On optimal control of a sweeping process coupled with an ordinary differential equation
By Lukáš Adam, Jirí Vladimír Outrata. 2014
57 citations recorded by the source corpus.
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.
Subfields: Computational Theory and Mathematics, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/007b54670fb4fa5adff27fe3b23feba50f1f4404
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In Computational Theory and Mathematics
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- René Henrion
- Nguyen D. Hoang
- Giovanni Colombo
- Alexander Y. Kruger
- Hung M. Phan
- Michel Baes
In Numerical Analysis
Citations in the corpus
- Optimality conditions for a controlled sweeping process with applications to the crowd motion model (2015, background): “Namely, [11] deals with controls only in perturbations addressing existence and relaxation issues for optimal solutions, while [1, 4] apply controls in associated differential equations with deriving necessary optimality conditions for discrete-time [1] and continuous-time [4] systems.”
- Optimal control of the sweeping process over polyhedral controlled sets (2015, background): “In the other line of development we mention the recent paper [8] and its subsequent extension [2], which address a different class of optimal control problems for an equivalent variational inequality description of the sweeping process of the rate-independent hysteresis type, where the convex moving”