Generalized Nash equilibrium search method and system based on neural network
By employing a neural network-based generalized Nash equilibrium search method, utilizing Lyapunov functions and SHLFNN to approximate nonlinear dynamics, and designing weight update rules and Lagrange multipliers, the high computational complexity and poor stability of existing clustered game solving methods are addressed, enabling rapid convergence and stability of the agent in dynamic environments.
Patent Information
- Application Number
- CN202511683078.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-17
- Publication Date
- 2026-02-17
AI Technical Summary
In existing technologies, the solution methods for clustered games have high computational complexity and large communication overhead when the scale of agents increases. Furthermore, distributed algorithms suffer from slow policy convergence, numerical instability, and poor robustness when dealing with nonlinear dynamics and strongly coupled constraints, especially when the communication topology changes dynamically.
A generalized Nash equilibrium search method based on neural networks is adopted. By constructing Lyapunov functions and Lipshitz constants, the range of adjustment parameters is scientifically determined. A single hidden layer feedforward neural network (SHLFNN) is combined to approximate nonlinear dynamics, a weight update rule is designed, and Lagrange multipliers are introduced to construct an estimator, forming a design-verification closed loop to ensure that the agent can quickly adjust and recover stability in dynamic environments.
It enhances the agent's adaptability in complex environments, ensures that the strategy converges quickly to the global optimum, simplifies the solution process, improves solution efficiency, and can quickly recover stability when faced with external disturbances or changes in internal parameters.
Smart Images
Figure CN121541467A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of distributed control technology, specifically to a generalized Nash equilibrium search method and system based on neural networks. Background Technology
[0002] With the rapid development of artificial intelligence and multi-agent system theory, clustered game theory, as a mathematical model describing the overall optimization achieved by multiple agents through policy interaction in a shared environment, has become a key tool for solving the coordination and control problems of complex systems. Its core challenge lies in the fact that agents need to maximize overall benefits through local decision-making under the condition of satisfying global coupling constraints. Such problems are widely found in fields such as smart grid economic dispatch, unmanned vehicle path planning, and supply chain collaborative optimization.
[0003] However, existing solutions for clustered games mainly fall into two categories: centralized optimization and distributed iterative algorithms. Centralized methods rely on global information aggregation and central node computation, which leads to an exponential increase in computational complexity and communication overhead as the scale of the agent expands. Furthermore, single-point failures can easily cause system paralysis. While distributed algorithms reduce computational burden through local communication, they have significant drawbacks when dealing with nonlinear dynamics and strongly coupled constraints: First, they do not consider the unknown and time-varying nature of the agent's dynamic model, resulting in the inability of control inputs to dynamically adapt to environmental disturbances, leading to slow or even divergent policy convergence. Second, global coupling constraints are usually transformed into unconstrained problems through penalty functions or Lagrange relaxations, but the selection of penalty coefficients lacks theoretical guidance, easily leading to numerical instability or constraint violations. Third, parameter tuning relies on empirical trial and error, lacking theoretical guarantees of convergence, especially when the communication topology changes dynamically, the robustness of the algorithm decreases significantly.
[0004] Therefore, a generalized Nash equilibrium search method and system based on neural networks is developed. Summary of the Invention
[0005] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a generalized Nash equilibrium search method and system based on neural networks. This invention constructs a Lyapunov function through Lyapunov stability theory and, in conjunction with key parameters such as the Lipshitz constant, scientifically determines the range of values for the adjustment parameters. This innovation not only ensures the convergence of the distributed time-varying generalized Nash equilibrium optimization method, but also satisfies mathematical requirements such as global Lipshitz conditions, non-empty closed convexity, and continuous differentiability. Furthermore, by monitoring the agent's policy evolution curve and constraint satisfaction, a design-verification closed loop is formed, ensuring that the optimal state can be continuously maintained during actual operation. Even in the face of external disturbances or changes in internal parameters, it can quickly adjust and recover stability.
