Searching method aiming at intra-cluster cross-correlation group resource scheduling game balance specified time

Abstract

The invention discloses an intra-cluster cross-correlation group resource scheduling game equilibrium specified time search method, and belongs to the technical field of multi-agent game decision making. Constructing an intra-cluster cross-correlation group resource scheduling game problem model under coupling equality resource constraint for the multi-agent system; secondly, constructing a communication topological structure for the multi-agent system; finally, in combination with a time planning method, designing an intra-cluster cross-correlation group resource scheduling game Nash equilibrium search method with specified time convergence for each agent; according to the method, the specified time convergence Nash equilibrium search of the intra-cluster cross-correlation group resource scheduling game problem can be realized aiming at the condition that coupling equality resource constraints and the individual interests of the agents are related to decision-making of other agents in all groups, and a basis is provided for distributed group resource scheduling in which complex cooperative competition relationships coexist.

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 a time-specified equilibrium in a game of resource scheduling for mutually related groups within a cluster. Background Art

[0002] With the development of swarm intelligence technology, distributed resource scheduling has become a hot research direction. The optimal scheduling decision is achieved through local information interaction, thereby improving resource utilization efficiency and reducing resource scheduling costs. In a networked cluster system, the entire network system is clustered into a single-group networked system that is fully cooperative and aims to maximize group benefits. However, in the resource scheduling of large-scale networked systems, the individual role relationship is complex and cooperative and competitive relationships coexist. This is reflected in the fact that the local benefits of each individual depend not only on its local decision, but also on the decisions of other related individuals and other groups in the cluster. There are not only cooperative relationships within the group, but also competitive relationships between groups. In this context, the single-group distributed resource scheduling method for full cooperation is no longer applicable. Therefore, it is necessary to establish a group resource scheduling game model that can characterize the intra-group cooperation and inter-group competition relationships and meet the balance of resource scheduling supply and demand, and to conduct research on its Nash equilibrium search method.

[0003] Among the existing group game Nash equilibrium algorithms, the literature ( Ye M, Hu G, Lewis F L. Nash equilibrium seeking for N-coalition noncooperative games[J]. Automatica, 2018, 95: 266-272. ) constructed an N-group non-cooperative game, used the dynamic average consensus protocol to estimate the average gradient of the group objective function, and used the estimated gradient information and gradient descent method to achieve exponential convergence of Nash equilibrium search. The limitation of this scheme is that the designed equilibrium search algorithm is only applicable to unconstrained group games. 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. ) further studied the discrete time algorithm for searching Nash equilibrium in group non-cooperative games under consistency constraints, and designed an equilibrium search algorithm for partial decision information scenarios using gradient tracking and projection methods. However, this algorithm can only achieve linear convergence and cannot achieve convergence in a specified time. The existing group game Nash equilibrium search algorithm 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 method for searching for a designated time equilibrium of a resource scheduling game of mutually related groups within a cluster, so as to solve the problem in the prior art that the Nash equilibrium of a multi-group resource scheduling game of intra-group cooperation and inter-group competition is difficult to converge within a designated time.

[0005] To achieve the above object, the present invention provides a method for searching for a designated time for a resource scheduling game equilibrium of a mutually related group within a cluster, comprising the following steps: Step 1: For the situation where the individual interests of each agent in the multi-agent system are related to the decisions of other agents in the cluster and other agents outside the cluster, a cluster-interrelated group resource scheduling game model under the coupled equality resource constraint 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 Nash equilibrium search method for cluster-interrelated group resource scheduling game with a specified time convergence is designed for each agent. The specific process is as follows: S31. Use variable substitution to transform the original problem under coupled equality constraints into an unconstrained dual problem; S32, in combination with the time planning method, each agent estimates the state information of other agents based on the leader-follower consistency, and uses the estimated state information to further estimate the gradient information based on gradient tracking; S33. Combined with the time planning problem, each agent uses the estimated gradient information and performs state updates of the auxiliary variables of the dual problem based on pseudo-gradient descent.

