Extended integral sliding mode robust sub-gradient extremum seeking control for tracking trajectory of autonomous underwater vehicle

The aim of this study is to design a robust controller for an autonomous underwater vehicle (AUV) based on the application of the extended Integral Sliding Mode (ISM) method. The control problem is reformulated here as an extremum seeking control problem realization for solving the tracking of attainable reference trajectories. The states of the uncertain dynamic corresponding to the AUV dynamics track the references restricted to the x-z plane. The dynamic nature of the AUV induces the application of the ISM extended version design based on the implementation of a sub-gradient strategy to perform the on-line optimization for the tracking error norm. The proposed control permits to minimize the tracking error without a complete knowledge of the AUV dynamics. The trajectory tracking results of the designed controller are compared with the corresponding outcomes enforced by a state feedback and twisting controllers. The proposed controller exhibits better tracking and smaller control magnitude than the state feedback and twisting form. These two results confirm the benefits of introducing the mixed extended strategy, including ISM and dual averaged extremum seeking control.