[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution: On the one hand, a generalized Nash equilibrium search method based on neural networks, the specific steps of which are as follows:
[0007] Definition and Dynamic Model Construction of Clustering Game Problem: Determine the clustering game system composed of N agents and define the dual integrator dynamic model of the agents; construct the optimization problem containing the aggregation function and local requirements, and clarify the global coupling constraints;
[0008] Perturbation approximation and constraint transformation design: Based on the dual integrator dynamic model, a unit control input based on a single hidden layer feedforward neural network SHLFNN is constructed to approximate unknown nonlinear dynamics and external perturbations, and the weight update rule is designed in two cases.
[0009] Aggregate estimation and optimization method design: Based on the individual behavior data of the agent, an aggregate quantity estimator is constructed to obtain the aggregate variable; combining the control input and the unconstrained optimization results, a distributed generalized Nash equilibrium search method based on neurodynamics is designed.
[0010] Parameter range determination: Based on the convergence conditions of the distributed time-varying generalized Nash equilibrium optimization method and combined with Lyapunov stability theory, the range of values for the adjustment parameters in the optimization method is determined.
[0011] Monitoring and Verification: Monitor the evolution curve of the agent's policy and the constraint satisfaction to verify whether the generalized Nash equilibrium search and global coupling constraint satisfaction are achieved, thus forming a design-verification closed loop.
[0012] Furthermore, in the definition and dynamic model construction of the clustering game problem, the clustering game system is denoted as: ,in, , and These are the set of agents, the policy space, and the cost function set; define the agents. The strategy space is The dual integrator dynamics model includes unknown nonlinear dynamics and external disturbances. The dual integrator dynamics model is as follows: ,in, For the first An intelligent agent. For the first The policy variables of each agent belong to the policy space. elements, for Regarding time The first derivative represents the first... The rate of change of the state variables of each agent For the first Each agent's velocity variable describes... The dynamic characteristics of the rate of change for Regarding time The first derivative represents the first... The rate of change of the velocity variable of each agent For the first Control input for an intelligent agent For unknown nonlinear dynamic terms, This represents the external disturbance term.
[0013] Furthermore, in the definition and dynamic model construction of the aggregation game problem, an optimization problem containing aggregation functions and local requirements is constructed: st ,in, For the first The strategy of an agent In the strategy space Minimize the operation within. For cost function, It is an aggregate function. For local needs; clarify the global coupling constraint characteristics of the clustered game system.
[0014] Furthermore, in the perturbation approximation and constraint transformation design, the unit control input based on the single hidden layer feedforward neural network SHLFNN is: ,in, For the first Each intelligent agent unit controls the input. For the first A speed variable for each agent. For Lagrange multipliers, , For SHLFNN and Approximation output, To adjust the parameters, the SHLFNN weight update rule has two cases: First, when the weights... At that time, the update formula is: ,in, For the first The first intelligent agent unit control input and the first The update rate of the connection weights between hidden layer neurons All are constants. To approximate the error, For the hidden layer The output of each neuron, sign For sign functions; when At that time, the update formula is: First, avoid overfitting by weights; second, introduce Lagrange multipliers. Construct the estimator: ,in, For intelligent agents The corresponding update rate of the Lagrange multipliers, To adjust the parameters, A collection of intelligent agents participating in a clustered game system. For intelligent agents in communication topology With intelligent agents The connection weights of the edges between them respectively intelligent agents and intelligent agents The corresponding Lagrange multipliers.
[0015] Furthermore, in the design of the aggregation estimation and optimization method, the aggregation quantity estimator is constructed as follows: ,in, For intelligent agents The rate of change of the estimated values of the aggregate variables, For intelligent agents Estimates of aggregate variables, For intelligent agents Estimates of aggregate variables.
[0016] Furthermore, in the design of the aggregation estimation and optimization method, the following is combined: Based on the unconstrained optimization results, a distributed generalized Nash equilibrium search method based on neurodynamics is designed: ,in, as auxiliary variables Time derivative, The Laplace matrix of the communication topology. For auxiliary variable vectors, For intelligent agents The gradient of the cost function and the policy update satisfy Furthermore, this distributed time-varying generalized Nash equilibrium optimization method satisfies three conditions: First, right Global Lipsus, secondly Non-empty closed convex and , It is continuously infinitesimally convex, and its communication topology is a strongly connected graph.
