Redundancy implies robustness for bang-bang strategies

TL;DR

This paper introduces a method to enhance robustness of bang-bang control strategies in nonlinear systems by adding needle-like control variations and optimizing a robustness criterion based on singular values.

Contribution

It develops a novel least-square approach for designing robust bang-bang controls using redundancy and introduces a robustness measure based on singular values.

Findings

Redundancy in control strategies enhances robustness.

The method successfully applies to attitude control of a 3D rigid body.

Optimization of the robustness criterion improves control reliability.

Abstract

We develop in this paper a method ensuring robustness properties to 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 overdeter-mined 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.