Viscosity solutions for an optimal control problem with Preisach hysteresis nonlinearities

Fabio Bagagiolo

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 10, Issue: 2, page 271-294
  • ISSN: 1292-8119

Abstract

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We study a finite horizon problem for a system whose evolution is governed by a controlled ordinary differential equation, which takes also account of a hysteretic component: namely, the output of a Preisach operator of hysteresis. We derive a discontinuous infinite dimensional Hamilton–Jacobi equation and prove that, under fairly general hypotheses, the value function is the unique bounded and uniformly continuous viscosity solution of the corresponding Cauchy problem.

How to cite

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Bagagiolo, Fabio. "Viscosity solutions for an optimal control problem with Preisach hysteresis nonlinearities." ESAIM: Control, Optimisation and Calculus of Variations 10.2 (2010): 271-294. <http://eudml.org/doc/90730>.

@article{Bagagiolo2010,
abstract = { We study a finite horizon problem for a system whose evolution is governed by a controlled ordinary differential equation, which takes also account of a hysteretic component: namely, the output of a Preisach operator of hysteresis. We derive a discontinuous infinite dimensional Hamilton–Jacobi equation and prove that, under fairly general hypotheses, the value function is the unique bounded and uniformly continuous viscosity solution of the corresponding Cauchy problem. },
author = {Bagagiolo, Fabio},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Hysteresis; optimal control; dynamic programming; viscosity solutions.; hysteresis; viscosity solutions},
language = {eng},
month = {3},
number = {2},
pages = {271-294},
publisher = {EDP Sciences},
title = {Viscosity solutions for an optimal control problem with Preisach hysteresis nonlinearities},
url = {http://eudml.org/doc/90730},
volume = {10},
year = {2010},
}

TY - JOUR
AU - Bagagiolo, Fabio
TI - Viscosity solutions for an optimal control problem with Preisach hysteresis nonlinearities
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 10
IS - 2
SP - 271
EP - 294
AB - We study a finite horizon problem for a system whose evolution is governed by a controlled ordinary differential equation, which takes also account of a hysteretic component: namely, the output of a Preisach operator of hysteresis. We derive a discontinuous infinite dimensional Hamilton–Jacobi equation and prove that, under fairly general hypotheses, the value function is the unique bounded and uniformly continuous viscosity solution of the corresponding Cauchy problem.
LA - eng
KW - Hysteresis; optimal control; dynamic programming; viscosity solutions.; hysteresis; viscosity solutions
UR - http://eudml.org/doc/90730
ER -

References

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