H∞ controller design using LMIs for high-speed underwater vehicles in presence of uncertainties and disturbances

• The kinematic and dynamic equations of SV are established.
• We reformulated SV model into a cascade form of subsystems.
• We proposed a novel LMIs including the nonlinear planing force.
• A new robust H∞ controller was developed based on LMIs.
• Simulation results verified the feasibility of the proposed controller.

Traditional underwater vehicles are limited in speed due to dramatic friction drag on the hull. Supercavitating vehicles exploit supercavitation to reduce drag and increase their underwater speed. Compared with fully wetted vehicles, the nonlinearities in the models of cavitator, fin, and particularly nonlinear planing force make the control design of supercavitating vehicles more challenging. For a widely cited benchmark model, this paper reformulates the supercavitating vehicle model in a cascade form of subsystems to facilitate the application of the backstepping control design. Based on linear matrix inequalities (LMIs), we developed a new robust H∞H∞ controller by introducing the sector conditions of the nonlinear characteristics of nonlinear planing force. Simulations are conducted for both initial and tracking responses to evaluate the performance and robustness of the proposed H∞H∞ controller for all admissible uncertainties and disturbance inputs.