Observer-based adaptive fuzzy finite time control for non-strict feedback nonlinear systems with unmodeled dynamics and input delay

In this paper, we consider observer-based adaptive fuzzy finite time control scheme for non-strict feedback uncertain nonlinear systems with unmodeled dynamics and input delay. A fuzzy state observer is employed to estimate the unmeasurable states and the unknown nonlinearities are identified by the fuzzy logic systems in each step. The design difficulty caused by the unmodeled dynamics and input delay is tackled by a dynamic signal and a compensation signal, respectively. Based on the proposed compensation signal, the considered input delay can be unknown and time varying. To decrease the computational burden, the dynamic surface control (DSC) scheme is adopted in the design process. In the framework of finite time Lyapunov theory, an effective adaptive fuzzy finite time controller has been obtained by combining the idea of backstepping technology with DSC scheme. The proposed method not only solves the algebraic loop problem, but also realizes the finite time stability performance constraint in the presence of input delay, unmodeled dynamics and unmeasurable states. Finally, the stability analysis shows that all signals of the closed-loop systems are bounded in finite time. Simulation results show the superiority of the devised scheme.