Control of Decentralized Systems Based on Nash Equilibrium Concept of Game Theory

Abstract

In this paper, a new control method for decentralized systems is proposed by using the concept of Nash equilibrium points of non co-operative game. The main reason for applying non co-operative game to decentralized systems is that multi-objective decentralized systems can be easily formulated without considering weighting factor of each objective function. It is supposed that the system stated in this article is composed of many subsystems including their own controllers, so each subsystem can be regarded as a player in the game. Each subsystem and its controller are described by the Universal Learning Networks which have been proposed to provide a universal framework for the class of neural networks. From the above assumptions it is theoretically shown that if the criterion function for each subsystem can be defined individually, the Nash equilibrium points can be calculated by the commonly used gradient learning algorithm of networks. Simulation studies on a decentralized tank network control system show that the Nash equilibrium points can be obtained systematically and effectively by the proposed method.