Robust sliding mode H<inf>∞</inf> control using time-varying delayed states for offshore steel jacket platforms

This paper is concerned with robust sliding mode H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> control using time-varying delayed states for an offshore steel jacket platforms subject to self-excited nonlinear wave force, external disturbance and parametric uncertainties. By intension-ally introducing a time-varying delay into the control channel, a delayed robust sliding mode H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> controller is designed to reduce the internal oscillations of the offshore platform. The positive effect of the introduced time-varying delay on robust sliding mode H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> control for the offshore platform is investigated. It is found through simulation results that the delayed robust sliding mode H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> controller is effective to attenuate the vibration of the offshore platform, and the control force required by the proposed controller is smaller than the one by robust sliding mode controller and robust sliding mode H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> controller.