Lyapunov-Based Model Predictive Control for Dynamic Positioning of Autonomous Underwater Vehicles

This paper presents a novel Lyapunov-based model predictive control (LMPC) framework for the dynamic positioning (DP) control of autonomous underwater vehicles (AUVs). Due to the optimization essential, LMPC can explicitly consider the practical constraints on the real system and generate the best possible DP control. Meanwhile, taking advantage of the existing Lyapunov-based DP controller, a contraction constraint can be imposed to the formulated optimal control problem, which guarantees the closed-loop stability. In addition, the thrust allocation (TA) subproblem can be solved simultaneously with LMPC-based DP control. The most widely used proportional-integral-derivative (PID) type DP controller is investigated for the construction of the contraction constraint. Sufficient conditions that ensure the recursive feasibility hence closed-loop stability of the LMPC are derived. An arbitrarily large region of attraction can be claimed. The proposed LMPC framework serves as a bridge connecting modern optimization technique and the conventional control theory, which enables a direct integration of online optimization into control system design to improve the control performance. Simulation results on the Saab SeaEye Falcon open-frame ROV/AUV reveal the effectiveness of the proposed method.