Design of a backstepping technique-based robust state feedback optimal control law for autonomous underwater vehicle in depth plane using semi-definite programming

This paper depicts the control of an autonomous underwater vehicle (AUV) in the vertical plane by employing the robust backstepping approach-based state feedback optimal control. The proposed control algorithm adopts a cascade structure for achieving the desired depth. The inner loop is controlled by robust state feedback optimal control law to control pitch orientation and the outer loop is controlled by the backstepping approach to control the depth. The formulation of a robust optimal control algorithm is implemented using semi-definite programming (SDP). Considering the parameter variation, a polytopic system is developed in the depth plane. The proposed control algorithm is realised in MATLAB/Simulink environment using the YALMIP tool. An efficacious tracking of the desired depth is exhibited from the proposed control algorithm by ensuring robust behaviour. Further, the robustness analysis is extended by considering different ranges of parameter uncertainty to highlight the efficacies of the proposed control law.