[0006] Preferably, in step 1, for the situation where the individual interests of each agent in the multi-agent system are related to the decisions of other agents in the cluster and other agents outside the cluster, a cluster-interrelated group resource scheduling game problem model under the coupled equation resource constraint is constructed for the multi-agent system as follows: ; Among them, number Represents a group among the N groups participating in the game ,serial number Indicates that it contains Groups of agents Middle j An intelligent agent, Indicates group The set of intelligent entities, represents the set of all agents, For intelligent agents status, Indicates group The joint state represents the joint state of all groups, is the total number of agents in all groups, and Respectively represent intelligent agents Owned local resources and groups Owned resources, groups The state satisfies the constraints, which are , a continuously differentiable convex function and Agent and Groups The cost function, function and have Li psch it z continuous gradient: ,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 an edge set. If agent pq receives agent information, then ,and is the neighbor of pq. Since the communication topology is undirected, if ,but , Group The internal communication topology uses an undirected communication topology subgraph express, Indicates group In The set of agents and the set of edges is , Agent Neighborhood set representation in the network , the in-degree is , Agent In Group 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 , the specific selection method is: ,in, is a constant, defining an undirected communication topology subgraph The corresponding doubly random matrix ,like ,but ,otherwise ,matrix The elements are selected as follows: diagonal elements , off-diagonal elements .

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

[0009] Preferably, the specific expression of converting the original problem under the coupled equality constraint into the unconstrained dual problem by using variable substitution in S31 is as follows: ; in, Representing an Agent exist t The state at the moment, its initial value , It is for intelligent agents exist The state at the moment is replaced by an auxiliary variable, and its initial value is , Represents the agent exist The auxiliary variable after the variable replacement of the state at the moment, Representing an Agent In Group 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, that is 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 state information of other agents based on the leader-follower consistency, and uses the estimated state information to further estimate the gradient information based on gradient tracking. The specific expression is as follows: ; In the formula, For intelligent agents Used to estimate the agent pq in Status of the moment Auxiliary variables, Representing an Agent Used to estimate the agent pq in t Status at all times The derivative of the auxiliary variable, Representing an Agent Used to estimate the agent pq in Status at all times Auxiliary variables, Indicates that the agent pq is The state of the moment, Representing an Agent To other agents t The state estimate at time Represents a cluster Meso Agent j The cost function of Representing an Agent status, is the estimate of agent im at time t Auxiliary variables, for The derivative of For intelligent agents Estimate at time t Auxiliary variables whose initial value is , is the weighted adjacency matrix W Line The elements of the column, is a doubly random matrix No. j Line Elements of a column.

[0011] Preferably, in S33, in combination with the time planning problem, each agent uses estimated gradient information and performs state update of auxiliary variables of the dual problem based on pseudo gradient descent. The specific expression is as follows: ; in, is a positive constant to be designed, It is for intelligent agents Auxiliary variable derivatives of the dual problem after variable substitution The value of the moment, For intelligent agents estimate At sampling time Auxiliary variables, is the estimate of agent ij at time t Auxiliary variables, For intelligent agents In Group The set of neighbors in .

[0012] Preferably, in step 3, the Nash equilibrium search method for the intra-cluster mutual correlation group resource scheduling game that converges within a specified time is designed to meet 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, is the coefficient of the strictly monotonic condition for pseudo gradient, is a constant, and is the Lipschitz constant, N is the number of groups, For Group The number of agents, for dimensional identity matrix, is the total number of agents in all groups, is an undirected communication topology subgraph The corresponding Laplacian matrix is, ,in Representation Matrix No. j OK, , for dimensional identity matrix, ,in Representation topology The corresponding doubly random matrix, Indicates that all elements are 1 dimensional column vector, consisting of an undirected topological subgraph It is known that it is connected. , ,matrix is a Schur matrix, there exists a symmetric positive definite matrix Make , W is the weighted adjacency matrix, and the elements of matrix W satisfy It can be seen that the matrix Elements , from the undirected topological 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 method for searching for a designated time for resource scheduling game equilibrium of mutually related groups within a cluster, which has the following beneficial effects: (1) The present invention aims at solving the problem of resource scheduling in which clusters are divided into multiple groups and there are complex cooperative and competitive relationships. Considering that the objective function of each individual is related to both other individuals in the cluster and individuals in other groups, a new multi-coalition game is established under the background of satisfying the resource constraints of the coupling equation. (2) In solving Nash equilibrium, the sampling interval is designed by introducing a convergent infinite series to achieve the solution of Nash equilibrium in a specified time. The convergence time does not depend on the initial action and method parameters. The convergence time can be determined in advance according to actual needs, and the communication cost is greatly reduced. (3) In the process of solving the Nash equilibrium, the resource scheduling balance equation is satisfied in real time, which can adapt to practical applications with real-time search equilibrium requirements.

