A robust type-2 fuzzy sliding mode controller for disturbed MIMO nonlinear systems with unknown dynamics

Abstract

In this paper, in order to achieve the best tracking control of a class of multi-input multi-output (MIMO) nonlinear systems with unknown dynamics and unknown disturbances, a new robust adaptive interval type-2 fuzzy sliding mode control law (AIT2-FSMCL) has been proposed. Based on developing interval type-2 fuzzy local models for some operating points of the controlled system, an interval type-2 fuzzy logic system (IT2-FLS) has been designed to better estimate the unknown nonlinear dynamics of the studied system. Then, to enhance the tracking control performance and ensure the system robustness in the presence of approximation errors, parameter variations, un-modelled dynamics and external disturbances, a new AIT2-fuzzy sliding mode system (AIT2-FSMS), has been introduced. In order to avoid the chattering phenomenon while keeping the system performance, the AIT2-FSMS uses three AIT2-fuzzy logic systems (AIT2-FLSs) to estimate the optimal gains of the AIT2-FSMCL. The adaptation laws have been derived using the Lyapunov stability approach. The mathematical proof shows that the closed-loop system with the proposed control approach is globally asymptotically stable. Finally, the proposed design method is applied to a two-link robot arm to validate the effectiveness of the proposed control approach.