Hysteresis and controllability of affine driftless systems: some case studies

Fabio Bagagiolo¹ ; Marta Zoppello²

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.

Mathematical modelling of natural phenomena, Tome 15 (2020), article no. 55.

Résumé

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.

Détail

DOI : 10.1051/mmnp/2020023

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