Adaptive fixed-time control for nonlinear systems subject to mismatched uncertainties and external disturbance: An ESO-based strategy

In this paper, the tracking problem is concerned for a class of nonlinear system. The primary objective is to achieve fixed-time control performance in the presence of nonvanishing mismatched uncertainties and nonparametric external disturbance. Firstly, in order to estimate disturbance, a fixed-time extended state observer with fractional power term is developed, the order of which is reduced to alleviate peaking value phenomenon. By reasonably switching among different estimation patterns, both transient and steady-state performances are balanced. Secondly, by means of fuzzy logic system theory, an ESO-based adaptive fuzzy control strategy with time-varying gains is presented, and thus the mismatched nonlinearities are approximated, and the external disturbance is compensated in real time simultaneously. Moreover, by constructing a mixed barrier and quadratic type of Lyapunov function, the fixed-time stability analysis is put forward for tracking error dynamics based on backstepping methodology. Finally, the advantages and effectiveness are illustrated by a numerical example on wheeled mobile robot. The main characteristic of this paper is to integrate ESO methodology into fuzzy control architecture in fixed-time sense. As a consequence, not only the output tracking purpose, but also desirable transient performance can be achieved.