Optimal control of a random sweeping process with probabilistic terminal point constraint
Authors
- Henrion, René
ORCID: 0000-0001-5572-7213 - Klein, Olaf
ORCID: 0000-0002-4142-3603
2020 Mathematics Subject Classification
- 49J21 49J53 34A60
Keywords
- Sweeping processes, chance constraints, optimal control
DOI
Abstract
This paper deals with controlled polyhedral sweeping processes under uncertainty and involving a terminal point constraint for the solution trajectory. More precisely, a cost-optimal (nominal) control is to be determined such that even after random perturbations of this control the terminal point of the resulting random trajectory falls into some target set with high probability. This leads to the well-known concept of chance constraints which have recently been successfully applied in the optimal control of partial or ordinary differential equations. Given the dynamics of sweeping processes - which are specific differential inclusions with unbounded and discontinuous right-hand side - a straightforward translation of these previous results is not possible. The focus of the paper lies on modeling of well-posed controlled polyhedral sweeping processes with randomly perturbed control and, as a main result, on the derivation of the existence of solutions to three types of such processes.
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