Direct adaptive fuzzy sliding mode decoupling control for a class of underactuated mechanical systems

Motivated by the dynamic characteristics of underactuated mechanical systems with 2 degrees of freedom, a decoupling adaptive fuzzy sliding mode decoupling controller (DAFSMDC) is presented in this paper. By exploiting the universal approximation property of fuzzy logic systems and the sliding mode control method, this paper proposes a new decoupling strategy of the system into 2 second-order subsystems and introduces an adaptive control algorithm that guarantees the convergence of both subsystems. Since fuzzy systems are used to approximate an unknown ideal controller, the adjustable parameters of the used fuzzy systems are updated using a gradient descent algorithm that is designed to minimize the error between the unknown ideal controller and the fuzzy controller. Based on Lyapunov stability theory, proofs and conditions are then given to ensure the stability of the closed-loop system. Two examples are provided to illustrate the effectiveness and potential of the DAFSMDC technique for the stabilization of underactuated mechanical systems.