Basin, Michael V ORCID: 0000-0002-7274-4303, Shi, Peng ORCID: 0000-0001-8218-586X and Calderon-Alvarez, Dario (2011) Central suboptimal H∞ control design for nonlinear polynomial systems. International Journal of Systems Science, 42 (5). pp. 801-808. ISSN 0020-7721

Abstract

This article presents the central finite-dimensional H∞ regulator for nonlinear polynomial systems, which is suboptimal for a given threshold γ with respect to a modified Bolza-Meyer quadratic criterion including the attenuation control term with the opposite sign. In contrast to the previously obtained results, the article reduces the original H∞ control problem to the corresponding optimal H2 control problem, using this technique proposed in Doyle et al. [Doyle, J.C., Glover, K., Khargonekar, P.P., and Francis, B.A. (1989), 'State-space Solutions to Standard H2 and H∞ Control Problems', IEEE Transactions on Automatic Control, 34, 831-847]. This article yields the central suboptimal H∞ regulator for nonlinear polynomial systems in a closed finite-dimensional form, based on the optimal H2 regulator obtained in Basin and Calderon-Alvarez [Basin, M.V., and Calderon-Alvarez, D. (2008b), 'Optimal Controller for Uncertain Stochastic Polynomial Systems', Journal of the Franklin Institute, 345, 293-302]. Numerical simulations are conducted to verify performance of the designed central suboptimal regulator for nonlinear polynomial systems against the central suboptimal H∞ regulator available for the corresponding linearised system.

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