Observer‐based controller for nonaffine time‐delayed systems subject to input nonlinearities, state constraints, and unknown control direction

Abstract

In this work, an adaptive observer-based control scheme has been designed for uncertain nonaffine nonstrict feedback systems subject to state time delay, various types of input nonlinearities, time-varying asymmetric state constraints, and unknown control direction. Compared to the existing controllers for systems with state constraints, the designed control scheme in this work can be applied to state-constrained systems with nonaffine structure subject to state delays, unknown control direction, and different types of input nonlinearities, while full-states measurement is not required. Moreover, by introducing a novel saturated Nussbaum function in the present work, not only has the problem of unknown control direction been handled, but also the probability of a control shock due to applying the conventional Nussbaum functions has been eliminated. The system unknown dynamics has been approximated by using neural networks (NNs), and by updating the maximum norm of NNs weight vectors, only one adaptive law is required for the controller implementation. By employing appropriate Lyapunov functions, it has been shown that all signals in the closed-loop system are bounded, state constraints are satisfied, and the output tracking error can be made small by selecting appropriate design parameters.The effectiveness of the designed control scheme has been shown through two simulation studies. Moreover, the superiority of the proposed saturated Nussbaum function in comparison with conventional Nussbaum functions has been shown via simulation. K E Y W O R D Sinput nonlinearity, intelligent approximator, nonstrict feedback systems, state constraints, unknown control direction INTRODUCTIONRecently, control of systems with constraints has attracted a great deal of attention because many real systems are subject to constraints such as wheeled mobile robotic systems 1 and chemical processes. 2 Constraints may appear as physical restrictions, performance requirements, or safety considerations. 3 Input, state, and output constraints are the three major types of constraints investigated in the literature. For example, an adaptive controller has been designed for a class of 2122