Intra-group irrelevant multi-cluster resource allocation game equilibrium specified time search method

Abstract

The invention discloses an intra-group irrelevant multi-cluster resource allocation game equilibrium specified time search method, which belongs to the technical field of multi-agent game decision making, and comprises the following steps: firstly, aiming at the situation that the interests of agent individuals of a multi-cluster system do not depend on the states of agents in an alliance and are only related to the own state and the states of the agents in other alliances; constructing an intra-group irrelevant multi-cluster resource allocation game model under the coupling equality resource constraint for the multi-agent system; secondly, constructing a communication topological structure for the multi-agent system; and finally, designing a multi-cluster resource allocation game Nash equilibrium search method with specified time convergence for each agent in combination with a time planning method. According to the method, the Nash equilibrium specified time search of the intra-group irrelevant multi-cluster resource allocation game problem can be realized aiming at the condition that coupling equality resource constraints and agent individual interests do not depend on the states of other agents in the alliance, and a basis is provided for distributed resource scheduling in a complex cooperation-competition environment.

Description

Technical Field

[0001] The invention belongs to the technical field of multi-agent game decision making, and in particular relates to a method for searching for a designated time for a balanced resource allocation game of unrelated multi-cluster resources within a group. Background Art

[0002] With the development of artificial intelligence, resource allocation has become an important factor in promoting the development of modern industrial systems. It can optimize resource utilization under limited resources and play an important role in economic development, cultural construction, green development, etc. In the resource allocation of large-scale networked systems, the system is clustered into multiple clusters that only focus on maximizing the interests of the group they belong to. Multi-cluster resource allocation can be regarded as a distributed optimization problem for multiple clusters under the resource equation coupling constraint to maximize the group benefits. The group benefits are usually only related to the decisions of individuals in the cluster. However, in the actual application of multi-cluster resource allocation, due to the complex interactions in large-scale networked systems, there are competitive and cooperative relationships between different cluster agents, and the local decisions of individuals will also affect the cost functions of other cluster agents. Therefore, it is urgent to establish a multi-cluster resource allocation game that can describe the conflicts of interest between different cluster agents, design and optimize the parameters of the multi-cluster resource allocation game model, and conduct research on its Nash equilibrium search method.

[0003] Among the existing multi-cluster game Nash equilibrium search algorithms, the literature ( Pang Y, Hu G. Nash equilibrium seeking in N - coalition games via a gradient - free method[J]. Automatica, 2022, 136: 110013. ) In the case where only local objective functions can be obtained, a discrete-time algorithm without gradient is proposed based on Gaussian smoothing. Under this algorithm, all agents converge to the minimum neighborhood of Nash equilibrium at a geometric rate. The limitation of this scheme is that it is not applicable to the situation with constraints and can only converge linearly to the neighborhood of Nash equilibrium. Meng M, Li X. On the linear convergence of distributed Nash equilibrium seeking for multi - cluster games under partial - decision information[J]. Automatica, 2023, 151: 110919 .) studied the Nash equilibrium search algorithm for multi-cluster games under consistency constraints, and designed a discrete time algorithm based on gradient tracking and projection method in partial decision information scenarios. However, this algorithm is only applicable to undirected topological graphs and can only achieve linear convergence, not specified time convergence. Zhou J, Lv Y, Wen G, et al. Distributed Nash equilibrium seeking in consistency - constrained multicoalition games[J]. IEEE Transactions on Cybernetics, 2022. ) further studied the multi-cluster game under the directed topology graph that satisfies the consistency constraint, and designed a discrete time algorithm using techniques such as leader-follower consistency and pseudo gradient descent, but this scheme can only achieve linear convergence. The above schemes can only achieve linear convergence and cannot achieve specified time convergence. Therefore, the existing technology is not suitable for practical applications with specified convergence time requirements. Summary of the invention

[0004] The purpose of the present invention is to provide a designated time search method for the equilibrium of multi-cluster resource allocation game that is unrelated within a group. For multiple clusters that are subject to resource equation coupling constraints and aim to minimize the group cost function, the input of the cost function of the intelligent agent in the multi-cluster is considered to be independent of the decision of other intelligent agents in the same cluster, and only includes its local decision and the decision of the intelligent agent in other clusters. By establishing a multi-coalition game model for multi-cluster resource allocation, a fast solution method for the designated time is provided for studying the equilibrium of the multi-coalition game, and a solution to the multi-cluster resource allocation problem is provided from the perspective of the coalition game.

