Observer-based adaptive interval type-2 fuzzy control of uncertain MIMO nonlinear systems with unknown asymmetric saturation actuators

Abstract

An observer-based controller is proposed for a class of uncertain MIMO nonlinear systems preceded by actuators with unknown asymmetric saturations. The gains of actuators are unknown nonlinear functions that are generally functions of states. The unknown nonlinearities are approximated by interval type-2 fuzzy systems where the consequent parameters are tuned adaptively. Meanwhile, the interval type-2 fuzzy systems due to their structure can cope with the uncertainties in antecedent membership functions. The states of the system do not need to be known. To tackle the unavailability of states an observer based on strictly positive real (SPR) theory is designed to estimate the states. To cope with the fuzzy approximation error and external disturbances an adaptive continuous robust structure is proposed. The continuous robust structure due to adaptiveness does not need the bound of uncertainties and due to continuity does not have the chattering problem. All the adaptive laws are derived via Lyapunov synthesis approach. Meanwhile, all the signals in the closed-loop system are guaranteed to be semi-globally uniformly ultimately bounded (SGUUB) and the mean-square tracking error can be made arbitrarily small. Simulation results reveal the effectiveness of the proposed method in terms of coping well with the uncertainties and saturation actuators while maintaining satisfactory performance.