# Viscosity solutions for an optimal control problem with Preisach hysteresis nonlinearities

ESAIM: Control, Optimisation and Calculus of Variations (2004)

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

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topBagagiolo, Fabio. "Viscosity solutions for an optimal control problem with Preisach hysteresis nonlinearities." ESAIM: Control, Optimisation and Calculus of Variations 10.2 (2004): 271-294. <http://eudml.org/doc/244969>.

@article{Bagagiolo2004,

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},

language = {eng},

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/244969},

volume = {10},

year = {2004},

}

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

PY - 2004

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

UR - http://eudml.org/doc/244969

ER -

## References

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