Abstract
This paper presents a robust mixed $$H_2 /H_\infty $$ control method for wave-excited offshore jacket platforms. Its objective was to design a controller that minimizes the upper bound of the $$H_2 $$ performance measure on platform dynamics satisfying some $$H_\infty $$ norm bound constraint simultaneously. Based on mixed $$H_2 /H_\infty $$ control theory and linear matrix inequality techniques, a novel approach to stabilize offshore platform vibration with constrained $$H_2 /H_\infty $$ performances is proposed. Uncertainties of the wave excitation are considered in dynamic performance analysis of offshore platforms. A reduced mode offshore platform structure under wave excitation is analyzed, and simulations are used to verify the effectiveness of the proposed approach. Compared with existing $$H_\infty $$ control methods, the proposed approach makes a significant improvement for dynamic performances of offshore platforms under random wave excitation.
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