[0005] To achieve the above object, the present invention provides a method for searching for a specified time for a game equilibrium of resource allocation among multiple clusters that are not related to each other within a group, comprising the following steps: Step 1: For the situation where the individual interests of agents in a multi-cluster system do not depend on the states of agents in the alliance, but are only related to their own states and the states of agents in other alliances, a game model of unrelated multi-cluster resource allocation within the group under coupled equality resource constraints is constructed for the multi-agent system; Step 2: Construct a communication topology for the multi-agent system; Step 3: Combined with the time planning method, a multi-cluster resource allocation game Nash equilibrium search method with a specified time convergence is designed for each agent. The specific process is as follows: S31. Using the variable substitution method, the Nash equilibrium problem under equality constraints is converted into the Nash equilibrium problem without constraints. S32, combined with the time planning method, each agent estimates the state information of all agents based on the leader-follower consistency; S33. Combined with the time planning method, the agent performs state iteration on the replaced variables based on pseudo-gradient descent and auxiliary variables of estimated state information.

[0006] Preferably, in step 1, for the situation where the individual interests of the agents in the multi-cluster system do not depend on the states of the agents in the alliance, but are only related to their own states and the states of the agents in other alliances, a resource allocation game model of unrelated multi-cluster resources within the group under the coupled equality resource constraint is constructed for the multi-agent system as follows: ; Among them, number Represents a cluster among the N clusters participating in the game ,serial number Indicates that it contains Clusters of agents Middle j An intelligent agent, Represents a cluster The set of intelligent entities, represents the set of all agents, For intelligent agents status, Represents a cluster The joint state represents the joint state of all clusters, is the total number of agents in all clusters, Indicates that no cluster is included The combined state of all other clusters of and Respectively represent intelligent agents Owned local resources and clusters Owned resources, cluster The state satisfies the constraints, which are , a continuously differentiable convex function and Intelligent Agent and clusters The cost function, function and It has a Lipschitz continuous gradient, specifically: ,have and ,in for Li psch it z constant, .

[0007] Preferably, in step 2, the communication topology structure for the multi-agent system is constructed as follows: The communication topology among all the agents participating in the game is modeled as an undirected communication topology graph ,in represents a node set, represents the edge set, if the agent pq Receiving Agent information, then ,and for pq Neighbors, since the communication topology is undirected, if ,but , cluster The internal communication topology uses an undirected communication topology subgraph express, Represents a cluster In The set of agents and the set of edges are , Agent Neighborhood set representation in the network , the in-degree is , Agent In cluster The neighbor set in is represented as , the in-degree is , define an undirected communication topology graph The adjacency matrix of ,in Represents the matrix A Line Elements of the columns, all diagonal elements of the matrix A ,like , off-diagonal elements ,otherwise , define the undirected communication topology subgraph The adjacency matrix of ,in Representation Matrix No. j Line The elements of the column define the undirected communication topology subgraph The Laplace matrix of ,in Representation Matrix No. j Line Column elements, diagonal elements , off-diagonal elements , define an undirected communication topology graph The weighted adjacency matrix of ,in Represents the matrix W Line Elements of the columns, all diagonal elements of the matrix W ,like , off-diagonal elements ,otherwise , the elements of the matrix W satisfy .

[0008] Optimally, undirected communication topology and undirected communication topology subgraph are all connected, among which Represents a set of N game clusters.

