equilibrium search and output tracking mechanisms, achieves rapid game equilibrium for heterogeneous uncertain clusters under constraints, providing reliable technical support for complex scenarios.

[0025] The present invention provides a method for controlling the preset time of a heterogeneous uncertain cluster constrained multi-alliance game. By constructing a constrained multi-alliance game model to clarify the game rules, establishing a heterogeneous uncertain dynamic model and communication topology to support information interaction, the equilibrium search layer finds the Nash equilibrium solution within a preset time, and the output tracking layer drives the cluster to accurately track the equilibrium solution. At the same time, the influence of uncertainty is suppressed to ensure rapid convergence and control accuracy.

[0026] Specifically, such as Figure 1As shown, a pre-set time control method for heterogeneous uncertain cluster constrained multi-alliance game is presented. This method implements fast game control of heterogeneous uncertain clusters through hierarchical design. The specific steps are as follows: S100. Establish a constrained multi-alliance game model, clarify the number of agents and alliances, numbering rules and cost function definitions, and define the conditions for determining the Nash equilibrium of the constrained multi-alliance game. S200. Establish a high-order heterogeneous agent dynamics model containing time-varying uncertainties, clarify the physical meaning and constraint relationship of each matrix and variable in the model, construct the communication topology between agents participating in the game within the alliance and the whole, and define the topology-related nodes, edges, weighted adjacency matrices and Laplace matrices. S300. Initialize the relevant parameters of the equilibrium search layer, including auxiliary variables, average gradient estimation variables and virtual Nash equilibrium search vector, and design a preset time gain operator with rate control parameters and exponential parameters based on the preset convergence time. S400: Design an equilibrium search layer algorithm that includes methods for calculating the virtual Nash equilibrium search vector update rate, auxiliary variable update rate, and average gradient estimation variable. Through interaction among agents within the alliance, it searches for the constrained multi-alliance game Nash equilibrium solution within a preset time. S500. Based on the Nash equilibrium solution, the high-order heterogeneous agent dynamics model, and the preset time gain operator, design an output tracking layer control law to generate the control input of the agent, so as to drive the actual output of the heterogeneous uncertain cluster to track to the Nash equilibrium solution within a preset time.

[0027] I. System Overall Architecture and Parameter Settings In its specific implementation, this embodiment uses an interference-countermeasure scenario involving two heterogeneous uncertain intelligent agent alliances as an example to illustrate the detailed implementation process of the invention, such as... Figure 2 The diagram shown is a communication topology diagram for this scenario. Specifically: (1) Basic parameter settings Agent and Coalition Configuration: Total number of agents participating in the game Based on the relationship of cooperation and competition, they are divided into two alliances, namely... Alliance 1 (Interference Alliance) includes Individual agents; Alliance 2 (Anti-interference Alliance) includes An intelligent agent, satisfying .

[0028] Decision variables and constraint sets: Decision variables for each agent It is a 2-dimensional real vector (representing positional information), that is Constraint set of Alliance 1 The constraint set of Alliance 2 ,in . The locations of the base stations for the two alliances are given, and the agents are restricted to moving near the base stations.

[0029] Cost function definition: agents in Coalition 1 ( The cost function of ) ,in For personalized private cost functions; This is used to maintain smooth communication within the alliance; The objective is to get close to Alliance 2 and disrupt them. This is the set of decision variables for all agents.

[0030] Agents in Alliance 2 ( Cost function: ,in For personalized private cost functions; This is used to maintain smooth communication within the alliance; The goal is to stay away from Alliance 1 and avoid interference.

[0031] Preset time: Set the preset convergence time. The requirement is that the cluster converges to the constrained multi-alliance game Nash equilibrium within 4 seconds.

[0032] (2) Parameters of the heterogeneous uncertain dynamic model The agents participating in the game are heterogeneous and uncertain agents, and a high-order heterogeneous dynamics model containing time-varying uncertainties is adopted. The specific parameters are as follows: like Figure 2 The circular symbol represents the dynamic model of the intelligent agent. It satisfies the dimension matching condition, and The order of the lines is satisfied.

[0033] like Figure 2 The square shown represents the dynamic model of the intelligent agent: It satisfies the dimension matching condition, and The order of the lines is satisfied.

[0034] (3) Communication topology construction Intra-alliance communication topology: Alliance 1 internal communication topology For a weighted balanced directed graph, the weight adjacency matrix is... Laplace matrix ,in (Diagonal elements are the node's in-degree).

