Attenuated-chattering adaptive second order variable structure controller for mismatched uncertain systems

Abstract

In this paper, an attenuated-chattering adaptive second order variable structure controller (ACASOVSC) is proposed for mismatched uncertain systems using a Moore-Penrose inverse method. The key achievements of this study include three tasks: 1) influence of the chattering in control input is diminished, 2) finite-time convergence of system states is guaranteed, and 3) external disturbance is generally assumed to be unknown in advance. Firstly, a switching manifold which comprises only output information is defined. Secondly, a reduced-order variable structure estimator (ROVSE) with lower dimension is designed to reduce the computation burden and enhance the robustness. Thirdly, an adaptive approach is used to guess the upper bound of the unknown exogenous disturbance. Next, an ACASOVSC is investigated for attenuating the chattering phenomenon and stabilizing the system. Then, a novel linear matrix inequality (LMI) constraint by the Lyapunov technique is given such that the plant is entirely invariant to matched uncertainties and asymptotically stable. Finally, a mathematical illustration is simulated, which exhibits the usefulness and the feasible application of the proposed method.