[0017] Furthermore, in determining the parameter range, a Lyapunov function is constructed based on Lyapunov stability theory: ,in, It is a Lyapunov function. To determine the equilibrium values of the Lagrange multipliers, and considering three conditions, the parameter range is as follows: , , ,in, for The Lipschitz constant, and the agent policy pass Iteration, asymptotically converges to the unique optimal equilibrium solution of the aggregate game system: ( ),in, For intelligent agents The generalized Nash equilibrium strategy This is a constant term in the cost function. This represents the coupling coefficient in the cost function. This represents the equilibrium value of the aggregated variables.
[0018] On the other hand, a generalized Nash equilibrium search system based on neural networks includes:
[0019] Clustering Game Problem Definition and Dynamic Model Construction Module: Determine the clustering game system composed of N agents and define the dual integrator dynamic model of the agents; construct the optimization problem containing aggregation functions and local requirements, and clarify the global coupling constraints;
[0020] The perturbation approximation and constraint transformation design module is based on the dual integrator dynamic model. It constructs a unit control input based on a single hidden layer feedforward neural network SHLFNN to approximate unknown nonlinear dynamics and external perturbations. The weight update rule is designed in two cases.
[0021] The aggregation estimation and optimization method design module: Based on the individual behavior data of the agent, an aggregation quantity estimator is constructed to obtain the aggregation variable; combining the control input and the unconstrained optimization results, a distributed time-varying generalized Nash equilibrium optimization method based on neurodynamics is designed.
[0022] Parameter range determination module: Based on the convergence conditions of the distributed time-varying generalized Nash equilibrium optimization method and combined with Lyapunov stability theory, the range of values for the adjustment parameters in the optimization method is determined.
[0023] Monitoring and Verification Module: Monitors the agent's policy evolution curve and constraint satisfaction to verify whether generalized Nash equilibrium search and global coupling constraint satisfaction are achieved, forming a design-verification closed loop.
[0024] Compared with existing technologies, this neural network-based generalized Nash equilibrium search method and system have the following advantages:
[0025] I. This invention, by introducing a unit control input mechanism based on SHLFNN (single hidden layer feedforward neural network), approximates the unknown nonlinear dynamic characteristics and external disturbances in the clustered game system, improving its adaptability to complex environments. Furthermore, a weight update rule is designed, employing different update strategies based on the weight size, ensuring both learning efficiency and avoiding overfitting. This enables the agent's strategy to converge quickly and stably to the global optimum. Moreover, by introducing Lagrange multipliers to construct the estimator, the globally coupled constraint optimization problem is transformed into an unconstrained optimization problem, simplifying the solution process and improving efficiency. In addition, the designed distributed time-varying generalized Nash equilibrium optimization method ensures that the agent can work collaboratively under a strongly connected communication topology, quickly reaching the global optimum equilibrium state.
[0026] Second, this invention constructs a Lyapunov function based on Lyapunov stability theory and, combined with key parameters such as the Lipshitz constant, scientifically determines the range of values for the adjustment parameters. This innovation not only ensures the convergence of the distributed time-varying generalized Nash equilibrium optimization method but also satisfies mathematical requirements such as global Lipshitz conditions, non-empty closed convexity, and continuous differentiability. Furthermore, by monitoring the agent's policy evolution curve and constraint satisfaction, a design-verification closed loop is formed, ensuring that the optimal state can be maintained continuously during actual operation. Even in the face of external disturbances or changes in internal parameters, it can quickly adjust and restore stability.
[0027] Other advantages, objectives and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination or study, or may be learned from the practice of the invention. Attached Figure Description
[0028] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.
[0029] Figure 1 The flowchart shows the generalized Nash equilibrium search method based on neural networks.
