Adaptive high-order sliding mode controller-observer for MIMO uncertain nonlinear systems

In this paper, an adaptive high-order sliding mode controller-observer is proposed for multi input-multi output uncertain systems with application to robotic manipulators. Firstly, a type-2 Takagi-Sugeno fuzzy system is used to model the original system. Next, with the unavailability of velocity measurement, a fuzzy high-order sliding mode observer is designed to estimate both the joint velocities and uncertainties. Moreover, based on a super twisting second-order sliding mode, the proposed robust controller generates smooth control and guarantees finite-time convergence to the third-order sliding set with respect to the sliding variable by keeping second-order sliding mode constraint. The controller gains are generated based on an adaptive estimation scheme without overestimation. The finite-time stability of the suggested controller is proved by using an homogeneous and strict Lyapunov function. Finally, the obtained simulation results for two-link robot manipulators demonstrate the effectiveness of the proposed controller.