[0035] Alliance 2 internal communication topology , For a weighted balanced directed graph, the weight adjacency matrix is... Laplace matrix ,in .

[0036] Overall communication topology: Overall communication topology , It includes intra-alliance communication edges and inter-alliance communication edges.

[0037] II. Implementation Steps of the Pre-set Time Control Method for Constrained Multi-Alliance Games S100. Establishing a constrained multi-alliance game model and defining Nash equilibrium. Model Construction: Based on the basic parameter settings in (1) above, the alliance ( The cost function is ,in For the alliance The resultant vector of decision variables The decision variables of the other alliances are combined into a vector, and each agent only knows its own cost function. The overall cost function of the alliance is minimized through interactions within the alliance.

[0038] Nash equilibrium is defined as follows: if there exists an optimal decision state vector... ,satisfy , ,and ,but To constrain the Nash equilibrium solution in a multi-alliance game.

[0039] S200, Establishing the dynamic model and communication topology Based on the heterogeneous uncertain dynamics model parameters and communication topology set above, the model building and topology construction were completed, and the physical meaning and constraint relationships of each matrix and variable were clarified, providing a foundation for the subsequent control algorithm design.

[0040] S300, Initialization of Equalization Search Layer Parameters and Design of Preset Time Gain Operator Parameter initialization: for each alliance The An intelligent agent initializes auxiliary variables. ( Average gradient estimated variables Virtual Nash equilibrium search vector (2-dimensional zero vector).

[0041] Preset time gain operator design: Selecting rate control parameters Exponential parameters Design a preset time gain operator : ,in, The preset time gain operator rate control parameters, This represents the first auxiliary dynamic function. Represents the first auxiliary dynamic function The derivative, This indicates a preset time gain operator, ensuring that within a preset time... The internal gain operator can drive the search process to converge quickly.

[0042] S400, Equilibrium Search Layer Algorithm Design and Implementation Regarding the first The first alliance An intelligent agent utilizes a preset time gain operator in S320. The algorithm for designing the equilibrium search layer is as follows: in, For vectors To the The first in the alliance The set of constraints satisfied by an intelligent agent The projection on the surface is calculated as follows: That is, to traverse the constraint set and find the one that minimizes the value. , The gain parameter is positive; additionally, the average gradient estimate variable... It is an alliance The Middle Individuals for the coalition cost function Regarding the Decision-Making Alliance The Middle Individual decision variables The estimation of the partial derivative, and its calculation method, Indicates the first The first in the alliance The cost function for each agent; Indicates the first The cost function of a coalition is the sum of the cost functions of all agents in that coalition. , Indicates the first The first in the alliance The agent for the first Cost function of a coalition about The estimated vector of the partial derivatives, Indicates the first The first in the alliance The agent for the first Cost function of a coalition about The estimated vector of partial derivatives By executing this algorithm, each agent achieves distributed gradient estimation of the global cost function through interaction within the alliance, within a preset time. Internal, virtual Nash equilibrium search vector Converging to Nash equilibrium solution As attached Figure 3 As shown, the agent in Alliance 1 moves closer to the agent in Alliance 2, while the agent in Alliance 2 avoids the agent within the constraint set, which aligns with the game objective.

[0043] S500 Output Tracking Layer Algorithm Design and Implementation S510, Initialization For positive numbers, select satisfy ; S520, Design of the first gain matrix based on the dynamic model Second gain matrix Regarding the first The first in the alliance An intelligent agent designs the first gain matrix. Second gain matrix ,in ; S530, based on the preset time gain operator in S320 Regarding the first The first alliance An intelligent agent designs time-varying exponential parameters. update rate ,in Let be the initial gain of the time-varying exponential parameter, and ; S540, based on the preset time gain operator in S320 The update rate of time-varying exponential parameters designed for S530 Regarding the first The first alliance An intelligent agent is designed to withstand uncertain parameter update rates. ; S550, Virtual Nash Equilibrium Search Vector Obtained from S400 The preset time gain operator in S320 The control input is designed based on the gain matrix in S520, the time-varying exponential parameter in S530, and the uncertainty resistance parameter in S540: ,in, For constant gain, its selection satisfies The tracking layer algorithm is executed to drive the heterogeneous uncertain cluster to a preset time. Converging inward to the Nash equilibrium solution of the constrained multi-alliance game; as shown in the appendix. Figure 4As shown, the error between the agent's output decision and the Nash equilibrium solution approaches 0 within 4 seconds, verifying the algorithm's fast convergence and tracking accuracy. At the same time, the uncertainty of the dynamic model is suppressed by the anti-uncertainty parameter, ensuring control accuracy.

