Observer-Based Adaptive Fuzzy Control of Nonstrict Feedback Nonlinear Systems With Function Constraints

In this article, an adaptive fuzzy tracking control scheme based on a fuzzy state observer is proposed for a class of uncertain, nonstrict feedback, nonlinear systems with function constraints. In the first place, based on the approximation characteristic of fuzzy logic systems (FLSs), a fuzzy state observer is designed to estimate the immeasurable state variables in the controlled system. Next, under the framework of adaptive backstepping control technology, FLSs are selected not only to approximate unknown nonlinear functions but also to avoid the algebraic loop problem caused by nonstrict feedback structure. At the same time, asymmetric Barrier Lyapunov functions are selected to solve the problem that system states are subject to function constraints, which are related to states and time. Then, Lyapunov stability theory is utilized to prove the stability of the controlled system, the realizability of function constraints, and the convergence of output tracking errors. Finally, a simulation is given to check the effectiveness of the proposed control scheme.