Computation of open-loop inputs for uniformly ensemble controllable systems

TL;DR

This paper develops computational techniques to design open-loop inputs for families of linear systems that are ensemble controllable, enabling parameter-independent control strategies for complex systems.

Contribution

It introduces a novel approach combining linear integral equations and finite-dimensional control theory to compute open-loop inputs for ensemble controllable systems.

Findings

Methods successfully compute open-loop inputs for parameter-dependent systems.

Approach bridges infinite-dimensional control problems with finite-dimensional solutions.

Applicable to a wide class of linear ensemble systems.

Abstract

This paper presents computational methods for families of linear systems depending on a parameter. Such a family is called ensemble controllable if for any family of parameter-dependent target states and any neighborhood of it there is a parameter-independent input steering the origin into the neighborhood. Assuming that a family of systems is ensemble controllable we present methods to construct suitable open-loop input functions. Our approach to solve this infinite-dimensional task is based on a combination of methods from the theory of linear integral equations and finite-dimensional control theory.