[0044] This embodiment, through the specific implementation steps described above, achieves preset time control for heterogeneous uncertain clusters in constrained multi-alliance game scenarios; such as Figure 3 The diagram shows the interference and adversarial trajectory of the agents. It can be seen that agent 1 tries to get as close as possible to agent 2 within the constraint set to apply interference, while agent 2 effectively avoids interference within the constraint set, which aligns with the game strategy objective. Figure 4 The algorithm outputs a decision error graph for the agents, showing that the decision errors of all agents converge to 0 within a preset time of 4 seconds, verifying the algorithm's convergence characteristics within the preset time. Furthermore, by incorporating anti-uncertainty parameters and time-varying exponential parameters, the algorithm effectively suppresses the heterogeneity and uncertainty of the dynamic model, ensuring convergence accuracy and solving the challenges of adaptability and rapid convergence in complex scenarios faced by existing technologies.

[0045] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A preset time control method for heterogeneous uncertain cluster-constrained multi-alliance game, characterized in that, This method implements fast game control of heterogeneous uncertain clusters through a hierarchical design. The specific steps are as follows: S100. Establish a constrained multi-alliance game model, clarify the number of agents and alliances, numbering rules and cost function definitions, and define the conditions for determining the Nash equilibrium of the constrained multi-alliance game. S200. Establish a high-order heterogeneous agent dynamics model containing time-varying uncertainties, clarify the physical meaning and constraint relationship of each matrix and variable in the model, construct the communication topology between agents participating in the game within the alliance and the whole, and define the topology-related nodes, edges, weighted adjacency matrices and Laplace matrices. S300. Initialize the relevant parameters of the equilibrium search layer, including auxiliary variables, average gradient estimation variables and virtual Nash equilibrium search vector, and design a preset time gain operator with rate control parameters and exponential parameters based on the preset convergence time. S400: Design an equilibrium search layer algorithm that includes methods for calculating the virtual Nash equilibrium search vector update rate, auxiliary variable update rate, and average gradient estimation variable. Through interaction among agents within the alliance, it searches for the constrained multi-alliance game Nash equilibrium solution within a preset time. S500. Based on the Nash equilibrium solution, the high-order heterogeneous agent dynamics model, and the preset time gain operator, design an output tracking layer control law to generate the control input of the agent, so as to drive the actual output of the heterogeneous uncertain cluster to track to the Nash equilibrium solution within a preset time.

2. The method for pre-setting time control in heterogeneous uncertain cluster-constrained multi-alliance game according to claim 1, characterized in that, In S100, the specific process of establishing the constrained multi-alliance game model and defining the constrained multi-alliance game Nash equilibrium is as follows: S110, Based on the total number of agents participating in the game. Each agent is divided into groups based on the cooperative and competitive relationships reflected in the cost function. There are 1 alliance, and each alliance has 1 alliance. There are [number] intelligent agents, and the number of individuals within the alliance satisfies [condition]. The alliance is a collection of ,alliance The set of IDs for all agents within the system is The cost function for each agent is: ,in, Indicates the first The sum vector of decision variables of all participating agents in a coalition, i.e. Indicates the first The first in the alliance The decision variables of each agent, and for 3D real vector, alliance Cost function ,in Indicates except the first The sum of decision variables of agents in all other alliances outside the alliance is the sum of the decision variables of the agents. Each agent minimizes the overall cost function of its alliance by adjusting its own decision state. Each agent can only obtain its own cost function information. The alliance participates in the upper-level game as a virtual entity. The strategy decision is jointly realized by the agents in the alliance. S120. When an optimal decision state vector exists. ,satisfy Then the state vector is the Nash equilibrium solution of the constrained multi-alliance game, where It is the first The set of constraints that the resultant vector of the decision variables of all participating agents in a coalition must satisfy is a non-empty convex compact set.