[0009] Preferably, in S31, the variable substitution method is used to convert the Nash equilibrium solution problem under the equality constraint into the Nash equilibrium solution problem under the unconstrained constraint as follows: ; in, Representing an Agent exist t The state at the moment, its initial value , Represents the agent exist The auxiliary variable after the variable replacement of the state at the moment, It is for intelligent agents exist The state at the moment is replaced by an auxiliary variable, and its initial value is , Representing an Agent In cluster The neighbor set in Indicates sampling time, the sampling interval sequence It is expressed as: ; The sampling interval sequence is designed as: ; In the formula, For the preset specified time, is a convergent infinite series, is limited, Indicates The sampling interval, represents the set of positive integers, represents the first j item, represents the first item.

[0010] Preferably, in S32, in combination with the time planning method, each agent estimates the specific expression of the state information of all agents based on the leader-follower consistency as follows: ; in, For intelligent agents To estimate the agent pq exist Status of the moment Auxiliary variables, Representing an Agent To estimate the agent pq exist t Status at all times The auxiliary variable derivative of Representing an Agent To estimate the agent pq exist Status at all times Auxiliary variables, Represents the weighted adjacency matrix W Line The elements of the column, is the weighted adjacency matrix W Line The elements of the column, the elements of the weighted adjacency matrix satisfy , the specific selection method is: ; in, is a constant, is the adjacency matrix A Line The elements of the column, For intelligent agents The in-degree of: .

[0011] Preferably, in S33, in combination with the time planning method, the agent performs state iteration on the replaced variables based on pseudo-gradient descent and auxiliary variables of estimated state information as follows: ; in, is a positive constant to be designed, For intelligent agents In cluster The neighbor set in Representing an Agent To estimate the agent state Auxiliary variables, Representing an Agent To estimate the agent state Auxiliary variables, Representing an Agent Eliminate clusters The state estimation of agents in other clusters other than Representing an Agent exist Always remove clusters The state estimation of agents in other clusters other than Representing an Agent For the resource allocation game of multiple clusters that are not related within the group, the cost function of each agent is only determined by its own state and the states of agents in other clusters. The pseudo gradient of each cluster exists in the equation: ; in, For cluster The cost function of cluster The sum of the cost functions of all agents in , represents the state of all agents, Indicates that clusters are not included All other agent states of the agents in , Representing an Agent status, Represents a cluster Meso Agent j The cost function of .

[0012] Preferably, the Nash equilibrium search method for the multi-cluster resource allocation game with a specified time convergence designed in step 3 satisfies certain prerequisites and parameter conditions.

[0013] Preferably, the prerequisite is specifically: the pseudo gradient function is required is strictly monotonic, and there exists a positive constant Make .

[0014] Preferably, the parameter conditions are specifically: ; in, ; ; ; ; ; In the formula, represents a strictly monotonic constant pseudo-gradient, is a constant, is the Lipschitz constant, is an undirected communication topology subgraph The Laplace matrix of is the total number of agents in all clusters, for dimensional identity matrix, W is the weighted adjacency matrix, and the elements of matrix W satisfy It turns out that the matrix is a diagonal matrix with diagonal elements , from the undirected communication topology graph is connected and Gershgor i The n-disk theorem yields the matrix is a Schur matrix, there exists a symmetric positive definite matrix Make .

[0015] Therefore, the present invention adopts the above-mentioned intra-group irrelevant multi-cluster resource allocation game equilibrium designated time search method, which has the following beneficial effects: (1) Aiming at the situation where there are conflicts of interest between different cluster agents, the present invention considers the Nash equilibrium search method of the resource allocation game of unrelated multi-cluster within the group under the constraint of coupling equality, and provides a solution to the resource allocation problem of multi-cluster with complex cooperative and competitive relationships; (2) In the process of searching for Nash equilibrium, the resource equality coupling constraint within the cluster always holds, which enables the method to be executed online, providing a solution to the multi-cluster resource allocation problem that requires real-time balance between resource supply and demand. (3) Compared with finite time convergence and fixed time convergence, the method proposed in the present invention can achieve Nash equilibrium solution under a specified time, and the specified convergence time is independent of the initial value and method parameters, which makes it easy to predetermine the convergence time according to actual needs.

