Inverse optimal controller for nonlinear systems with convex input constraints

In this paper, we propose an inverse optimal controller design method for nonlinear systems with convex input constraints. The proposed design method constructs a state feedback controller as an optimal solution of a parametric convex optimization problem. The necessary and sufficient condition for inverse optimality is given by the Karush-Kuhn-Tucker (KKT) condition. We also show that the Lagrange multiplier for the optimization problem characterizes the asymptotically stabilizable domain and the robustness of the proposed controller. The effectiveness of the proposed method is confirmed by computer simulation.