Multi-variable adaptive back-stepping control of submersibles using SDU decomposition

A multi-variable adaptive autopilot for the dive-plane control of submarines is designed. The vehicle is equipped with bow and stern hydroplanes for maneuvering. It is assumed that the system parameters are not known, and the disturbance force is acting on the vehicle. Based on a back-stepping design approach, an adaptive control law is derived for the trajectory control of the depth and the pitch angle. To prevent singularity in the control law, the SDU decomposition of the high-frequency gain matrix is used for the design. In the closed-loop system, asymptotic tracking of the reference depth and pitch angle trajectories is accomplished. Simulation results are presented which show that the submarine performs dive-plane maneuvers in spite of the uncertainties in the system parameters and disturbance forces.