[0016] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a schematic diagram of the steps of the method for searching for a designated time for a game equilibrium of resource allocation of unrelated multiple clusters within a group according to the present invention; Figure 2 A specific flow chart of the method for searching for a time-specific game equilibrium for resource allocation among multiple clusters within a group that is unrelated to each other in the present invention; Figure 3 is a communication topology diagram of a multi-agent system provided by an embodiment of the present invention; Figure 4 It is an evolution diagram provided by an embodiment of the present invention in which the states of each agent converge to equilibrium at a specified time of 1s; Figure 5 It is an evolution diagram in which the cost function of each cluster converges to the optimum at a specified time of 1s provided by an embodiment of the present invention; Figure 6 This is a graph showing changes in the total number of resources of each cluster during a balanced search process provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0018] The following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0019] See also Figures 1 - 6 , a method for searching for a specified time for a game equilibrium of resource allocation among multiple clusters that are not related within a group, comprising the following steps: Step 1: For the situation where the individual interests of agents in a multi-cluster system do not depend on the states of agents in the alliance, but are only related to their own states and the states of agents in other alliances, a game model of unrelated multi-cluster resource allocation within the group under coupled equation resource constraints is constructed for the multi-agent system; specifically: ; Among them, number Represents a cluster among the N clusters participating in the game ,serial number Indicates that it contains Clusters of agents Middle j An intelligent agent, Represents a cluster The set of intelligent entities, represents the set of all agents, For intelligent agents status, Represents a cluster The joint state represents the joint state of all clusters, is the total number of agents in all clusters, Indicates that no cluster is included The combined state of all other clusters of and Respectively represent intelligent agents Owned local resources and clusters Owned resources, cluster The state satisfies the constraints, which are , a continuously differentiable convex function and Intelligent Agent and clusters The cost function, function and It has a Lipschitz continuous gradient, specifically: ,have and ,in for Li psch it z constant, .

[0020] Step 2: Construct a communication topology for the multi-agent system; specifically: The communication topology among all the agents participating in the game is modeled as an undirected communication topology graph ,in represents a node set, represents the edge set, if the agent pq Receiving Agent information, then ,and for pq Neighbors, since the communication topology is undirected, if ,but , cluster The internal communication topology uses an undirected communication topology subgraph express, Represents a cluster In The set of agents and the set of edges are , Agent Neighborhood set representation in the network , the in-degree is , Agent In cluster The neighbor set in is represented as , the in-degree is , define an undirected communication topology graph The adjacency matrix of ,in Represents the matrix A Line Elements of the columns, all diagonal elements of the matrix A ,like , off-diagonal elements ,otherwise , define the undirected communication topology subgraph The adjacency matrix of ,in Representation Matrix No. j Line The elements of the column define the undirected communication topology subgraph The Laplace matrix of ,in Representation Matrix No. j Line Column elements, diagonal elements , off-diagonal elements , define an undirected communication topology graph The weighted adjacency matrix of ,in Represents the matrix W Line Elements of the columns, all diagonal elements of the matrix W ,like , off-diagonal elements ,otherwise , the elements of the matrix W satisfy Among them, the undirected communication topology graph and undirected communication topology subgraph are all connected, among which Represents a set of N game clusters.

[0021] Step 3: Combined with the time planning method, a multi-cluster resource allocation game Nash equilibrium search method with a specified time convergence is designed for each agent. The specific process is as follows: S31. Using the variable substitution method, the Nash equilibrium problem under equality constraints is converted into the Nash equilibrium problem without constraints. The specific expression is as follows: ; in, Representing an Agent exist t The state at the moment, its initial value , Represents the agent exist The auxiliary variable after the variable replacement of the state at the moment, It is for intelligent agents exist The state at the moment is replaced by an auxiliary variable, and its initial value is , Representing an Agent In cluster The neighbor set in Indicates sampling time, the sampling interval sequence It is expressed as: ; The sampling interval sequence is designed as: ; In the formula, For the preset specified time, is a convergent infinite series, is limited, Indicates The sampling interval, represents the set of positive integers, represents the first j item, represents the first item.

