A finite-time adaptive sliding mode control based on DOB for AUVs subject to matched and mismatched disturbances

This paper proposes an adaptive sliding mode control (SMC) based on disturbance observer (DOB) for trajectory tracking problem of autonomous underwater vehicles (AUVs). Due to sensitivity of the SMC to mismatched disturbances, this paper presents an adaptive SMC based on a new exponential reaching law. The controller uses a DOB to estimate both matched and mismatched time-varying disturbances. The stability of DOB in the presence of time-varying disturbances is proved via the Lyapunov stability theorem. To design the controller, sliding surfaces containing estimation of the matched and mismatched disturbances are defined. In order to increase the speed of reaching to the surfaces and avoid chattering, the gains of the proposed reaching law have been adapted based on the sliding surfaces. It has been proved that the proposed reaching law converges to the sliding surfaces in a finite time. The stability of the overall system with DOB and controller has also been proved using the Lyapunov technique. A simulation study has conducted to test how the proposed method controls the AUVs to track a desired trajectory when the vehicles are exposed to both matched and mismatched disturbances. The results demonstrate that the performance of the proposed controller is superior to the controllers previously reported in the literature.