Fixed-time observer-based homogeneous controller with state-dependent exponent for fault tolerant control of an underwater vehicle

This paper is concerned with designing a fault tolerant control system in the presence of unknown vehicle dy-namics and saturation and rate limits of the thrusters for an underwater remotely operated vehicle. For this, a novel variable-exponent finite-time controller based on homogeneity is proposed for the underwater vehicle. The error-dependent exponent is introduced to provide better performance in transient and obtain faster converge to the desired states. Stability analyses are carried out for the controller and it is proven that system states will converge to the origin in finite time. In addition, phase plane analyses are performed and it is shown that system trajectories converge to the origin faster under proposed controller compared to controller with constant ex-ponents. A fixed-time extended state observer with a new fault detection and identification unit is introduced which provides faster estimation of failures in transients despite the presence of uncertainties and disturbances. State estimation error dynamics is proven to be fixed-time convergent and fault estimation error is globally uniformly ultimately bounded. Simulations are carried out and comparisons are made with several FTCSs. The results show that the performance of the proposed algorithm is superior to previous works both in transients and upon the failures.