[0022] S32. Combined with the time planning method, each agent estimates the state information of all agents based on the leader-follower consistency; the specific expression is as follows: ; in, For intelligent agents To estimate the agent pq exist Status of the moment Auxiliary variables, Representing an Agent To estimate the agent pq exist tStatus at all times The auxiliary variable derivative of Representing an Agent To estimate the agent pq exist Status at all times Auxiliary variables, Represents the weighted adjacency matrix W Line The elements of the column, is the weighted adjacency matrix W Line The elements of the column, the elements of the weighted adjacency matrix satisfy , the specific selection method is: ; in, is a constant, is the adjacency matrix A Line The elements of the column, For intelligent agents The in-degree of: .

[0023] S33. Combined with the time planning method, the agent performs state iteration on the replaced variables based on pseudo gradient descent and auxiliary variables of estimated state information. The specific expression is as follows: ; in, is a positive constant to be designed, For intelligent agents In cluster The neighbor set in Representing an Agent To estimate the agent state Auxiliary variables, Representing an Agent To estimate the agent state Auxiliary variables, Representing an Agent im Eliminate clusters The state estimation of agents in other clusters other than Representing an Agent exist Always remove clusters The state estimation of agents in other clusters other than Representing an Agent For the resource allocation game of multiple clusters that are not related within the group, the cost function of each agent is only determined by its own state and the states of agents in other clusters. The pseudo gradient of each cluster exists in the equation: ; in, For cluster The cost function of cluster The sum of the cost functions of all agents in , represents the state of all agents, Indicates that clusters are not included All other agent states of the agents in , Representing an Agent status, Represents a cluster Meso-agent j The cost function of .

[0024] In addition, the Nash equilibrium search method for the multi-cluster resource allocation game designed in step 3 with a specified time convergence meets certain prerequisites and parameter conditions; the prerequisites are as follows: the pseudo gradient function is required to is strictly monotonic, and there exists a positive constant Make ; The specific parameter conditions are: ; in, ; ; ; ; ; in, represents a strictly monotonic constant pseudo-gradient, is a constant, is the Lipschitz constant, is an undirected communication topology subgraph The Laplace matrix of is the total number of agents in all clusters, for dimensional identity matrix, W is the weighted adjacency matrix, and the elements of matrix W satisfy It turns out that the matrix is a diagonal matrix with diagonal elements , from the undirected communication topology graph is connected and Gershgor i The n-disk theorem yields the matrix is a Schur matrix, there exists a symmetric positive definite matrix Make .

[0025] Example Step 1: Consider N=3 containing , , The number of resources in each cluster is , and , Agent The cost function is , the correlation coefficient is: , , , , , , , , , , , , , , , , , , , , , , , , .

[0026] Step 2: The communication topology of the multi-agent system is as follows: Figure 3 shown.

[0027] Step 3: For the specified time convergence Nash equilibrium search method of the designed intra-group unrelated multi-cluster resource allocation game, the initial node state is selected as .

[0028] Step 4: Design method parameters as . It is specified that the states of all cluster agents converge to the Nash equilibrium in 1 second, and the state convergence curve is as follows Figure 4 As shown, the cost function convergence curves of the three clusters are as follows Figure 5 As shown in the figure, the total number of resources in the cluster is Figure 6 The simulation results show that the state of each agent and the cost of each cluster converge to the Nash equilibrium in 1 second: , , , The resources of each cluster remain unchanged during the balanced search process, and the supply and demand balance is always satisfied. Therefore, the present invention adopts the above-mentioned designated time search method for the equilibrium of multi-cluster resource allocation game that is unrelated within the group. For multiple clusters that are subject to resource equation coupling constraints and aim to minimize the group cost function, the input of the cost function of the intelligent agent in the multi-cluster is considered to be independent of the decisions of other intelligent agents in the same cluster, and only includes its local decision and the decision of the intelligent agent in other clusters. By establishing a multi-coalition game model for multi-cluster resource allocation, a fast solution method for a designated time is provided for studying the equilibrium of the multi-coalition game, and a solution to the multi-cluster resource allocation problem is provided from the perspective of coalition game.