3. The method for pre-setting time control in heterogeneous uncertain cluster-constrained multi-alliance game according to claim 1, characterized in that, The specific process of establishing a high-order heterogeneous agent dynamics model and constructing topology communication in S200 is as follows: S210. The agents participating in the constrained multi-alliance game are heterogeneous and uncertain agents, and their dynamic model is as follows: ,in Indicates the first The first in the alliance Decision variables for an agent Indicates the first The first in the alliance Control input for an intelligent agent Indicates the first The first in the alliance The internal state of an agent Indicates the first The first in the alliance The update rate of the internal state of an agent. Indicates the first The first in the alliance The system dynamics matrix of each agent is a real constant matrix. Indicates the first The first in the alliance The system input matrix for each agent is a real constant matrix. Indicates the first The first in the alliance The decision matrix of each agent is a real constant matrix, and the matrix... The condition of full rank for rows is met. It is a time-varying matrix, representing the uncertainty in the agent's policy evolution process, and , All matrices satisfy dimension matching; S220, Building Alliances Internal communication topology ,in This represents the set of all intelligent agents within the alliance. This represents the set of communication edges between intelligent agents within the alliance. Refers to the first The first in the alliance The agent points to the first The first in the alliance The communication edge of an agent, when there exists and If the graph is a directed graph, then the weighted adjacency matrix of the communication topology graph is... For a square matrix, its first... Line number Column elements If and only if Otherwise, it is 0, defining the first The first in the alliance Nodes in-degree is Out-degree is If all nodes have the same out-degree and in-degree, then the graph is a weighted directed graph, and its Laplace matrix is ​​defined as follows: ,in It is a diagonal matrix constructed from the in-degree information of all nodes in the alliance; it constructs the communication topology among the intelligent agents participating in the game as a whole. ,in For a set of intelligent agents For the set of communication edges between intelligent agents, Refers to the first The first in the alliance The agent points to the first The first in the alliance The communication edges of the agents, and the overall communication topology of the game are as follows: .

4. The method for pre-setting time control in heterogeneous uncertain cluster-constrained multi-alliance game according to claim 1, characterized in that, In S300, the specific process of initializing the relevant parameters of the equalization search layer and designing the preset time gain operator is as follows: S310, Regarding the first The first in the alliance An intelligent agent initializes auxiliary variables. Average gradient estimated variables All are 0, virtual Nash equilibrium search vector Let be the zero vector, where , ; S320, Select preset time Design a preset time gain operator : ,in, The preset time gain operator rate control parameters, This represents the first auxiliary dynamic function. Represents the first auxiliary dynamic function The derivative, This indicates the preset time gain operator.

5. The method for pre-setting time control in heterogeneous uncertain cluster-constrained multi-alliance game according to claim 1 or 4, characterized in that, In S400, the specific process of designing the equilibrium search layer algorithm is as follows: Regarding the first The first alliance An intelligent agent utilizes a preset time gain operator in S320. The equilibrium search layer algorithm is designed as follows: in, For vectors To the The first in the alliance The set of constraints satisfied by an intelligent agent The projection on the surface is calculated as follows: That is, to traverse the constraint set and find the one that minimizes the value. , The gain parameter is positive; additionally, the average gradient estimate variable... It is an alliance The Middle Individuals for the coalition cost function Regarding the Decision-Making Alliance The Middle Individual decision variables The estimation of the partial derivative, and its calculation method, Indicates the first The first in the alliance The cost function for each agent; Indicates the first The cost function of a coalition is the sum of the cost functions of all agents in that coalition. , Indicates the first The first in the alliance The agent for the first Cost function of a coalition about The estimated vector of the partial derivatives, Indicates the first The first in the alliance The agent for the first Cost function of a coalition about The estimated vector of the partial derivatives; Execute the equilibrium search layer algorithm, the first... The first alliance An intelligent agent at a preset time Internal control virtual Nash equilibrium search vector The search found the Nash equilibrium in a constrained multi-alliance game.

6. The method for pre-setting time control in heterogeneous uncertain cluster-constrained multi-alliance game according to claim 1, characterized in that, In S500, the specific process of initializing the relevant constant parameters of the output tracking layer and converging the Nash equilibrium solution is as follows: S510, Initialization For positive numbers, select satisfy ; S520, Design of the first gain matrix based on the dynamic model Second gain matrix Regarding the first The first in the alliance An intelligent agent designs the first gain matrix. Second gain matrix ,in ; S530, based on the preset time gain operator in S320 Regarding the first The first alliance An intelligent agent designs time-varying exponential parameters. update rate ,in Let be the initial gain of the time-varying exponential parameter, and ; S540, based on the preset time gain operator in S320 The update rate of time-varying exponential parameters designed for S530 Regarding the first The first alliance An intelligent agent is designed to withstand uncertain parameter update rates. ; S550, Virtual Nash Equilibrium Search Vector Obtained from S400 The preset time gain operator in S320 The control input is designed based on the gain matrix in S520, the time-varying exponential parameter in S530, and the uncertainty resistance parameter in S540: ,in, For constant gain, its selection satisfies The tracking layer algorithm is executed to drive the heterogeneous uncertain cluster to a preset time. It converges inward to the Nash equilibrium solution of the constrained multi-alliance game.

