Finite-time robust H∞ control for high-speed underwater vehicles subject to parametric uncertainties and disturbances

Traditional underwater vehicles are limited in speed due to dramatic friction drag on the hull. Supercavitating vehicles exploit supercavitation as a means to reduce drag and increase their underwater speed. Compared with fully wetted vehicles, the nonlinearities in modeling of cavitator, fin, and in particular, nonlinear planing force make the control design of supercavitating vehicles more challenging. By combining cascaded design and backstepping approach, this paper reformulates the supercavitating vehicle model into a novel cascade model with two error tracking subsystems. Based on linear matrix inequalities (LMIs) and by introducing the sector conditions of the nonlinear characteristics of planing force, a new finite-time robust H∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_{\infty }$$\end{document} control scheme is proposed for the error tracking subsystems which ensures that the closed-loop system is finite-time bounded and the effect of the disturbance input on the controlled output is reduced to a prescribed level. A sufficient condition is presented for the solvability of the design problem, which is further reduced to a feasibility problem of a set of LMIs. Simulations have been conducted for both initial and tracking responses to evaluate the performance and robustness of the proposed H∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_{\infty }$$\end{document} controller for all admissible uncertainties and the disturbance inputs.