Central suboptimal H∞ control design for nonlinear polynomial systems

This article presents the central finite-dimensional H-infinity regulator for nonlinear polynomial systems, which is suboptimal for a given threshold gamma 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-infinity control problem to the corresponding optimal H-2 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 H-2 and H-infinity Control Problems', IEEE Transactions on Automatic Control, 34, 831-847]. This article yields the central suboptimal H-infinity regulator for nonlinear polynomial systems in a closed finite-dimensional form, based on the optimal H-2 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-infinity regulator available for the corresponding linearised system.