Observer-Based Adaptive Fuzzy Control for Nonlinear State-Constrained Systems Without Involving Feasibility Conditions

For nonlinear full-state-constrained systems with unmeasured states, an adaptive output feedback control strategy is developed. The main challenge of this article is how to avoid that the unmeasured states exceed the constrained spaces. To achieve a good tracking performance for the considered systems, a stable state observer is structured to estimate unmeasured states which are not available in the control design. In addition, the constraints existing in most practical engineering are the source of reducing control performance and causing the system instability. The main limitation of current barrier Lyapunov functions is the feasibility conditions for intermediate controllers. The nonlinear mappings are used to achieve the satisfaction of full-state constraints directly and avoid feasibility conditions for intermediate controllers. By the Lyapunov theorem, the closed-loop system stability is proven. Simulation results are given to confirm the validity of the developed strategy.

I. Introduction

It is well known that nonlinearities and uncertainties inevitably occur in modern industrial systems. There were numerous notable adaptive control approaches proposed for stabilizing many categories of uncertain nonlinear systems in [1]–[6]. The nonlinearities in [1]–[6] were required to be linearly parameterized, however, it is a conservative limitation in the real world. Based on neural networks (NNs) and fuzzy-logic systems, some adaptive approximation control strategies were developed for nonlinear systems in the literature, for instance, stochastic nonlinear switched systems in [7], stochastic systems with hysteresis in [8], strict-feedback systems with input saturation in [9] or unknown time delays in [10], and nonlinear multi-input–multioutput (MIMO) systems with unknown dynamics in [11]. Apart from these results, some adaptive approximation control strategies were proposed for robotic manipulators in [12], flapping wing microaerial vehicle in [13] and [14], and wheeled mobile robotic systems in [15]. However, the adaptive control strategy above mentioned is presented to control nonlinear systems with the states measured case.