Nonlinear Robust Optimal Control via Inverse Problem of Optimal Regulator

Recently, an approach to derive solutions of HamiltonJacobi equation with high accuracy, called stable manifold theory, is proposed. So far some researches about nonlinear optimal control via stable manifold are subjected. However, research of robustness for nonlinear optimal control is not reported. This report proposes a new framework to enhance robustness to the nonlinear optimal control system designed by the stable manifold method using the inverse problem of optimal regulator and linear matrix inequality. To verify the effectiveness, the swing-up and stabilization problem for the Acrobot is considered. The Acrobot is underactuated mechanical system, which is composed of two links. The system is typical problem in nonlinear control theory. Simulation results are presented in order to evaluate the control performance.