A Robust State Feedback Optimal Control Law with Backstepping Approach for Steering Control of an Autonomous Underwater Vehicle Using Semi-definite Programming

In this paper, the desired yaw orientation for an autonomous underwater vehicle is attained by acquiring a cascaded control structure based on a robust optimal control algorithm with a backstepping approach. A robust state feedback optimal control law is designed to control the yaw rate. Hence, the desired yaw rate is intended to be obtained by the backstepping controller by controlling the desired yaw orientation. The implementation of the proposed robust control algorithm is formulated by using semi-definite programming. A linear quadratic regulator in terms of linear matrix inequality is designed to address the control problem. The design of robust optimal control law in the steering plane is achieved by considering an uncertain polytopic AUV system. Realization of the proposed control algorithm is conducted in MATLAB/Simulink environment using the YALMIP tool. Robust behavior is ensured by the proposed control algorithm while tracking the desired yaw. The robustness analysis is extended by considering the various ranges of specific uncertain parameters to highlight the efficacies of the proposed control algorithm.