Relaxation and optimisation of a phase-field control system with hysteresis

Pavel Krejčí; Sergey A. Timoshin; Alexander A. Tolstonogov

doi:10.1080/00207179.2016.1268270

Relaxation and optimisation of a phase-field control system with hysteresis

Pavel Krejčí
, Sergey A. Timoshin^*
, Alexander A. Tolstonogov

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

The present paper is concerned with a nonlinear partial differential control system arising in phase transition modelling. The control constraint is given by a state-dependent nonconvex-valued multivalued mapping. We study the problem of minimisation of a given integral cost functional over solutions to the above system. The cost integrand is nonconvex in the control variable. Relaxation results of Bogolyubov-type are obtained for this problem.

Original language	English
Pages (from-to)	85-100
Number of pages	16
Journal	International Journal of Control
Volume	91
Issue number	1
DOIs	https://doi.org/10.1080/00207179.2016.1268270
Publication status	Published - 2 Jan 2018
Externally published	Yes

Keywords

Evolution control system
hysteresis
relaxation
state-dependent constraint

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10.1080/00207179.2016.1268270

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abstract = "The present paper is concerned with a nonlinear partial differential control system arising in phase transition modelling. The control constraint is given by a state-dependent nonconvex-valued multivalued mapping. We study the problem of minimisation of a given integral cost functional over solutions to the above system. The cost integrand is nonconvex in the control variable. Relaxation results of Bogolyubov-type are obtained for this problem.",

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author = "Pavel Krej{\v c}{\'i} and Timoshin, \{Sergey A.\} and Tolstonogov, \{Alexander A.\}",

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AB - The present paper is concerned with a nonlinear partial differential control system arising in phase transition modelling. The control constraint is given by a state-dependent nonconvex-valued multivalued mapping. We study the problem of minimisation of a given integral cost functional over solutions to the above system. The cost integrand is nonconvex in the control variable. Relaxation results of Bogolyubov-type are obtained for this problem.

KW - Evolution control system

KW - hysteresis

KW - relaxation

KW - state-dependent constraint

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Relaxation and optimisation of a phase-field control system with hysteresis

Abstract

Keywords

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