[0030] Figure 2 This is a framework diagram of a generalized Nash equilibrium search system based on neural networks. Detailed Implementation
[0031] To further illustrate the technical means and effects of the present invention in achieving its intended purpose, the following detailed description of the specific implementation methods, structures, features, and effects of the present invention, in conjunction with the accompanying drawings and preferred embodiments, is provided below.
[0032] Example 1:
[0033] Definition and Dynamic Model Construction of Aggregation Game Problem: In the scenario of distributed energy storage scheduling in a smart grid, an aggregation game system is defined, consisting of 10 distributed energy storage unit agents. The aggregation game system is denoted as: ,in, , and These are the set of agents, the policy space, and the cost function set; define the agents. The strategy space is A dual integrator dynamic model is established for each energy storage unit. The dual integrator dynamic model is as follows: ,in, For the first An intelligent agent. For the first The policy variables of each agent belong to the policy space. elements, for Regarding time The first derivative represents the first... The rate of change of the state variables of each agent For the first Each agent's velocity variable describes... The dynamic characteristics of the rate of change for Regarding time The first derivative represents the first... The rate of change of the velocity variable of each agent For the first Control input for an intelligent agent For unknown nonlinear dynamic terms, The external disturbance term is used; and an optimization problem is constructed with the total energy storage output as the aggregation function and the charging and discharging power demand of each energy storage unit as the local demand: st ,in, For the first The strategy of an agent In the strategy space Minimize the operation within. For cost function, It is an aggregate function. For local demand; clarify the global coupling constraint characteristics of the aggregation game system; clarify the global coupling constraint that the total energy storage output must match the real-time load of the power grid, such as Figure 1 As shown.
[0034] Perturbation Approximation and Constraint Transformation Design: Based on the dual integrator dynamic model, constructing unit control inputs based on a single hidden layer feedforward neural network (SHLFNN): ,in, For the first Each intelligent agent unit controls the input. For the first A speed variable for each agent. For Lagrange multipliers, , For SHLFNN and Approximation output, To adjust parameters and approximate the nonlinear losses during the charging and discharging process of the energy storage unit and the external disturbances caused by grid voltage fluctuations, the weight update rule of SHLFNN is designed according to two cases: First, when the weights... At that time, the update formula is: ,in, For the first The first intelligent agent unit control input and the first The update rate of the connection weights between hidden layer neurons All are constants. To approximate the error, For the hidden layer The output of each neuron, sign For sign functions; when At that time, the update formula is: First, avoid overfitting by weights; second, introduce Lagrange multipliers. Construct the estimator: ,in, For intelligent agents The corresponding update rate of the Lagrange multipliers, To adjust the parameters, A collection of intelligent agents participating in a clustered game system. For intelligent agents in communication topology With intelligent agents The connection weights of the edges between them respectively intelligent agents and intelligent agents The corresponding Lagrange multipliers transform the globally coupled constraint optimization problem of matching total output with load into an unconstrained optimization problem.
[0035] Aggregate estimation and optimization method design: Based on the real-time charging and discharging power data of each energy storage unit, an aggregate quantity estimator is constructed to obtain the estimated value of the total energy storage output. The constructed aggregate quantity estimator is as follows: ,in, For intelligent agents The rate of change of the estimated values of the aggregate variables, For intelligent agents Estimates of aggregate variables, For intelligent agents Estimate the aggregated variables; and combine the unit control inputs with the unconstrained optimization results to design a distributed generalized Nash equilibrium search method based on neurodynamics: ,in, as auxiliary variables Time derivative, The Laplace matrix of the communication topology. For auxiliary variable vectors, For intelligent agents The gradient of the cost function and the policy update satisfy Furthermore, this distributed time-varying generalized Nash equilibrium optimization method satisfies three conditions: First, right Global Lipsus, secondly Non-empty closed convex and , It is continuously infinitesimally convex, and its communication topology is a strongly connected graph.
