Output-feedback-based adaptive risk-sensitive tracking control for stochastic nonlinear uncertain systems

This paper addresses the design problem of practical (or satisfaction) adaptive output-feedback tracking control for stochastic strict-feedback nonlinear uncertain systems in observer canonical form with stable zero-dynamics under long-term average tracking error risk-sensitive cost criteria. The cost function adopted here is of quadratic-integral type usually encountered in practice, rather than of quartic-integral one commonly used to avoid difficulty in control design and performance analysis of the closed-loop system. A sequence of coordinate transformations are first introduced to separate the zero-dynamics from the entire system so that the transformed system has an appropriate form suitable for observer design and integrator backstepping design. Then, for any given risk- sensitivity parameter and desired cost value, by using the integrator backstepping methodology, an adaptive output-feedback tracking control is constructively designed such that (a) the closed-loop system is bounded in probability and, (b) the long- term average risk-sensitive cost is upper bounded by the desired value. Among others, this paper does not require the uniform boundedness of the gain functions of the system noises. This paper can be regarded as the further research of [21].