Hysteresis and controllability of affine driftless systems: some case studie

TL;DR

This paper explores the controllability of driftless affine systems with hysteresis effects, demonstrating approximate controllability with play operators and controllability of hysteretic delayed systems, thus advancing understanding of hysteresis in control systems.

Contribution

It introduces methods to analyze controllability in hysteretic systems, providing new results for systems with play operators and delayed relays, and explores their connections.

Findings

Approximate controllability for systems with play hysteresis.

Controllability of hysteretic delayed switching systems.

Connections between different hysteresis models.

Abstract

We investigate the controllability of some kinds of driftless affine systems where hysteresis effects are taken into account, both in the realization of the control and in the state evolution. In particular we consider two cases: the one when hysteresis is represented by the so-called play operator, and the one when it is represented by a so-called delayed relay. In the first case we prove that, under some hypotheses, whenever the corresponding non-hysteretic system is controllable, then we can also, at least approximately, control the hysteretic one. This is obtained by some suitably constructed approximations for the inputs in the hysteresis operator. In the second case we prove controllability for a generic hysteretic delayed switching system. Finally, we investigate some possible connections between the two cases.