Optimal control of ode systems involving a rate independent variational inequality

Martin Brokate; Pavel Krejčí

doi:10.3934/dcdsb.2013.18.331

Optimal control of ode systems involving a rate independent variational inequality

Martin Brokate
, Pavel Krejčí

Chair of Numerical Mathematics and Control Theory (2008 — 2025)

Academy of Sciences of the Czech Republic

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

95 Scopus citations

Abstract

This paper is concerned with an optimal control problem for a system of ordinary differential equations with rate independent hysteresis modelled as a rate independent evolution variational inequality with a closed convex constraint Z R^m. We prove existence of optimal solutions as well as necessary optimality conditions of first order. In particular, under certain regularity assumptions we completely characterize the jump behaviour of the adjoint.

Original language	English
Pages (from-to)	331-348
Number of pages	18
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	18
Issue number	2
DOIs	https://doi.org/10.3934/dcdsb.2013.18.331
State	Published - Mar 2013

Keywords

Evolution variational inequalities
Hysteresis
Necessary optimality conditions
Optimal control

Access to Document

10.3934/dcdsb.2013.18.331

Cite this

@article{6c4e4cfa85804be5955e0d83fb9015d0,

title = "Optimal control of ode systems involving a rate independent variational inequality",

abstract = "This paper is concerned with an optimal control problem for a system of ordinary differential equations with rate independent hysteresis modelled as a rate independent evolution variational inequality with a closed convex constraint Z Rm. We prove existence of optimal solutions as well as necessary optimality conditions of first order. In particular, under certain regularity assumptions we completely characterize the jump behaviour of the adjoint.",

keywords = "Evolution variational inequalities, Hysteresis, Necessary optimality conditions, Optimal control",

author = "Martin Brokate and Pavel Krej{\v c}{\'i}",

year = "2013",

month = mar,

doi = "10.3934/dcdsb.2013.18.331",

language = "English",

volume = "18",

pages = "331--348",

journal = "Discrete and Continuous Dynamical Systems - Series B",

issn = "1531-3492",

publisher = "American Institute of Mathematical Sciences",

number = "2",

}

TY - JOUR

T1 - Optimal control of ode systems involving a rate independent variational inequality

AU - Brokate, Martin

AU - Krejčí, Pavel

PY - 2013/3

Y1 - 2013/3

N2 - This paper is concerned with an optimal control problem for a system of ordinary differential equations with rate independent hysteresis modelled as a rate independent evolution variational inequality with a closed convex constraint Z Rm. We prove existence of optimal solutions as well as necessary optimality conditions of first order. In particular, under certain regularity assumptions we completely characterize the jump behaviour of the adjoint.

AB - This paper is concerned with an optimal control problem for a system of ordinary differential equations with rate independent hysteresis modelled as a rate independent evolution variational inequality with a closed convex constraint Z Rm. We prove existence of optimal solutions as well as necessary optimality conditions of first order. In particular, under certain regularity assumptions we completely characterize the jump behaviour of the adjoint.

KW - Evolution variational inequalities

KW - Hysteresis

KW - Necessary optimality conditions

KW - Optimal control

UR - https://www.scopus.com/pages/publications/84874884911

U2 - 10.3934/dcdsb.2013.18.331

DO - 10.3934/dcdsb.2013.18.331

M3 - Article

AN - SCOPUS:84874884911

SN - 1531-3492

VL - 18

SP - 331

EP - 348

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

IS - 2

ER -

Optimal control of ode systems involving a rate independent variational inequality

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this