Central suboptimal H∞ control design for nonlinear polynomial systems

This paper presents the central finite-dimensional H∞ regulator for nonlinear polynomial systems, that is suboptimal for a given threshold γ with respect to a modified BolzaMeyer quadratic criterion including the attenuation control term with the opposite sign. In contrast to the previously obtained results, the paper reduces the original H∞ control problem to the corresponding optimal H2 control problem, using the technique proposed in [1]. The paper yields the central suboptimal H∞ regulator for nonlinear polynomial systems in a closed finite-dimensional form, based on the optimal H2 regulator obtained in [2]. 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 linearized system.