Search Method for Designated Time of Equilibrium of Intra-Group Unrelated Multi-Cluster Resource Allocation Game

Abstract

The present invention discloses a method for searching for the equilibrium of intra-group uncorrelated multi-cluster resource allocation within a specified time, belonging to the technical field of multi-agent game decision-making. First, for the situation where the individual interests of agents in a multi-cluster system do not depend on the states of agents in the same coalition, but only on their own states and the states of agents in other coalitions, a game model of intra-group uncorrelated multi-cluster resource allocation under coupled equality resource constraints is constructed for the multi-agent system. Secondly, a communication topology structure is constructed for the multi-agent system. Finally, combined with the time planning method, a search method for the Nash equilibrium of multi-cluster resource allocation with specified-time convergence is designed for each agent. The present invention can achieve the search for the Nash equilibrium of the intra-group uncorrelated multi-cluster resource allocation problem within a specified time for the case of coupled equality resource constraints and the individual interests of agents not depending on the states of other agents in the same coalition, providing a basis for distributed resource scheduling in complex cooperative-competitive environments.

Description

Technical Field

[0001] The present invention belongs to the technical field of multi-agent game decision-making, and in particular relates to a method for searching for the equilibrium of multi-cluster resource allocation with uncorrelated agents within a group at a specified time. 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 rate under limited resource quantities and plays an important role in economic development, cultural construction, green development, etc. In large-scale networked system resource allocation, the system is clustered into multiple clusters that only focus on maximizing the interests of their own groups. Multi-cluster resource allocation can be regarded as a distributed optimization problem in which multiple clusters under resource equation coupling constraints aim to maximize the group's benefits. The group's benefits are usually only related to the decisions of individuals within the cluster. However, in the actual application of multi-cluster resource allocation, due to the complex interactions within 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 interest conflicts 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] In the existing multi-cluster game Nash equilibrium search algorithms, in the literature ( Pang Y, Hu G. Nash equilibrium seeking in N - coalition games via a gradient - free method[J]. Automatica, 2022, 136: 110013. ), for the case where only local objective functions can be obtained, a gradient-free discrete-time algorithm is proposed based on Gaussian smoothing. Under this algorithm, all agents converge to the smallest neighborhood of the Nash equilibrium at a geometric rate. The limitation of this scheme is that it is not applicable to the case with constraints and can only linearly converge to the neighborhood of the Nash equilibrium. In the literature ( 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 .), a multi-cluster game Nash equilibrium search algorithm under consistency constraints is studied. A discrete-time algorithm is designed based on gradient tracking and projection method in the scenario of partial decision information. However, this algorithm is only applicable to undirected topological graphs and can only achieve linear convergence and cannot achieve specified-time convergence. In the literature ( Zhou J, Lv Y, Wen G, et al. Distributed Nash equilibrium seeking in consistency - constrained multicoalition games[J]. IEEE Transactions on Cybernetics, 2022. ), a multi-cluster game satisfying consistency constraints under a directed topological graph is further studied, and a discrete-time algorithm is designed using techniques such as leader-follower consistency and pseudo-gradient descent. However, this scheme can also only achieve linear convergence. The above-mentioned schemes can only achieve linear convergence and cannot achieve specified-time convergence. Therefore, the existing technologies are not applicable to practical applications with specified convergence time requirements. Summary of the Invention

[0004] The object of the present invention is to provide a method for searching for the equilibrium of a multi-cluster resource allocation game that is uncorrelated within a group. For multiple clusters subject to resource equality coupling constraints and aiming to minimize the group cost function, considering the case where the input of the cost function of an agent in a multi-cluster is independent of the decisions of other agents in the same cluster and only includes its local decision and the decisions of agents in other clusters, a multi-coalition game model for multi-cluster resource allocation is established, and a fast solution method for the equilibrium of the multi-coalition game at a specified time is provided, providing a solution idea for the multi-cluster resource allocation problem from the perspective of coalition game.

