Multi-agent Cooperative Control Based On Potential Game Theory

Game cybernetics is a theory produced by the combination of traditional game theory and cybernetics,which combines the theories and methods of game and control.The research of related multi-agent cooperative control systems has also become a hot research direction in the field of game control in recent years.Due to the non-intuitive static properties of the problem when analyzing the cooperative control system through the Pareto optimal method,and the low Pareto efficiency,it is not suitable for the actual system.Therefore,this paper combines the potential game and Nash equilibrium to study the system cooperative control method from the perspective of local dynamics.The profit function of the agent is used as the potential function,and the overall profit of the system is maximized by analyzing the potential function.First,the game rules of the cooperative control system in this paper are proposed.The income function of the individual agent in the system is used as the individual potential function,and the cooperative control system of n agents game is studied.Secondly,since each agent's revenue-based reasoning and strategy process have fuzzy attributes,the strategy process is modeled as a model with fixed noise,the noise parameter ? is introduced into the system,and the Logit equalization is used for continuous simulation of the system,and the individual intelligence The profit function of the entity is combined with the Logit probability selection model to analyze the stochastic cooperative control system.Through the discussion of Logit equilibrium,it is proved that the system exists and there is only one Logit equilibrium,which solves the dilemma of the system in multiple equilibrium.At the same time,Logit quantitative response equilibrium is used to analyze the influence of the changes in the cost parameter c and the number of agents n in the system on the agent strategy,and solves the unpredictable defect of Nash equilibrium.Finally,the potential function that expresses individual income is extended to the group potential function,and the standard measurement entropy is added to the traditional group potential function to further analyze the random multi-agent cooperative control system.It is proved that the logit equilibrium probability distribution achieves the maximization of the overall revenue of the system.