Optimal Robust Control Laws for Uncertain Nonlinear Systems

Randy Freeman, Electrical and Computer Engineering, UC Santa Barbara

We first introduce the concept of a robust control Lyapunov function (rclf) and show that its existence is equivalent to robust stabilizability via continuous state feedback. This extends Artstein's theorem on nonlinear stabilizability to systems with uncertainties. We then use the rclf to formulate and solve an inverse optimal control problem in a differential game setting, the opposing players being the control and the disturbance. We show that every rclf globally satisfies the steady-state Hamilton-Jacobi-Isaacs (HJI) equation associated with a meaningful game. For those classes of systems for which systematic methods for constructing rclf's exist, our analysis provides a recipe for computing optimal robustly stabilizing feedback laws without solving the HJI partial differential equation.