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

0434417 - ÚTIA 2015 RIV US eng J - Journal Article
Adam, Lukáš - Outrata, Jiří
On optimal control of a sweeping process coupled with an ordinary differential equation.
Discrete and Continuous Dynamical Systems-Series B. Roč. 19, č. 9 (2014), s. 2709-2738. ISSN 1531-3492. E-ISSN 1553-524X
R&D Projects: GA ČR(CZ) GAP201/12/0671
Grant - others:GA MŠk(CZ) SVV-2013-267315
Institutional support: RVO:67985556
Keywords : optimal control * variational inequality * variational analysis * coderivative * solution map * queuing theory
Subject RIV: BA - General Mathematics
Impact factor: 0.768, year: 2014
http://library.utia.cas.cz/separaty/2014/MTR/adam-0434417.pdf

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.
Permanent Link: http://hdl.handle.net/11104/0239354