[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 scheduling of mutually related groups within a cluster according to the present invention; Figure 2 A schematic diagram of a specific process of the method for searching for a time-specific equilibrium for resource scheduling game of mutually related groups within a cluster according to 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 group converges to the optimum at a specified time 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 group 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 Figure 1-6 , a time-specified search method for the game equilibrium of resource scheduling of mutually related groups within a cluster, comprising the following steps: Step 1: For the situation where the individual interests of each agent in the multi-agent system are related to the decisions of other agents in the cluster and other agents outside the cluster, a cluster-interrelated group resource scheduling game model under the coupled equation resource constraint is constructed for the multi-agent system; specifically: ; Among them, number Represents a group among the N groups participating in the game ,serial number Indicates that it contains Groups of agents Middle j An intelligent agent, Indicates group The set of intelligent entities, represents the set of all agents, For intelligent agents status, Indicates group The joint state represents the joint state of all groups, is the total number of agents in all groups, and Respectively represent intelligent agents Owned local resources and groups Owned resources, groups The state satisfies the constraints, which are , a continuously differentiable convex function and Agent and Groups The cost function, function and have Li psch it z continuous gradient: ,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 an edge set. If agent pq receives agent information, then ,and is the neighbor of pq. Since the communication topology is undirected, if ,but , Group i The internal communication topology uses an undirected communication topology subgraph express, Indicates group In The set of agents and the set of edges is , Agent Neighborhood set representation in the network , the in-degree is , Agent In Group 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 , the specific selection method is: ,in, is a constant, defining an undirected communication topology subgraph The corresponding doubly random matrix ,like ,but ,otherwise ,matrix The elements are selected as follows: diagonal elements , off-diagonal elements , where 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 Nash equilibrium search method for cluster-interrelated group resource scheduling game with a specified time convergence is designed for each agent. The specific process is as follows: S31. Use variable substitution to transform the original problem under coupled equality constraints into an unconstrained dual problem. The specific expression is as follows: ; in, Representing an Agent exist t The state at the moment, its initial value , It is for intelligent agents exist The state at the moment is replaced by an auxiliary variable, and its initial value is , Represents the agent exist The auxiliary variable after the variable replacement of the state at the moment, Representing an Agent In Group 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, that is 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 other agents based on the leader-follower consistency, and uses the estimated state information to further estimate the gradient information based on gradient tracking; the specific expression is as follows: ; In the formula, For intelligent agents Used to estimate the agent pq in Status of the moment Auxiliary variables, Representing an Agent Used to estimate the agent pq in t Status at all times The derivative of the auxiliary variable, Representing an Agent Used to estimate the agent pq in Status at all times Auxiliary variables, Indicates that the agent pq is The state of the moment, Representing an Agent To other agents t The state estimate at time Represents a cluster Meso-agent j The cost function of Representing an Agent status, is the estimate of agent im at time t Auxiliary variables, for The derivative of For intelligent agents Estimate at time t Auxiliary variables whose initial value is , is the weighted adjacency matrix W Line The elements of the column, is a doubly random matrix No. j Line Elements of a column.

[0023] S33. Combined with the time planning problem, each agent uses the estimated gradient information and performs state updates of the auxiliary variables of the dual problem based on pseudo-gradient descent; the specific expression is as follows: ; in, is a positive constant to be designed, It is for intelligent agents Auxiliary variable derivatives of the dual problem after variable substitution The value of the moment, For intelligent agents estimate At sampling time Auxiliary variables, For intelligent agents Estimate at time t Auxiliary variables, For intelligent agents In Group The set of neighbors in .