7. A preset time control system for heterogeneous uncertain cluster-constrained multi-alliance game, applicable to the preset time control method for heterogeneous uncertain cluster-constrained multi-alliance game as described in any one of claims 1-6, characterized in that, The system includes: The game model construction module establishes a constrained multi-alliance game model, clarifies the number of agents and alliances, numbering rules, and cost function definitions, and defines the conditions for determining the Nash equilibrium of the constrained multi-alliance game. The Dynamics and Topology Construction Module is used to build a high-order heterogeneous agent dynamics model containing time-varying uncertainties, clarify the physical meaning and constraint relationship of each matrix and variable in the model, construct the communication topology between agents participating in the game within the alliance and the whole, and define the topology-related nodes, edges, weighted adjacency matrices and Laplace matrices. The equilibrium search layer initialization module is used to initialize the relevant parameters of the equilibrium search layer, including auxiliary variables, average gradient estimation variables and virtual Nash equilibrium search vectors. It designs a preset time gain operator with rate control parameters and exponential parameters based on the preset convergence time. The equilibrium search module is used to design an equilibrium search layer algorithm that includes methods for calculating the virtual Nash equilibrium search vector update rate, auxiliary variable update rate, and average gradient estimation variable. Through the interaction of agents within the alliance, it searches for the Nash equilibrium solution of the constrained multi-alliance game within a preset time. The output tracking module, based on the Nash equilibrium solution, the high-order heterogeneous agent dynamics model, and the preset time gain operator, designs the output tracking layer control law, generates the control input of the agent, and executes the tracking layer algorithm to drive the actual output of the heterogeneous uncertain cluster to track to the Nash equilibrium solution within a preset time.

8. The heterogeneous uncertain cluster-constrained multi-alliance game preset time control system according to claim 7, characterized in that, The game model construction module includes: The agent decision state dynamics model construction unit is used to construct a constrained multi-alliance game agent decision state dynamics model, clarify the number and numbering rules of agents and alliances, and define the cost functions of agents and alliances, where the alliance cost function is the sum of the cost functions of all agents in the alliance; The Nash equilibrium definition unit is used to define the Nash equilibrium in constrained multi-alliance games, and to clarify the conditions that the optimal decision state vector must satisfy and the property that the constraint set is a non-empty convex compact set.

9. The heterogeneous uncertain cluster-constrained multi-alliance game preset time control system according to claim 7, characterized in that, The dynamics and topology construction module includes: The heterogeneous uncertain dynamics model building unit is used to establish a high-order heterogeneous agent dynamics model containing time-varying uncertain terms. It clarifies that the system dynamics matrix, system input matrix, and decision matrix in the model are all real constant matrices, the product of the decision matrix and the system input matrix satisfies the full-rank condition, and the time-varying uncertain term matrix and the system input matrix satisfy a linear relationship of dimension matching. The topology communication construction unit is used to construct communication topologies within the alliance and between agents as a whole. It clarifies that the nodes of the communication topology graph are agents and the edges are communication links between agents. The elements of the weighted adjacency matrix are assigned values ​​according to the existence of the communication edges. The Laplace matrix is ​​composed of the difference between the in-degree diagonal matrix and the weighted adjacency matrix.

10. The heterogeneous uncertain cluster-constrained multi-alliance game preset time control system according to claim 7, characterized in that, The balanced search module includes: The search algorithm design unit is used to design the virtual Nash equilibrium search vector update rate, auxiliary variable update rate and average gradient estimation variable calculation method based on the preset time gain operator. The average gradient estimation variable is calculated by the partial derivative of the cost function of the agents in the alliance and the mean of the auxiliary variables. The equilibrium search execution unit is used to execute the equilibrium search layer algorithm and control the virtual Nash equilibrium search vector to search for the Nash equilibrium solution of the constrained multi-alliance game within a preset time. The output tracking module includes: The tracking parameter design unit is used to design the update rate of the output tracking layer's gain matrix, time-varying exponential parameters, and anti-uncertainty parameters, where the gain matrix is ​​constructed based on the gain matrix of the dynamic model parameters. The control input design and execution unit is used to design the control input of the intelligent agent based on the virtual Nash equilibrium search vector, the preset time gain operator and the tracking parameters, so as to drive the heterogeneous uncertain cluster to track and converge to the Nash equilibrium solution.

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