Polynomial methods to construct inputs for uniformly ensemble reachable linear systems

TL;DR

This paper develops polynomial-based algorithms to construct parameter-independent inputs for linear systems with parameter dependence, focusing on discrete-time systems and extending some methods to continuous-time cases.

Contribution

It introduces constructive polynomial methods for input design in ensemble reachability, providing algorithms for discrete-time systems and extending applicability to certain continuous-time systems.

Findings

Algorithms for discrete-time systems demonstrated effective input construction.

Polynomial methods based on complex approximation improve ensemble reachability.

Extension of methods to some continuous-time systems shown to be feasible.

Abstract

This paper is concerned with linear parameter-dependent systems and considers the notion uniform ensemble reachability. The focus of this work is on constructive methods to compute suitable parameter-independent open-loop inputs for such systems. In contrast to necessary and sufficient conditions for ensemble reachability, computational methods have to distinguish between continuous-time and discrete-time systems. Based on recently derived sufficient conditions and techniques from complex approximation we present two algorithms for discrete-time single-input linear systems. Moreover, we illustrate that one method can also be applied to certain continuous-time single-input systems.