Observer-based adaptive fuzzy controller for uncertain non-strict state-delayed nonlinear systems subject to input and output constraints

This paper addresses the design of an observer-based adaptive fuzzy controller for a class of uncertain non-strict nonlinear systems subject to time-delays, unknown direction, input saturation, and output constraint. The Barrier Lyapunov Function (BLF) has been utilized to keep the system output inside the desired bounds. The state and input delays have been handled by using the Lyapunov–Krasovskii function and including an integral compensator term in the controller, respectively. A state observer has been designed to estimate the unmeasured states. The Lipschitz condition for proving boundedness of the estimated states has been relaxed. The Nussbaum gain function has been exploited to deal with the problem of unknown control directions. The fuzzy logic approximation has been utilized to avoid the “explosion of complexity” occurring in the traditional backstepping technique. It has been shown that all closed-loop signals are semi-globally uniformly ultimately bounded (SGUUB) and the output tracking error converges to a small neighborhood of the origin by choosing the design parameters appropriately. Effectiveness of the proposed control scheme has been demonstrated via two practical examples.