[0024] Among them, the Nash equilibrium search method for cluster-interrelated group resource scheduling game with a specified time convergence meets certain prerequisites and parameter conditions. The prerequisites are as follows: the pseudo gradient function is required is strictly monotonic, and there exists a positive constant Make ; The specific parameter conditions are: ; in, ; ; ; ; In the formula, is the coefficient of the strictly monotonic condition for pseudo gradient, is a constant, and is the Lipschitz constant, N is the number of groups, For Group The number of agents, for dimensional identity matrix, is the total number of agents in all groups, is an undirected communication topology subgraph The corresponding Laplacian matrix is, ,in Representation Matrix No. j OK, , for dimensional identity matrix, ,in Representation topology The corresponding doubly random matrix, Indicates that all elements are 1 dimensional column vector, consisting of an undirected topological subgraph It is known that it is connected. , ,matrix is a Schur matrix, there exists a symmetric positive definite matrix Make , W is the weighted adjacency matrix, and the elements of matrix W satisfy It can be seen that the matrix Elements , from the undirected topological 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 amount of resources in each group is , and, Agent ij The cost function is , correlation coefficient: , , , , , , , , , , , , , , , , , , , , , , , , , , .

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

[0027] Step 3: For the specified time search method of Nash equilibrium of the intra-cluster mutual correlation group resource scheduling game, the initial node state is selected as .

[0028] Step 4: Design method parameters as . It is specified that the states of all groups of 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 each group are as follows Figure 5 As shown in the figure, the total number of resources in each group changes as shown in Figure 6The simulation results show that the state of each agent and the cost of each group converge to the Nash equilibrium in 1 second. , And the resource supply and demand balance of each group is always met.

[0029] Therefore, the present invention adopts the above-mentioned specified time search method for the equilibrium of the intra-cluster mutual-correlation group resource scheduling game, which can describe the complex interaction of intra-group cooperation and inter-group competition in resource scheduling of large-scale networked systems, and can realize the specified time search of the Nash equilibrium of the group resource scheduling game; and the specified time search method of the Nash equilibrium of the intra-cluster mutual-correlation group resource scheduling game can be applied to complex group resource scheduling tasks with online real-time execution requirements, and has broad practical application value.

[0030] 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 time-specific search method for resource scheduling game equilibrium of mutually related groups within a cluster, characterized in that: The following steps are involved: Step 1: For the situation where the individual interests of each agent in the multi-agent system are related to the decisions of other agents in the cluster and other agents outside the cluster, a cluster-interrelated group resource scheduling game model under the coupled equality resource constraint 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 Nash equilibrium search method for cluster-interrelated group resource scheduling game with a specified time convergence is designed for each agent. The specific process is as follows: S31. Use variable substitution to transform the original problem under coupled equality constraints into an unconstrained dual problem; S32, in combination with the time planning method, each agent estimates the state information of other agents based on the leader-follower consistency, and uses the estimated state information to further estimate the gradient information based on gradient tracking; S33. Combined with the time planning problem, each agent uses the estimated gradient information and performs state updates of the auxiliary variables of the dual problem based on pseudo-gradient descent.

2. The method for searching for a designated time for a game equilibrium of resource scheduling for mutually related groups within a cluster according to claim 1, characterized in that: In step 1, for the situation where the individual interests of each agent in the multi-agent system are related to the decisions of other agents in the cluster and other agents outside the cluster, the model of the intra-cluster mutual-correlation group resource scheduling game problem under the coupled equality resource constraint is constructed for the multi-agent system as follows: ； Among them, number Represents a group among the N groups participating in the game ,serial number Indicates that it contains Groups of agents Middle j An intelligent agent, Indicates group The set of intelligent entities, represents the set of all agents, For intelligent agents status, Indicates group The joint state represents the joint state of all groups, is the total number of agents in all groups, and Respectively represent intelligent agents Owned local resources and groups Owned resources, groups The state satisfies the constraints, which are , a continuously differentiable convex function and Agent and Groups The cost function, function and have Li psch it z continuous gradient: ,have and ,in for Li psch it z constant, .