[0005] To achieve the above object, the present invention provides a method for searching for the equilibrium of a multi-cluster resource allocation game that is uncorrelated within a group, including the following steps:

[0006] Step 1: For the case where the individual interests of agents in a multi-cluster system do not depend on the states of agents in the coalition they belong to and are only related to their own states and the states of agents in other coalitions, construct a multi-cluster resource allocation game model that is uncorrelated within a group under coupled equality resource constraints for the multi-agent system;

[0007] Step 2: Construct a communication topology structure for the multi-agent system;

[0008] Step 3: Combining the time planning method, design a method for searching for the Nash equilibrium of the multi-cluster resource allocation game with specified-time convergence for each agent. The specific process is as follows:

[0009] S31: Using the variable substitution method, convert the problem of solving the Nash equilibrium under equality constraints into the problem of solving the Nash equilibrium without constraints;

[0010] S32: Combining the time planning method, each agent estimates the state information of all agents based on leader-follower consensus;

[0011] S33: Combining the time planning method, the agent performs state iteration on the substituted variables based on pseudo-gradient descent and auxiliary variables of the estimated state information.

[0012] Preferably, in Step 1, for the case where the individual interests of agents in a multi-cluster system do not depend on the states of agents in the coalition they belong to and are only related to their own states and the states of agents in other coalitions, constructing a multi-cluster resource allocation game model that is uncorrelated within a group under coupled equality resource constraints for the multi-agent system is specifically as follows:

[0013]

[0014] Among them, the number represents the cluster in the N clusters participating in the game, and the number represents including agents in the cluster the th agent, representing the set of agents in the cluster ; denoting the set of all agents, being the state of the agent ; representing the joint state of the cluster ; denoting the joint state of all clusters, being the total number of agents in all clusters, representing the joint state of all other clusters excluding the cluster ; and respectively represent the local resources owned by the agent and the resources owned by the cluster ; the state of the cluster satisfies the constraint, and the constraint is specifically , the continuously differentiable convex function and are respectively the cost functions of the agent and the cluster ; the functions and have Lipschitz continuous gradients, specifically: , there is and , where is the Li psch it z constant, .

[0015] Preferably, the construction of the communication topology for the multi-agent system in step 2 is specifically as follows: Model the communication topology among all the agents participating in the game as an undirected communication topology graph , where represents the set of nodes, represents the set of edges. If the agent receives the information of the agent , then , and is the 's neighbor. Since the communication topology is undirected, if , then . The communication topology within the cluster is represented by an undirected communication topology subgraph ; represents the set of agents in the cluster , and the set of edges is . The agent Neighbor set representation in the network , with an in-degree of , the agent in the cluster The neighbor set representation is , with an in-degree of , define the adjacency matrix of the undirected communication topology graph as , where represents the element in the th row and th column of matrix A. All diagonal elements of matrix A , if , non-diagonal elements , otherwise , define the adjacency matrix of the undirected communication topology subgraph as , where represents the element in the th row and th column of matrix , define the Laplacian matrix of the undirected communication topology subgraph as , where represents the element in the th row and th column of matrix , diagonal elements , non-diagonal elements , where , define the weighted adjacency matrix of the undirected communication topology graph as , where represents the element in the th row and th column of matrix W. All diagonal elements of matrix W , if , non-diagonal elements , otherwise , the elements of matrix W satisfy .

[0016] Preferably, both the undirected communication topology graph and the undirected communication topology subgraph are connected, where represents the set of N game clusters.

[0017] Preferably, in S31, using the variable substitution method, the expression for converting the problem of solving the Nash equilibrium under equality constraints into the problem of solving the Nash equilibrium under unconstrained conditions is as follows:

[0018]

[0019] Among them, represents the state of the agent at moment, and its initial value , represents the auxiliary variable after variable substitution of the state of the agent at moment. is the auxiliary variable after variable substitution of the state of the agent at moment, and its initial value , represents the neighbor set of the agent in the cluster . represents the th sampling moment, which is represented by the sampling interval sequence as:

[0020]

[0021] Among them, the sampling interval sequence is designed as:

[0022]

[0023] In the formula, is the preset specified time, is a convergent infinite series sequence, where , is finite, represents the th sampling interval, represents the set of positive integers, represents the th term of the convergent infinite series sequence, represents the th term of the convergent infinite series sequence.

