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.