3. The method for searching for a designated time for a game equilibrium of resource scheduling of mutually related groups within a cluster 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 an edge set. If agent pq receives agent information, then ,and is the neighbor of pq. Since the communication topology is undirected, if ,but , Group The internal communication topology uses an undirected communication topology subgraph express, Indicates group In The set of agents and the set of edges are , Agent Neighborhood set representation in the network , the in-degree is , Agent In Group 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 , the specific selection method is: ,in, is a constant, defining an undirected communication topology subgraph The corresponding doubly random matrix ,like ,but ,otherwise ,matrix The elements are selected as follows: diagonal elements , off-diagonal elements .

4. The method for searching for a designated time for a game equilibrium of resource scheduling of mutually related groups within a cluster 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 a game equilibrium of resource scheduling for mutually related groups within a cluster according to claim 4, characterized in that: The specific expression of using variable substitution in S31 to transform the original problem under coupled equality constraints into an unconstrained dual problem is as follows: ； in, Representing an Agent exist t The state at the moment, its initial value , It is for intelligent agents exist The state at the moment is replaced by an auxiliary variable, and its initial value is , Represents the agent exist The auxiliary variable after the variable replacement of the state at the moment, Representing an Agent In Group 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, that is is limited, Indicates The sampling interval, represents the set of positive integers, represents the first j item, represents the first item.

6. The method for searching for a designated time for a game equilibrium of resource scheduling for mutually related groups within a cluster according to claim 5, characterized in that: In S32, combined with the time planning method, each agent estimates the state information of other agents based on the leader-follower consistency, and uses the estimated state information to further estimate the gradient information based on gradient tracking. The specific expression is as follows: ； In the formula, For intelligent agents Used to estimate the agent pq in Status of the moment Auxiliary variables, Representing an Agent Used to estimate the agent pq in t Status at all times The derivative of the auxiliary variable, Representing an Agent Used to estimate the agent pq in Status at all times Auxiliary variables, Indicates that the agent pq is The state of the moment, Representing an Agent To other agents t The state estimate at time Represents a cluster Meso-agent j The cost function of Representing an Agent status, is the estimate of agent im at time t Auxiliary variables, for The derivative of For intelligent agents Estimate at time t Auxiliary variables whose initial value is , is the weighted adjacency matrix W Line The elements of the column, is a doubly random matrix No. j Line m Elements of a column.

7. The method for searching for a designated time for a game equilibrium of resource scheduling for mutually related groups within a cluster according to claim 6, characterized in that: In S33, combined with the time planning problem, each agent uses the estimated gradient information and performs the state update of the auxiliary variables of the dual problem based on pseudo-gradient descent. The specific expression is as follows: ； in, is a positive constant to be designed, It is for intelligent agents Auxiliary variable derivatives of the dual problem after variable substitution The value of the moment, For intelligent agents estimate At sampling time Auxiliary variables, is the estimate of agent ij at time t Auxiliary variables, For intelligent agents In Group The set of neighbors in .

8. The method for searching for a designated time for a game equilibrium of resource scheduling for mutually related groups within a cluster according to claim 7, characterized in that: In step 3, the Nash equilibrium search method for the intra-cluster mutual correlation group resource scheduling game with a specified time convergence is designed to meet the prerequisites and parameter conditions.

9. The method for searching for a designated time for a game equilibrium of resource scheduling for mutually related groups within a cluster 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 a game equilibrium of resource scheduling for mutually related groups within a cluster according to claim 9, characterized in that: The specific parameter conditions are: ; in, ； ； ； ； In the formula, is the coefficient of the strictly monotonic condition for pseudo gradient, is a constant, and is the Lipschitz constant, N is the number of groups, For Group The number of agents, for dimensional identity matrix, is the total number of agents in all groups, is an undirected communication topology subgraph The corresponding Laplacian matrix is, ,in Representation Matrix No. j OK, , for dimensional identity matrix, ,in Representation topology The corresponding doubly random matrix, Indicates that all elements are 1 dimensional column vector, consisting of an undirected topological subgraph It is known that it is connected. , ,matrix is a Schur matrix, there exists a symmetric positive definite matrix Make , W is the weighted adjacency matrix, and the elements of matrix W satisfy It can be seen that the matrix Elements , from the undirected topological 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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