On optimal control of a sweeping process coupled with an ordinary differential equation

Lukáš Adam; Jiří Outrata

doi:10.3934/dcdsb.2014.19.2709

Article Contents

2014, Volume 19, Issue 9: 2709-2738. Doi: 10.3934/dcdsb.2014.19.2709

This issue Previous Article Next Article Transport semigroup associated to positive boundary conditions of unit norm: A Dyson-Phillips approach

On optimal control of a sweeping process coupled with an ordinary differential equation

Lukáš Adam^1, and
Jiří Outrata^1,

1.
ÚTIA, Czech Academy of Sciences, Pod Vodárenskou věží 4, Prague 8

Received: May 31, 2013

Revised: February 28, 2014

Published: October 2014

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Abstract

We study a special case of an optimal control problem governed by a differential equation and a differential rate--independent variational inequality, both with given initial conditions. Under certain conditions, the variational inequality can be reformulated as a differential inclusion with discontinuous right-hand side. This inclusion is known as sweeping process.
We perform a discretization scheme and prove the convergence of optimal solutions of the discretized problems to the optimal solution of the original problem. For the discretized problems we study the properties of the solution map and compute its coderivative. Employing an appropriate chain rule, this enables us to compute the subdifferential of the objective function and to apply a suitable optimization technique to solve the discretized problems. The investigated problem is used to model a situation arising in the area of queuing theory.

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Mathematics Subject Classification: Primary: 49M37, 90C30; Secondary: 90C33.

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