[0029] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A method for searching for a specified time for a game equilibrium of resource allocation among multiple clusters that are not related within a group, characterized in that: The following steps are involved: Step 1: For the situation where the individual interests of agents in a multi-cluster system do not depend on the states of agents in the alliance, but are only related to their own states and the states of agents in other alliances, a game model of unrelated multi-cluster resource allocation within the group under coupled equality resource constraints is constructed for the multi-agent system; Step 2: Construct a communication topology for the multi-agent system; Step 3: Combined with the time planning method, a multi-cluster resource allocation game Nash equilibrium search method with a specified time convergence is designed for each agent. The specific process is as follows: S31. Using the variable substitution method, the Nash equilibrium problem under equality constraints is converted into the Nash equilibrium problem without constraints. S32, combined with the time planning method, each agent estimates the state information of all agents based on the leader-follower consistency; S33. Combined with the time planning method, the agent performs state iteration on the replaced variables based on pseudo-gradient descent and auxiliary variables of estimated state information.

2. The method for searching for a designated time for game equilibrium of resource allocation of unrelated multiple clusters within a group according to claim 1, characterized in that: In step 1, for the situation where the individual interests of the agents in the multi-cluster system do not depend on the states of the agents in their alliance, but are only related to their own states and the states of the agents in other alliances, the intra-group unrelated multi-cluster resource allocation game model under the coupled equality resource constraint is constructed for the multi-agent system as follows: ； Among them, number Represents a cluster among the N clusters participating in the game ,serial number Indicates that it contains Clusters of agents Middle j An intelligent agent, Represents a cluster The set of intelligent entities, represents the set of all agents, For intelligent agents status, Represents a cluster The joint state represents the joint state of all clusters, is the total number of agents in all clusters, Indicates that no cluster is included The combined state of all other clusters of and Respectively represent intelligent agents Owned local resources and clusters Owned resources, cluster The state satisfies the constraints, which are , a continuously differentiable convex function and Agent and clusters The cost function, function and It has a Lipschitz continuous gradient, specifically: ,have and ,in for Li psch it z constant, .

3. The method for searching for a designated time for game equilibrium of resource allocation of multiple clusters within a group that is unrelated to each other according to claim 2, characterized in that: In step 2, the communication topology structure for the multi-agent system is constructed as follows: The communication topology among all the agents participating in the game is modeled as an undirected communication topology graph ,in represents a node set, represents the edge set, if the agent pq Receiving Agent information, then ,and for pq Neighbors, since the communication topology is undirected, if ,but , cluster The internal communication topology uses an undirected communication topology subgraph express, Represents a cluster In The set of agents and the set of edges is , Agent Neighborhood set representation in the network , the in-degree is , Agent In cluster The neighbor set in is represented as , the in-degree is , define an undirected communication topology graph The adjacency matrix of ,in Represents the matrix A Line Elements of the columns, all diagonal elements of the matrix A ,like , off-diagonal elements ,otherwise , define the undirected communication topology subgraph The adjacency matrix of ,in Representation Matrix No. j Line The elements of the column define the undirected communication topology subgraph The Laplace matrix of ,in Representation Matrix No. j Line Column elements, diagonal elements , off-diagonal elements , define an undirected communication topology graph The weighted adjacency matrix of ,in Represents the matrix W Line Elements of the columns, all diagonal elements of the matrix W ,like , off-diagonal elements ,otherwise , the elements of the matrix W satisfy .

4. The method for searching for a designated time for game equilibrium of resource allocation of multiple clusters within a group that is unrelated to each other according to claim 3, characterized in that: Undirected communication topology graph and undirected communication topology subgraph are all connected, among which Represents a set of N game clusters.

