- Title
- On optimal control of a sweeping process coupled with an ordinary differential equation
- Creator
- Adam, Lukas; Outrata, Jiri
- Date
- 2014
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/72255
- Identifier
- vital:6872
- Identifier
-
https://doi.org/10.3934/dcdsb.2014.19.2709
- Identifier
- ISSN:15313492
- 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.
- Publisher
- Southwest Missouri State University
- Relation
- Discrete and Continuous Dynamical Systems - Series B Vol. 19, no. 9 (November 2014 2014), p. 2709-2738
- Rights
- © American Institute of Mathematical Sciences
- Rights
- This metadata is freely available under a CCO license
- Subject
- 0101 Pure Mathematics; 0102 Applied Mathematics; Coderivative; Optimal control; Queuing theory; Solution map; Variational analysis; Variational inequality
- Reviewed
- Hits: 2311
- Visitors: 2314
- Downloads: 0