Adaptive Prescribed Performance Trajectory Tracking Control for Autonomous Underwater Vehicles without Initial Condition Limitation and Control Singularity

Abstract

The problem of the trajectory tracking control with prescribed performance for an autonomous underwater vehicle (AUV) under model uncertainties and sudden disturbances is investigated in this paper. Classical prescribed performance control (PPC) methods typically impose strict requirements on the initial conditions of tracking errors and are susceptible to control singularity caused by error boundary violations when encountering sudden disturbances, which consequently restricts their practical engineering applications. To this end, this paper proposes an adaptive prescribed performance trajectory tracking control for autonomous underwater vehicles without initial condition limitation and control singularity. First, this study designs an improved prescribed performance function (PPF) to characterize the convergence time and steady-state accuracy of the tracking error. And the control singularity due to the sudden disturbances is avoided by including an adaptive regulation term in the PPF. Then, nonlinear mapping functions are designed to address the issues of classical PPC method with initial condition limitations. Furthermore, the error transformation function is proposed to convert control objectives from constraint control to stability control. Finally, the study designs and employs the radial basis function neural network (RBF NN) to approximate unknown nonlinear continuous functions containing disturbances during the controller design process. Through Lyapunov theorem, it is proved that the errors not only are ultimately bounded but also converge to a preset range in a predefined time under the action of the designed controller. Simulation experiments validated the effectiveness of the proposed method under multiple operational conditions. The results demonstrate that even when the initial tracking error exceeds the bounds of the prescribed performance function or sudden external disturbances occur, the designed controller still guarantees precise AUV trajectory tracking. The tracking errors satisfy the preset transient and steady-state performance specifications, and the proposed method exhibits clear advantages in convergence speed and control accuracy compared with existing approaches.

Keywords

AUV trajectory tracking / Prescribed performance control / Adaptive neural network control / Improved prescribed performance functions / Initial condition limitations

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Harbin Engineering University and Springer-Verlag GmbH Germany, part of Springer Nature