5. The method for searching for a designated time for game equilibrium of resource allocation of multiple clusters within a group that is unrelated to each other according to claim 4, characterized in that: In S31, the variable substitution method is used to convert the Nash equilibrium solution problem under equality constraints into the Nash equilibrium solution problem under no constraints as follows: ； in, Representing an Agent exist t The state at the moment, its initial value , Represents the agent exist The auxiliary variable after the variable replacement of the state at the moment, It is for intelligent agents exist The state at the moment is replaced by an auxiliary variable, and its initial value is , Representing an Agent In cluster The neighbor set in Indicates sampling time, the sampling interval sequence It is expressed as: ； The sampling interval sequence is designed as: ； In the formula, For the preset specified time, is a convergent infinite series, is limited, Indicates The sampling interval, represents the set of positive integers, represents the first item, represents the first item.

6. The method for searching for a designated time for game equilibrium of resource allocation of multiple clusters within a group that is unrelated to each other according to claim 5, characterized in that: In S32, combined with the time planning method, each agent estimates the specific expression of all agent state information based on leader-follower consistency as follows: ； in, For intelligent agents To estimate the agent pq exist Status of the moment Auxiliary variables, Representing an Agent To estimate the agent pq exist t Status at all times The auxiliary variable derivative of , Representing an Agent To estimate the agent pq exist Status at all times Auxiliary variables, Representing an Agent pq exist The state of the moment, Represents the weighted adjacency matrix W Line The elements of the column, is the weighted adjacency matrix W Line The elements of the column, the elements of the weighted adjacency matrix satisfy , the specific selection method is: ； in, is a constant, is the adjacency matrix A Line The elements of the column, For intelligent agents The in-degree of: .

7. The method for searching for a designated time for game equilibrium of resource allocation of multiple clusters within a group that is unrelated to each other according to claim 6, characterized in that: In S33, combined with the time planning method, the agent uses pseudo-gradient descent and auxiliary variables of estimated state information to perform state iteration on the replaced variables. The specific expression is as follows: ； in, is a positive constant to be designed, For intelligent agents In cluster The neighbor set in Representing an Agent To estimate the agent state Auxiliary variables, Representing an Agent To estimate the agent state Auxiliary variables, Representing an Agent Eliminate clusters The state estimation of agents in other clusters other than Representing an Agent exist Always remove clusters The state estimation of agents in other clusters other than Representing an Agent For the resource allocation game of multiple clusters that are not related within the group, the cost function of each agent is only determined by its own state and the states of agents in other clusters. The pseudo gradient of each cluster exists in the equation: ； in, For cluster The cost function of cluster The sum of the cost functions of all agents in , represents the state of all agents, Indicates that clusters are not included All other agent states of the agents in , Representing an Agent status, Represents a cluster Meso Agent j The cost function of .

8. The method for searching for a designated time for game equilibrium of resource allocation of multiple clusters within a group that is unrelated to each other according to claim 7, characterized in that: The Nash equilibrium search method for the multi-cluster resource allocation game with specified time convergence designed in step 3 meets certain prerequisites and parameter conditions.

9. The method for searching for a designated time for game equilibrium of resource allocation of multiple clusters within a group that is unrelated to each other according to claim 8, characterized in that: The specific prerequisites are: pseudo gradient function is required is strictly monotonic, and there exists a positive constant Make .

10. The method for searching for a designated time for game equilibrium of resource allocation of multiple clusters within a group that is unrelated to each other according to claim 9, characterized in that: The specific parameter conditions are: ； in, ； ； ； ； ； In the formula, represents a strictly monotonic constant pseudo-gradient, is a constant, is the Lipschitz constant, is an undirected communication topology subgraph The Laplace matrix of is the total number of agents in all clusters, for dimensional identity matrix, W is the weighted adjacency matrix, and the elements of matrix W satisfy It turns out that the matrix is a diagonal matrix with diagonal elements , from the undirected communication topology graph is connected and Gershgor i The n-disk theorem yields the matrix is a Schur matrix, there exists a symmetric positive definite matrix Make .

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