[0024] Preferably, in S32, combined with the time planning method, the specific expression for each agent to estimate the state information of all agents based on leader-follower consistency is as follows:

[0025]

[0026] Among them, is the auxiliary variable used by the agent to estimate the state of the agent at moment, represents the agent used to estimate the state of the agent Moment state The derivative of the auxiliary variable, represents the agent used to estimate the agent at moment state The auxiliary variable, represents the element in the th row and th column of the weighted adjacency matrix W, is the element in the th row and th column of the weighted adjacency matrix W. The elements of the weighted adjacency matrix satisfy , and the specific selection method is:

[0027]

[0028] Among them, is a constant, is the element in the th row and th column of the adjacency matrix A, is the in-degree of the agent : .

[0029] Preferably, in S33, combined with the time planning method, the specific expression for the agent to perform state iteration on the replaced variable based on the pseudo-gradient descent and the auxiliary variable of the estimated state information is as follows:

[0030]

[0031] Among them, is a positive constant to be designed, is the neighbor set of the agent in the cluster , represents the agent used to estimate the agent state The auxiliary variable, represents the agent used to estimate the agent state The auxiliary variable, represents the agent at moment for the state estimation of the agents in other clusters except the cluster , represents the agent at moment for the state estimation of the agents in other clusters except the cluster , represents the agent For the state of , in the non - related multi - cluster resource allocation game within the group, the cost function of each agent is only determined by its own state and the states of agents in other clusters. There is an equation for the pseudo - gradient of each cluster:

[0032]

[0033] where, is the cost function of cluster , that is, the sum of the cost functions of all agents in cluster . represents the states of all agents, represents the states of all other agents excluding the agents in cluster , represents the state of agent , represents the cost function of agent in cluster .

[0034] Preferably, the Nash equilibrium search method for the multi - cluster resource allocation game with specified - time convergence designed in step 3 satisfies the pre - condition and parameter condition.

[0035] Preferably, the pre - condition is specifically: it is required that the pseudo - gradient function is strictly monotonic, and there exists a positive constant such that .

[0036] Preferably, the parameter condition is specifically:

[0037]

[0038] where,

[0039]

[0040]

[0041]

[0042]

[0043]

[0044] In the formula, represents the pseudo - gradient strict monotonic constant, is a constant, is the Lipschitz constant, is the Laplacian matrix of the undirected communication topology sub - graph , is the total number of agents for all clusters, is the - dimensional identity matrix, W is the weight adjacency matrix, and the elements of matrix W satisfy obtained. Matrix is a diagonal matrix, and its diagonal elements are , from the undirected communication topology graph is connected and Gershgor i n - disk theorem, it is concluded that matrix is a Schur matrix, and there exists a symmetric positive - definite matrix such that .

[0045] Therefore, the present invention adopts the above - mentioned method for searching the equilibrium at a specified time for the intra - group uncorrelated multi - cluster resource allocation game, and has the following beneficial effects:

[0046] (1) Aiming at the situation where there are interest conflicts among different cluster agents, the present invention considers the Nash equilibrium search method for the intra - group uncorrelated multi - cluster resource allocation game subject to coupled equality constraints, providing a solution idea for the multi - cluster resource allocation problem with complex cooperation - competition relationships;

[0047] (2) In the search process of solving the Nash equilibrium, the resource equality coupling constraint within the cluster always holds, enabling this method to be executed online, providing a solution idea for the multi - cluster resource allocation problem that needs to satisfy the resource supply - demand balance in real time;

[0048] (3) Compared with finite - time convergence and fixed - time convergence, the method proposed by the present invention can achieve the solution of the Nash equilibrium at a specified time, and the specified convergence time is independent of the initial value and method parameters, facilitating the pre - determination of the convergence time according to actual needs.

