Stability-Preserving Optimization in the Presence of Fast Disturbances

Abstract

We present a method to robustly optimize a set of design parameters for a dynamical system which is subject to fast disturbances. These disturbances are themselves parameterized by a finite number of parameters. Robustness is ensured by requiring the disturbance parameters to stay sufficiently far away from critical manifolds in the parameter space, at which the system would lose stability. These manifolds are defined by an algebraic condition on the system trajectories. The closest distance to the critical manifolds is measured along their normal vectors.