Adaptive Sliding Mode Fixed-Time Tracking Control Based on Fixed-Time Sliding Mode Disturbance Observer with Dead-Zone Input

Aiming at the problem of fixed-time trajectory tracking control for high-order dynamic systems with external time-varying disturbance and input dead-zone, an adaptive fixed-time sliding mode control algorithm is proposed by employing a fixed-time sliding mode disturbance observer (FTSMDO) and high-order fixed-time sliding mode algorithm. Firstly, a FTSMDO is presented for the problem that estimating the compound disturbance is composed of input dead-zone and time-varying external disturbance in the higher-order dynamic system, which cannot be measured accurately. Furthermore, for the case that the total disturbance of the system has an unknown upper bound, the corresponding adaptive law is designed to estimate the unknown upper bound, and the fixed-time controller is designed based on FTSMDO algorithm to make all state variables converge in a fixed-time. Based on Lyapunov technique, the fixed-time convergence performance of the proposed algorithm is proved. The effectiveness of the presented fixed-time control algorithm is verified by simulating the depth tracking control of the underactuated underwater vehicle.