Observer based direct adaptive fuzzy second-order-like sliding mode control for unknown nonlinear systems

This work proposes a novel observer based direct adaptive fuzzy second-order-like sliding mode control (SMC) method for a certain class of high order unknown nonlinear dynamical systems with unmeasurable states. An observer is firstly developed to estimate the tracking error vector directly, and the stability of the observer is analyzed based on Meyer-Kalman-Yakubovich (MKY) lemma. Based on the observer, the equivalent control law is approximated by a double-input single-output fuzzy logic system (FLS), in which the observation of the sliding surface and its derivative are applied as the inputs. In addition, an adaptive switching control law is added to mitigate the system chattering and improve the stability of the system. The free parameters of the controller are adjusted online by the adaptive laws that are derived from the Lyapunov stability analysis. Finally, the convergence of the overall closed-loop system is demonstrated, and the simulation examples illustrate the efficacy of the proposed control method.