Hybrid Constructive Strategy for Time-Delay Nonlinear Dynamics in Autonomous Underwater Vehicle Vertical Motion

Abstract The article proposes a hybrid control method that integrates backstepping control with nonlinear model predictive control (NMPC) to achieve precise regulation of a nonlinear dynamic system with time-delay characteristics. The backstepping controller is designed to regulate the pitch angle and vertical velocity through a structured inner- and outer-loop control mechanism, incorporating adaptive gain parameters to supply the initial control inputs to the NMPC. This ensures the initial stabilization of the system's dynamic behavior. To address the system's inherent complexity and time-delay characteristics, the proposed NMPC strategy introduces real-time optimization in conjunction with advanced delay compensation techniques. A penalty term for time delays is incorporated into the cost function, with adaptive parameter adjustment to effectively mitigate the negative impacts of input delays. By predicting future system states and continuously optimizing the control inputs over the prediction horizon, the NMPC significantly enhances control accuracy and robustness, ensuring that delay-compensated control inputs are applied at each time-step. The results demonstrate the effectiveness of the proposed approach, showcasing its ability to precisely track desired target states and maintain system stability in the vertical-plane control of an autonomous underwater vehicle (AUV) with time-delay nonlinearities. These findings highlight the innovative nature of the hybrid control strategy and affirm its potential as a robust solution for controlling complex nonlinear systems, particularly in environments where input delays and disturbances pose significant challenges.