Decentralized control of interconnected singularly perturbed systems

Abstract

Designing a controller for large scale systems usually involve a high degree of complexity and computation ability. When talking about decentralized interconnected systems, the complexity and computation are not the only snags encountered when designing the controllers; channel bandwidth is another constraint to design procedures. The stability and optimization process can shift dramatically when an external noise is affecting the measurements at the output sensors or disturbing the controlled input. The investigated model in this research of a large scale stochastic decentralized interconnected system was a reduced order quasi-steady state model of the original system using singular perturbation techniques. Two methods of analyzing and minimizing the cost function of the full order system were proposed. The first method was to design a controller by standard stochastic control theory techniques using LQG approach and Kalman filter design. In the second method, game theory strategies were applied to the decentralized interconnected singularly perturbed systems. A Stackelberg game was designed and implemented to the reduced order model with one of the controllers designated leader in the game. The minimization of conditions and constraints reaches a solution which applies Lyapunov equations coupled with constraints equations to optimize the performance index of the reduced-order and the full order system.