Tridimensional autonomous motion robust control of submersible ship based on averaged sub-gradient integral sliding mode approach

The design of a state feedback and robust controller for regulating the tridimensional (3D) movement of autonomous underwater mobile crafts (AUMCs). The controller design is based on the application of Averaged Sub-Gradient Integral Sliding Mode Realisation (ASGISMR). The application of the ASGISMR yields the solution of the closed-loop extreme seeking control for a non-strictly convex functional depending on the tracking error between reference and 3D position of the AUMC. The design of reference trajectories was proposed to enforce the AUMC to follow a continued submersion and ellipsoidal detouring. The mechanical dynamical form of AUMC is well posed for applying the extended version of ASGISMR, considering that integral term represents an ASG associated to the euclidean norm of the tracking error. The time evolution of the functional over the controlled trajectories of the AUMC is compared with the corresponding functional enforced by a traditional state feedback controller with gravity effect compensation. The proposed controller exhibits better tracking and similar control magnitude than the considered reference state feedback realisation. These outcomes justify the potential contributions of the suggested ASGISMR to obtain the local minimisation of the evaluated functional, considering such controller as an extreme seeking realisation for the proposed AUMC.