[0049] The technical solution of the present invention will be further described in detail below through the accompanying drawings and embodiments. Brief Description of the Drawings

[0050] Figure 1 is a schematic diagram of the steps of the method for searching the equilibrium at a specified time for the intra - group uncorrelated multi - cluster resource allocation game of the present invention;

[0051] Figure 2 is a schematic diagram of the specific process of the method for searching the equilibrium at a specified time for the intra - group uncorrelated multi - cluster resource allocation game of the present invention;

[0052] Figure 3 is the communication topology structure diagram of the multi - agent system provided by the embodiment of the present invention;

[0053] Figure 4 is the evolution diagram of the states of each agent converging to the equilibrium at the specified time of 1 s provided by the embodiment of the present invention;

[0054] Figure 5 is the evolution graph in which the cost functions of each cluster converge to the optimal at the specified time of 1 s provided by the embodiment of the present invention;

[0055] Figure 6 is the graph of the change in the total resources of each cluster during the equilibrium search process provided by the embodiment of the present invention. Detailed implementation manners

[0056] The following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present invention without creative efforts shall fall within the scope of protection of the present invention.

[0057] Please refer to Figures 1 - 6 , the method for searching for the equilibrium at the specified time of the resource allocation game for uncorrelated multi-clusters within a group, comprising the following steps:

[0058] Step 1. For the case where the individual interests of the agents in the multi-cluster system do not depend on the states of the agents in the coalition where they are located, but only on their own states and the states of the agents in other coalitions, construct a resource allocation game model for uncorrelated multi-clusters within a group under the coupled equality resource constraints for the multi-agent system; specifically:

[0059]

[0060] Among them, the number represents the cluster in the N clusters participating in the game, represents the -th agent in the cluster containing agents, represents the set of agents in the cluster , represents the set of all agents, is the state of the agent , represents the joint state of the cluster , represents the joint state of all clusters, is the total number of agents in all clusters, represents the joint state of all other clusters excluding the cluster , and respectively represent the local resources owned by the agent and the resources owned by the cluster , and the cluster The state satisfies the constraints, specifically , a continuously differentiable convex function and are the cost functions of the agent and the cluster respectively. The functions and have Lipschitz continuous gradients, specifically: , there is and , where is Li psch it z constant, .

[0061] Step 2: Construct a communication topology for the multi-agent system; specifically: Model the communication topology among all the agents participating in the game as an undirected communication topology graph , where represents the node set, represents the edge set. If the agent receives the information of the agent , then , and is 's neighbor. Since the communication topology is undirected, if , then , the communication topology within the cluster i is represented by an undirected communication topology subgraph . represents the in the cluster agent set, the edge set is . The neighbor set of the agent in the network is represented as , and the in-degree is . The neighbor set of the agent in the cluster is represented as , and the in-degree is . Define the adjacency matrix of the undirected communication topology graph as , where represents the element in the th row and th column of the matrix A. All diagonal elements of the matrix A . If , the non-diagonal elements , otherwise . Define the adjacency matrix of the undirected communication topology subgraph as , where Denote the matrix The element in the th row and th column defines the Laplacian matrix of the undirected communication topology subgraph , where denotes the matrix The element in the th row and th column, the diagonal element , where , define the weighted adjacency matrix of the undirected communication topology graph as , where denotes the element in the th row and th column of the matrix W. All diagonal elements of the matrix W . If , the off - diagonal element , otherwise . The elements of the matrix W satisfy . Among them, the undirected communication topology graph and the undirected communication topology subgraph are both connected, where represents the set of N game clusters.

[0062] Step 3: Combine the time - planning method to design a multi - cluster resource allocation game Nash equilibrium search method with specified - time convergence for each agent. The specific process is as follows:

[0063] S31: Use the variable substitution method to convert the Nash equilibrium solving problem under equality constraints into an unconstrained Nash equilibrium solving problem. The specific expression is as follows:

[0064]

[0065] where represents the state of agent at time , and its initial value . represents the auxiliary variable after variable substitution for the state of agent at time . is the auxiliary variable after variable substitution for the state of agent at time , and its initial value . represents the neighbor set of agent in cluster . Indicates the th sampling time, represented by the sampling interval sequence as:

[0066]

[0067] where the sampling interval sequence is designed as:

[0068]

[0069] In the formula, is a preset specified time, is a convergent infinite series sequence, where , is finite, Indicates the th sampling interval, represents the set of positive integers, represents the th term of the convergent infinite series sequence, represents the th term of the convergent infinite series sequence.