[0036] Parameter range determination: Based on Lyapunov stability theory, a Lyapunov function is constructed that includes the squares of auxiliary variables, the squares of approximation errors, and the squares of Lagrange multiplier deviations. The Lyapunov function is: ,in, It is a Lyapunov function. Given the equilibrium values of the Lagrange multipliers, and considering three conditions, determine the parameter range: , , ,in, for The Lipschitz constant, and the agent policy pass Iteration, asymptotically converges to the unique optimal equilibrium solution of the aggregate game system: ( ),in, For intelligent agents The generalized Nash equilibrium strategy This is a constant term in the cost function. This represents the coupling coefficient in the cost function. This represents the equilibrium value of the aggregated variables.
[0037] Monitoring and verification: Real-time monitoring of the evolution curves of the charging and discharging power of each energy storage unit and the matching of the total energy storage output with the real-time load of the power grid, verifying whether the generalized Nash equilibrium search and global coupling constraint satisfaction are achieved, forming a closed loop of design and verification.
[0038] In summary, firstly, a clustered game system consisting of 10 distributed energy storage unit agents is established, and a dual integrator dynamic model is built for each unit. Simultaneously, an optimization problem is constructed, including the aggregate function of total energy storage output and the local demand of each unit's charging and discharging power requirements. The global coupling constraint that the total energy storage output must match the real-time load of the power grid is clarified. Next, based on the dual integrator dynamic model, a single hidden-layer feedforward neural network (SHLFNN) is used to construct unit control inputs to approximate nonlinear charging and discharging losses and voltage fluctuation disturbances. The SHLFNN weights are updated according to two rules, and Lagrange multipliers are introduced to transform the global constraint optimization into an unconstrained optimization. Subsequently, an aggregate quantity estimator is constructed based on the real-time data of each unit to obtain the estimated value of the total energy storage output. Combining the control input and the unconstrained optimization results, a distributed generalized Nash equilibrium search method based on neural dynamics is designed. Then, based on Lyapunov stability theory, the range of adjustment parameters is determined, enabling the energy storage power strategy to iteratively converge to the optimal equilibrium solution. Finally, the energy storage power evolution curve and load matching are monitored to form a design-verification closed loop, achieving the generalized Nash equilibrium search and the satisfaction of global coupling constraints.
[0039] Example 2:
[0040] Definition and Dynamic Model Construction of Cluster Game Problem: In the scenario of drone collaborative task allocation, a cluster game system consisting of 8 drone agents is defined, denoted as: ,in, , and These are the set of agents, the policy space, and the cost function set; define the agents. The strategy space is A dual integrator dynamic model is established for each UAV. The dual integrator dynamic model is as follows: And construct an optimization problem with the total task completion efficiency as the aggregation function and the task execution capability requirements of each UAV as the local requirements: st This establishes a global coupling constraint that the total resource consumption of the task should not exceed the total amount of available resources.
[0041] Perturbation approximation and constraint transformation design: based on the dual integrator dynamics model, such as Figure 2 As shown, the unit control input is constructed based on the single-hidden-layer feedforward neural network SHLFNN: To approximate the nonlinear air resistance characteristics and external disturbances caused by ambient wind during UAV flight, the weight update rule of SHLFNN is designed in two cases: First, when the weights... At that time, the update formula is: ;when At that time, the update formula is: First, avoid overfitting by weights; second, introduce Lagrange multipliers. Construct the estimator: The optimization problem constrained by total resource consumption is transformed into an unconstrained optimization problem.
[0042] Aggregate estimation and optimization method design: Based on the real-time flight status and mission execution progress data of each UAV, an aggregate quantity estimator is constructed to obtain an estimate of the total mission completion efficiency. The constructed aggregate quantity estimator is as follows: Furthermore, combining unit control inputs and unconstrained optimization results, a distributed generalized Nash equilibrium search method based on neurodynamics is designed: Furthermore, this distributed time-varying generalized Nash equilibrium optimization method satisfies three conditions: firstly... right Global Lipsus, secondly Non-empty closed convex and , It is continuously infinitesimally convex, and its communication topology is a strongly connected graph.
[0043] Parameter range determination: Based on Lyapunov stability theory, a Lyapunov function is constructed that includes the squares of auxiliary variables, the squares of approximation errors, and the squares of Lagrange multiplier deviations. The Lyapunov function is: And by combining the three conditions, the parameter range is determined: , , And agent strategy pass Iteration, asymptotically converges to the unique optimal equilibrium solution of the aggregate game system: ( ).
