| Issue |
Math. Model. Nat. Phenom.
Volume 15, 2020
Systems with Hysteresis and Switching
|
|
|---|---|---|
| Article Number | 55 | |
| Number of page(s) | 25 | |
| DOI | https://doi.org/10.1051/mmnp/2020023 | |
| Published online | 19 November 2020 | |
Hysteresis and controllability of affine driftless systems: some case studies*
1
Dipartimento di Matematica, Università degli studi di Trento via Sommarive,
14 38123
Povo,
Trento, Italy.
2
Politecnico di Torino, Corso Duca degli Abruzzi,
24 10129
Torino, Italy.
** Corresponding author: fabio.bagagiolo@unitn.it
Received:
3
February
2020
Accepted:
11
June
2020
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.
Mathematics Subject Classification: 34H05 / 47J40 / 93B05
Key words: Hysteresis / controllability / play operator / switching
© The authors. Published by EDP Sciences, 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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