Research On Distributed Nash Equilibrium Seeking Algorithms Under Uncertainty

Game theory is a theoretical basis for studying the coexistence of win-win cooperation and conflicts of interest between multiple participants(which can be extended to multi-agents).With the development of computer networks,scholars have applied game theory to many practical problems in the computer field,such as big data cloud computing,wireless networks,etc.When dealing with complex computer system engineering problems,scholars often use game theory for modeling,and seeking the optimal solution(i.e.,Nash equilibrium)of the game model by analyzing the corresponding income function,loss function,action strategy,etc.to obtain the maximum benefit of the system.Distributed games,which have developed rapidly in recent years,are attracting attention as a new research field combining game theory and distributed optimization,and are widely applied to power system energy management,network congestion control,economic modeling,etc.Different from the traditional distributed optimization problem in which individuals cooperate with each other to achieve a global optimum,there are often conflicts of interest and competition between individuals in a distributed game system,and each individual pursues the optimal value of its own objective function.This paper mainly considers the multi-agent non-cooperative game problem in interference environment.The main content is summarized as follows:1.Considering the actual harsh communication system environment,we analyze the possible channel noise,and consider the possible noise problems in the real communication system on the distributed game model proposed by scholars,and analyze the convergence of noise to existing algorithms Impact.In the game part,each player cannot obtain accurate information about the rest of the players,and can only estimate the state and behavior of other players,so as to achieve their own relatively optimal return function,and the return function is closely related to every other player.Inspired by the consensus algorithm,the attenuation factor is finally introduced to resist interference,and the results are verified through a large number of simulation experiments.2.In the case that most of the existing researches are based on undirected communication topology diagrams,this paper considers a distributed aggregative game problem for high-order systems with uncertain disturbances under a directed communication topology.The embedded technique is used to decouple the original problem into two subproblems:path planning and tracking control.We first construct a virtual single-integrator system and design a distributed dynamic average consensus algorithm to estimate the unknown aggregative parameter,and then propose a gradient-based distributed game algorithm for this virtual system to generate the reference trajectory of the aggregative game.In the tracking part,we design a dynamic state feedback controller for the high-order system to track the reference trajectory and reject external disturbances.Finally,simulations are given to validate the effectiveness of the theoretical analysis.