[0070] S32. Combining with the time planning method, each agent estimates the state information of all agents based on leader-following consistency; the specific expression is as follows:

[0071]

[0072] where, is the auxiliary variable for agent to estimate the state of agent at time , represents the derivative of the auxiliary variable for agent to estimate the state of agent at time , represents the auxiliary variable for agent to estimate the state of agent at time , represents the element in the th row and th column of the weight adjacency matrix W, is the element in the th row and th column of the weight adjacency matrix W. The elements of the weight adjacency matrix satisfy , and the specific selection method is:

[0073]

[0074] Among them, is a constant, is the element in the th row and th column of the adjacency matrix A, is the in-degree of the agent : .

[0075] S33. Combining with the time planning method, the agent performs state iteration on the replaced variables based on the pseudo-gradient descent and the auxiliary variables of the estimated state information. The specific expression is as follows:

[0076]

[0077] Among them, is a positive constant to be designed, is the neighbor set of the agent in the cluster , represents the auxiliary variable used by the agent to estimate the state of the agent , represents the auxiliary variable used by the agent to estimate the state of the agent , represents the state estimation of the agents in other clusters except the cluster by the agent at the moment , represents the state estimation of the agents in other clusters except the cluster by the agent at the moment , represents the state of the agent . For the intra-group uncorrelated multi-cluster resource allocation game, the cost function of each agent is only determined by its own state and the states of the agents in other clusters. There is an equation for the pseudo-gradient of each cluster:

[0078]

[0079] Among them, is the cost function of the cluster , that is, the sum of the cost functions of all agents in the cluster , represents the states of all agents, represents the states of all other agents except the agents in the cluster . Represents the state of the agent , Represents the cost function of the agents in the cluster .

[0080] In addition, the Nash equilibrium search method for the multi-cluster resource allocation game with specified-time convergence designed in Step 3 satisfies the prerequisite conditions and parameter conditions; where the prerequisite conditions are specifically: it is required that the pseudo-gradient function is strictly monotonic, and there exists a positive constant such that ; the parameter conditions are specifically:

[0081]

[0082] Among them,

[0083]

[0084]

[0085]

[0086]

[0087]

[0088] Among them, represents the pseudo-gradient strict monotonic constant, is a constant, is the Lipschitz constant, is the Laplacian matrix of the undirected communication topology subgraph , is the total number of agents in all clusters, is dimensional identity matrix, W is the weight adjacency matrix, and the elements of matrix W satisfy obtained, matrix is a diagonal matrix, and its diagonal elements are , from the undirected communication topology graph is connected and Gershgor i n disk theorem, it is concluded that matrix is a Schur matrix, and there exists a symmetric positive definite matrix such that .

[0089] Example

[0090] Step 1: Consider N = 3, each containing , , A cluster of agents, with the resource amounts of each cluster being , and respectively. The cost function of agent is , and the correlation coefficients are: , , , , , , , , , , , , , , , , , , , , , , , , .

[0091] Step 2: The communication topology of the multi-agent system is as Figure 3 shown.

[0092] Step 3: For the designed method of searching for the time-convergent Nash equilibrium in the intra-group uncorrelated multi-cluster resource allocation game, the initial node state is selected as .

[0093] Step 4: The method parameters are designed as . It is specified that the states of all cluster agents converge to the Nash equilibrium in 1 second. Its state convergence curve is as Figure 4 shown, the cost function convergence curves of the three clusters are as Figure 5 shown, and the total resources of the clusters are as Figure 6 shown. The simulation results show that the states of each agent and the costs of each cluster converge to the Nash equilibrium at 1 second:

[0094] ,

[0095] ,

[0096] and the resources of each cluster remain unchanged throughout the equilibrium search process, and the supply-demand balance is always satisfied

[0097] Therefore, the present invention adopts the above-mentioned method for searching for the equilibrium of the specified time of the uncorrelated multi-cluster resource allocation within the group. For multiple clusters that are constrained by resource equality coupling and aim to minimize the group cost function, considering the situation where the input of the cost function of the agents in the multi-cluster is independent of the decisions of other agents in the same cluster and only includes their local decisions and the decisions of the agents in other clusters, a multi-coalition game model is established for the multi-cluster resource allocation, providing a fast solution method for the specified time to study the equilibrium of the multi-coalition game, and providing a solution idea for the multi-cluster resource allocation problem from the perspective of the coalition game.

