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On optimal control of a sweeping process coupled with an ordinary differential equation
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SYSNO ASEP 0434417 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title On optimal control of a sweeping process coupled with an ordinary differential equation Author(s) Adam, Lukáš (UTIA-B)
Outrata, Jiří (UTIA-B) RID, ORCIDNumber of authors 2 Source Title Discrete and Continuous Dynamical Systems-Series B. - : AIMS Press - ISSN 1531-3492
Roč. 19, č. 9 (2014), s. 2709-2738Number of pages 30 s. Publication form Print - P Language eng - English Country US - United States Keywords optimal control ; variational inequality ; variational analysis ; coderivative ; solution map ; queuing theory Subject RIV BA - General Mathematics R&D Projects GAP201/12/0671 GA ČR - Czech Science Foundation (CSF) Institutional support UTIA-B - RVO:67985556 UT WOS 000341776500001 EID SCOPUS 84907249388 DOI 10.3934/dcdsb.2014.19.2709 Annotation 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. Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2015
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