[0044] Monitoring and Verification: Real-time monitoring of the evolution curves of each UAV task allocation strategy and the matching of total task resource consumption with total available resources, verifying whether generalized Nash equilibrium search and global coupling constraint satisfaction are achieved, forming a closed loop of design and verification.
[0045] In summary, we first define an aggregated game system consisting of eight UAV agents. A dual-integrator dynamics model is established for each UAV, constructing an optimization problem that includes an aggregate function of total task completion efficiency and local requirements for each UAV's task execution capabilities. We clarify the global coupling constraint that total task resource consumption does not exceed the total available resources. Then, based on the dual-integrator dynamics model, we construct unit control inputs using a single-hidden-layer feedforward neural network (SHLFNN) to approximate nonlinear air resistance and environmental wind disturbances. We update the SHLFNN weights according to two rules and introduce Lagrange multipliers to transform resource-constrained optimization into unconstrained optimization. Next, based on real-time flight and task data of each UAV, we construct an aggregate quantity estimator to obtain an estimate of the total task completion efficiency. Combining the control inputs and unconstrained optimization results, we design a distributed generalized Nash equilibrium search method based on neurodynamics. We determine the range of adjustment parameters based on Lyapunov stability theory to ensure the task allocation strategy iteratively converges to the optimal equilibrium solution. Finally, we monitor the evolution curve of the task allocation strategy and resource consumption to form a design-verification closed loop, achieving generalized Nash equilibrium search and satisfaction of global coupling constraints.
[0046] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.
Claims
1. A neural network-based generalized Nash equilibrium search method, characterized by, The specific steps of the method are: Aggregation game problem definition and dynamic model construction: determine the aggregation game system composed of N agents, and define the double integrator dynamics model of the agent; construct an optimization problem containing aggregation function and local demand, and clarify the global coupling constraint; Disturbance approximation and constraint transformation design: based on the double integrator dynamics model, construct the unit control input based on single hidden layer feedforward neural network SHLFNN, approximate the unknown nonlinear dynamics and external disturbance, and the weight update rule is designed in two cases; Aggregation estimation and optimization method design: based on the individual behavior data of the agent, construct an aggregation variable estimator to obtain the aggregation variable; combine the control input and the unconstrained optimization result to design a distributed generalized Nash equilibrium search method based on neural dynamics; Parameter range determination: based on the convergence condition of the distributed time-varying generalized Nash equilibrium optimization method, and combining Lyapunov stability theory, determine the value range of the adjustment parameters in the optimization method; Monitoring and verification: monitor the agent strategy evolution curve and constraint satisfaction, so as to verify whether the generalized Nash equilibrium search and global coupling constraint satisfaction are realized, and form a design-verification closed loop.
2. The neural network-based generalized Nash equilibrium search method of claim 1, wherein, In the definition and dynamic model construction of the clustering game problem, the clustering game system is denoted as: ,in, , and These are the set of agents, the policy space, and the cost function set; define the agents. The strategy space is The dual integrator dynamics model includes unknown nonlinear dynamics and external disturbances. The dual integrator dynamics model is as follows: ,in, For the first An intelligent agent. For the first The policy variables of each agent belong to the policy space. elements, for Regarding time The first derivative represents the first... The rate of change of the state variables of each agent For the first Each agent's velocity variable describes... The dynamic characteristics of the rate of change for Regarding time The first derivative represents the first... The rate of change of the velocity variable of each agent For the first Control input for an intelligent agent For unknown nonlinear dynamic terms, This represents the external disturbance term.
3. The neural network-based generalized Nash equilibrium search method of claim 1, wherein, In the definition and dynamic model construction of the aggregation game problem, an optimization problem containing aggregation functions and local demands is constructed: st ,in, For the first The strategy of an agent In the strategy space Minimize the operation within. For cost function, It is an aggregate function. For local needs; clarify the global coupling constraint characteristics of the clustered game system.
