Adaptive output feedback tracking control for non‐linear switched stochastic systems with unknown control directions

Abstract

The problem of adaptive fuzzy output feedback tracking control for a class of switched stochastic non-linear systems with time-varying delay and unknown control directions is addressed in this study. During the adaptive controller design procedure, a state observer is introduced to estimate the unmeasurable system states, an appropriate stochastic Lyapunov-Krasovskii functional is utilised to compensate the time-varying delay terms, and fuzzy logic systems are employed to approximate a suitable unknown function which is composed of all the unknown non-linearities of the switched systems. In addition, the Nussbaum-type function is used to detect the unknown control directions. With the help of the designed controller independent of switching signals, the semi-globally uniformly ultimately boundedness of all the closed-loop signals is guaranteed and the tracking error converges to a small neighbourhood of the origin. Finally, a simulation example is given to illustrate the effectiveness of the proposed approach.