[0098] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify or equivalently replace the technical solutions of the present invention, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for searching for the equilibrium of the intra-group uncorrelated multi-cluster resource allocation game at a specified time, characterized in that, It includes the following steps: Step 1: For the case where the individual interests of agents in a multi-cluster system do not depend on the states of agents in the coalition they belong to, but only on their own states and the states of agents in other coalitions, construct an intra-group uncorrelated multi-cluster resource allocation game model for the multi-agent system under coupled equality resource constraints; Step 2: Construct a communication topology structure for the multi-agent system; Step 3: Combine the time planning method to design a multi-cluster resource allocation game Nash equilibrium search method that converges at a specified time for each agent. The specific process is as follows: S31: Use the variable substitution method to transform the Nash equilibrium solution problem under equality constraints into a Nash equilibrium solution problem without constraints; S32: Combine the time planning method, and each agent estimates the state information of all agents based on leader-follower consensus; S33: Combine the time planning method, and the agent performs state iteration on the substituted variables based on pseudo-gradient descent and the auxiliary variables of the estimated state information.

2. The method for searching the specified time of the game equilibrium of the uncorrelated multi-cluster resource allocation within the group according to claim 1, wherein: In Step 1, for the case where the individual interests of agents in a multi-cluster system do not depend on the states of agents in the coalition they belong to, but only on their own states and the states of agents in other coalitions, the specific construction of the intra-group uncorrelated multi-cluster resource allocation game model for the multi-agent system under coupled equality resource constraints is as follows: ； Among them, the number represents the cluster among N clusters participating in the game , the number represents the -agent cluster the th agent in , represents the set of agents in cluster , represents the set of all agents, is the state of agent , represents the joint state of cluster , represents the joint state of all clusters, is the total number of agents in all clusters, represents the joint state of all other clusters excluding cluster , and respectively represent the local resources owned by agent and the resources owned by cluster . The state of cluster satisfies the constraint, and the constraint is specifically , the continuously differentiable convex functions and are the cost functions of agent and cluster respectively. The functions and have Lipschitz continuous gradients, specifically: , there is and , where is the Li psch it z constant, .​​​​​​​​​​​​​​​​​​​​​​​​​ 3. The method for searching for the specified time of the in-group uncorrelated multi-cluster resource allocation game equilibrium according to claim 2, characterized in that In step 2, the construction of the communication topology for the multi-agent system is specifically as follows: The communication topology among all the agents participating in the game is modeled as an undirected communication topology graph where represents the node set, represents the edge set. If agent receives information from agent , then , and is 's neighbor. Since the communication topology is undirected, if , then . The communication topology within the cluster is represented by the undirected communication topology subgraph . represents the set of agents in the cluster . The edge set is . The neighbor set of agent in the network is represented as , and the in-degree is . The neighbor set of agent in the cluster is represented as , and the in-degree is . The adjacency matrix of the undirected communication topology graph is defined as , where represents the element in the -th row and -th column of matrix A. All the diagonal elements of matrix A . If , the non-diagonal element , otherwise . The adjacency matrix of the undirected communication topology subgraph is defined as , where represents the element in the -th row and -th column of matrix . The Laplacian matrix of the undirected communication topology subgraph is defined as , where represents the element in the -th row and -th column of matrix . The diagonal element , and the non-diagonal element , where . The weighted adjacency matrix of the undirected communication topology graph is defined as , where Denote the element at the -th row and -th column of matrix W. All diagonal elements of matrix W are . If , the off-diagonal elements are . Otherwise . The elements of matrix W satisfy .

