Fixed-time full-state constrained control considering time delay of autonomous underwater vehicle based on prescribed performance and tan-type barrier Lyapunov function

Abstract

In this paper, a fixed-time control strategy based on prescribed performance function (PPF) and tan-type Barrier Lyapunov Function (tan-type BLF) is proposed for full-state constrained Autonomous Underwater Vehicle (AUV) considering input time delay. A prescribed performance function and a tan-type BLF are designed for the errors to prevent states from violating constraints, which guarantee the transient and steady state performance of the errors. A virtual control scheme is introduced to solve the singularity problem. The complexity explosion problem is resolved by employing a fixed-time differentiator, which simplifies the computational process and reduces the number of control parameters required. In addition, a radial basis function neural network (RBFNN) is used to estimate external disturbances and model uncertainties. It is proved through the fixed-time stability theory that the proposed control strategy ensures that the errors converge to a small neighborhood near the origin in fixed time considering time delay. Finally, simulation results and comparisons are presented to demonstrate the effectiveness and superiority of the proposed strategy.