Central suboptimal control design for nonlinear polynomial systems

Michael V. Basin, Peng Shi and Dario Calderon-Alvarez

International Journal of Systems Science, 2011, vol. 42, issue 5, 801-808

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.

Date: 2011
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DOI: 10.1080/00207721.2010.543491

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