Redundancy implies robustness for bang‐bang strategies

Abstract

Summary We develop in this paper a method ensuring robustness properties of bang‐bang strategies, for general nonlinear control systems. Our main idea is to add bang arcs in the form of needle‐like variations of the control. With such bang‐bang controls having additional degrees of freedom, steering the control system to some given target amounts to solving an overdetermined nonlinear shooting problem, what we do by developing a least‐square approach. In turn, we design a criterion to measure the quality of robustness of the bang‐bang strategy, based on the singular values of the end‐point mapping, and which we optimize. Our approach thus shows that redundancy implies robustness, and we show how to achieve some compromises in practice, by applying it to the attitude control of a 3d rigid body.