Output‐feedback control for a class of Markovian jump non‐linear systems under a risk‐sensitive cost criterion with unknown transition probabilities

Abstract

This study addresses the output-feedback control problem for a class of Markovian jump non-linear systems under a quadratic risk-sensitive cost function criterion. The transition probabilities of the Markov process are assumed to be completely unknown. By employing the high-gain scaling technique, common Lyapunov function method and backstepping technique, a control law is constructed that guarantees any arbitrary small risk-sensitive cost for a given risk-sensitive parameter. Moreover, the resulted closed-loop system solutions are bounded in probability. Compared with some previous results, this study does not require the uniform boundedness of the gain functions of the system noise, and the control law further achieves a zero risk-sensitive cost and asymptotically stable in the large for the closed-loop system solutions when the vector field of the disturbance vanishes at the origin. A numerical example is given to illustrate the proposed protocol.