4. The neural network-based generalized Nash equilibrium search method of claim 1, wherein, In the perturbation approximation and constraint transformation design, the unit control input based on the single hidden layer feedforward neural network SHLFNN is: ,in, For the first Each intelligent agent unit controls the input. For the first A speed variable for each agent. For Lagrange multipliers, , For SHLFNN and Approximation output, To adjust the parameters, the SHLFNN weight update rule has two cases: First, when the weights... At that time, the update formula is: ,in, For the first The first intelligent agent unit control input and the first The update rate of the connection weights between hidden layer neurons All are constants. To approximate the error, For the hidden layer The output of each neuron, sign For sign functions; when At that time, the update formula is: First, avoid overfitting by weights; second, introduce Lagrange multipliers. Construct the estimator: ,in, For intelligent agents The corresponding update rate of the Lagrange multipliers, To adjust the parameters, A collection of intelligent agents participating in a clustered game system. For intelligent agents in communication topology With intelligent agents The connection weights of the edges between them respectively intelligent agents and intelligent agents The corresponding Lagrange multipliers.
5. The neural network-based generalized Nash equilibrium search method of claim 1, wherein, The aggregate estimation is used in the design of the optimization method, and the aggregate quantity estimator is constructed as: wherein, is an agent the rate of change of the estimate of the aggregate variable, is an agent the estimate of the aggregate variable, is an agent the estimate of the aggregate variable.
6. The neural network-based generalized Nash equilibrium search method of claim 1, wherein, In the design of the aggregation estimation and optimization method, the following is combined Based on the unconstrained optimization results, a distributed generalized Nash equilibrium search method based on neurodynamics is designed: ,in, as auxiliary variables Time derivative, The Laplace matrix of the communication topology. For auxiliary variable vectors, For intelligent agents The gradient of the cost function and the policy update satisfy Furthermore, this distributed time-varying generalized Nash equilibrium optimization method satisfies three conditions: First, right Global Lipsus, secondly Non-empty closed convex and , It is continuously infinitesimally convex, and its communication topology is a strongly connected graph.
7. The neural network-based generalized Nash equilibrium search method of claim 1, wherein, In the parameter range determination, a Lyapunov function is constructed based on Lyapunov stability theory: wherein, is the Lyapunov function, is the equilibrium value of the Lagrange multiplier, and the parameter range is determined in combination with three conditions: , , wherein, is the Lipschitz constant of the agent strategy gradually converges to the unique optimal equilibrium solution of the aggregate game system through iteration: ( ), wherein, is the generalized Nash equilibrium strategy of the agent , is the constant term in the cost function, is the coupling coefficient in the cost function, is the equilibrium value of the aggregate variable.
8. A neural network-based generalized Nash equilibrium search system, the method being applied to the neural network-based generalized Nash equilibrium search method according to any one of claims 1 to 7, characterized in that, The system comprises: Aggregation game problem definition and dynamic model construction module: determine the aggregation game system composed of N agents, and define the double integrator dynamics model of the agent; construct an optimization problem containing aggregation function and local demand, and clarify the global coupling constraint; Disturbance approximation and constraint transformation design module: based on the double integrator dynamics model, construct the unit control input based on single hidden layer feedforward neural network SHLFNN, approximate the unknown nonlinear dynamics and external disturbance, and the weight update rule is designed in two cases; Aggregation estimation and optimization method design module: based on the individual behavior data of the agent, construct an aggregation variable estimator to obtain the aggregation variable; combine the control input and the unconstrained optimization result to design a distributed time-varying generalized Nash equilibrium optimization method based on neural dynamics; Parameter range determination module: based on the convergence condition of the distributed time-varying generalized Nash equilibrium optimization method, and combining Lyapunov stability theory, determine the value range of the adjustment parameters in the optimization method; Monitoring and verification module: monitor the agent strategy evolution curve and constraint satisfaction, so as to verify whether the generalized Nash equilibrium search and global coupling constraint satisfaction are realized, and form a design-verification closed loop.