Efficient Implementation Algorithms for NMPC-Based AUV Trajectory-Tracking Control

Two distinct fast implementation strategies are proposed for the NMPC-based trajectory tracking control of an AUV. The first strategy is based on the numerical continuation method. Assuming that the solution of the associated optimization problem is not obtained at singular points, the NMPC control signals can be approximated without undergoing the successive linearization step which is inevitable in off-the-shelf NLP algorithms, therefore, the computational complexity can be significantly reduced. The convergence of the solution is proved. The second strategy exploits the dynamic properties of the AUV motion, and solves the optimization problems in a distributed fashion. The recursive feasibility and closed-loop stability of the distributed implementation are proved. The proposed fast implementation strategies considerably alleviate the heavy computational burden and hence greatly increase the possibility of implementing NMPC-based motion control on various AUVs including those with limited onboard computing resources.