Decentralized Stabilization of Interconnected Stochastic Nonlinear Systems under a Risk-sensitive Cost Criterio

Abstract

This paper studies decentralized stabilization for interconnected large-scale stochastic nonlinear systems. The class of systems focused on is a set of stochastic nonlinear systems which interact through partial observable states and performance is measured with respect to a risk sensitive cost criterion. The unknown interconnection terms are assumed to be bounded by some known functions of the observable states of the subsystems, multiplied by some unknown parameters. First the strict-feedback forms for each subsystems via diffeomorphism coordinate transformation are obtained based on the assumed existence of necessary and sufficient conditions and then to design the stabilizing controllers for each subsystem using backstepping technique, which have access only the information available with regard to the respective subsystem, and they achieve an arbitrarily small value for the risk-sensitive for the overall system. Under this completely decentralized control scheme, all closed-loop signals remain bounded in probability.