Singularity avoidance adaptive output‐feedback fixed‐time consensus control for multiple autonomous underwater vehicles subject to nonlinearities

Abstract This article investigates the singularity avoidance adaptive output‐feedback fixed‐time consensus control problem for multiple autonomous underwater vehicles (AUVs) subject to nonlinearities. A distributed state observer is designed to reconstruct the unmeasurable coupling states of each AUV system. In order to handle the unknown nonlinearities of the multi‐AUV systems, the fuzzy logic systems are adopted to approximate unknown hydrodynamic parameters. By combining adaptive fixed‐time control with backstepping technology, an adaptive singularity avoidance fixed‐time consensus control algorithm is developed, where a new error switching mechanism is designed for avoiding the singularity problem caused by the differentiation of the virtual control law. Subsequently, a singularity avoidance distributed adaptive output‐feedback fixed‐time fuzzy controller is presented, under which an auxiliary function is designed to handle the difficulty of the fixed‐time stability analysis under the output‐feedback control strategy, where two types of observer errors are needed in the designed Lyapunov function to achieve the fixed‐time stability. Then, based on the fixed‐time stability criterion, it is proved that both the consensus tracking performance and the closed‐loop stability can be guaranteed in fixed time. Finally, a simulation example verifies the effectiveness of the developed control strategy.