Optimal nonlinear robust control for nonlinear uncertain cascade systems

Abstract

We develop an optimality-based robust control framework for uncertain cascade systems with structured parametric uncertainty. Specifically, using an optimal nonlinear robust control framework we develop a family of globally stabilizing robust backstepping controllers parametrized by the cost functional that is minimized. Furthermore, it is shown that the robust control Lyapunov function guaranteeing closed-loop stability over a prescribed range of structured system parametric uncertainty is a solution to the steady-state Hamilton-Jacobi-Bellman equation for the controlled system and thus guarantees robust stability and robust performance. The results are then used to design robust controllers for jet engine compression systems with uncertain compressor characteristic performance maps.