Adaptive Output Feedback Control Design for a Class of Stochastic Nonlinear Systems with General Unknown Output Gain

Abstract

In this paper, we consider the global adaptive output feedback control design problem for a class of stochastic nonlinear systems with general unknown output gain. Different from the existing literature, the uncertainty on the output gain of the considered system is more general, that is to say, only the sign of the gain is known, which directly leads to the ineffectiveness of the existing methods. In order to achieve the control objective, besides designing a full-order observer, inspired by the existing adaptive design technique, a new unknown parameter is introduced to depict the system uncertainties and facilitate the adaptive control design. Then, by adopting the adding a power integrator technique and the homogeneous control method, we successfully design an adaptive output feedback controller to render the uncertain stochastic nonlinear systems globally asymptotically stable in probability, which means that all the closed-loop system states are bounded almost surely, and especially the original system states converge to the origin with probability one.