4. The method for searching for the specified time of the in-group uncorrelated multi-cluster resource allocation game equilibrium according to claim 3, characterized in that: Undirected communication topology graph and undirected communication topology sub-graph are both connected, where represents the set of N game clusters.

5. The method for searching the specified time of the game equilibrium of the intra-group uncorrelated multi-cluster resource allocation according to claim 4, characterized in that In S31, the expression for using the variable substitution method to transform the Nash equilibrium solution problem under equality constraints into a Nash equilibrium solution problem without constraints is as follows: ； Among them, represents the state of the agent at moment, and its initial value , represents the auxiliary variable after variable substitution for the state of the agent at moment. is the auxiliary variable after variable substitution for the state of the agent at moment, and its initial value , represents the neighbor set of the agent in the cluster . represents the th sampling moment, which is represented by the sampling interval sequence as: ； where the sampling interval sequence is designed as: ； wherein, is a preset specified time, is a convergent infinite series sequence, where , is finite, represents the th sampling interval, represents the set of positive integers, represents the th term of the convergent infinite series sequence, represents the th term of the convergent infinite series sequence.

6. The method for searching for the specified time of the in-group uncorrelated multi-cluster resource allocation game equilibrium according to claim 5, characterized in that: In S32, the specific expression for each agent to estimate the state information of all agents based on leader-follower consensus by combining the time planning method is as follows: ； Among them, is the agent used to estimate the state of the agent at time, which is an auxiliary variable, representing the agent used to estimate the derivative of the auxiliary variable of the state of the agent at time, which is an auxiliary variable derivative, representing the agent used to estimate the state of the agent at time, which is an auxiliary variable, representing the state of the agent at time, representing the element in the -th row and -th column of the weighted adjacency matrix W, is the element in the -th row and -th column of the weighted adjacency matrix W. The elements of the weighted adjacency matrix satisfy , and the specific selection method is as follows: ； Among them, is a constant, is the element of the th row and th column of the adjacency matrix A, is the in-degree of the agent : .

7. The method for searching the specified time of the intra-group uncorrelated multi-cluster resource allocation game equilibrium according to claim 6, characterized in that: In S33, the specific expression for the agent to perform state iteration on the substituted variables based on pseudo-gradient descent and the auxiliary variables of the estimated state information by combining the time planning method is as follows: ； Among them, is a positive constant to be designed, is the agent in the cluster in the neighbor set, represents the agent used to estimate the state of the agent state auxiliary variable, represents the agent used to estimate the state of the agent state auxiliary variable, represents the agent at time for the state estimation of agents in other clusters except the cluster outside, represents the agent at time for the state estimation of agents in other clusters except the cluster outside, represents the state of the agent For the non - cooperative multi - cluster resource allocation game within the group, the cost function of each agent is only determined by its own state and the states of agents in other clusters. There is an equation for the pseudo - gradient of each cluster: ； Among them, is the cost function of the cluster , that is, the sum of the cost functions of all agents in the cluster . represents the states of all agents, represents all other agent states excluding the agents in the cluster . represents the state of agent , represents the cluster in which the agent has a cost function.

8. The method for searching for the specified time of the game equilibrium of the intra-group uncorrelated multi-cluster resource allocation according to claim 7, characterized in that: The Nash equilibrium search method for the multi-cluster resource allocation game designed in Step 3 satisfies the prerequisite conditions and parameter conditions; The prerequisite conditions are specifically as follows: It is required that the pseudo-gradient function is strictly monotonic, and there exists a positive constant such that ; The parameter conditions are specifically: ； where, ； ； ； ； ； wherein, represents a pseudo-gradient strictly monotonic constant, is a constant, is a Lipschitz constant, is the Laplacian matrix of the undirected communication topology subgraph . is the total number of agents in all clusters, is dimensional identity matrix, W is the weight adjacency matrix, and the elements of matrix W satisfy obtained. Matrix is a diagonal matrix, and its diagonal elements are , and from the undirected communication topology graph is connected and Gershgor i n disk theorem, it is concluded that matrix is a Schur matrix, and there exists a symmetric positive definite matrix such that .

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