WIAS Preprint No. 3050, (2023)

Pontryagin's principle for some probabilistic control problems


Authors

  • van Ackooij, Wim
  • Henrion, René
    ORCID: 0000-0001-5572-7213
  • Zidani, Hasnaa

2020 Mathematics Subject Classification

  • 49J15 93E03 90C15

Keywords

  • Optimal control problems, Pontryagin maximum principle, probabilistic cost, probust control, state constraints

DOI

10.20347/WIAS.PREPRINT.3050

Abstract

In this paper we investigate optimal control problems perturbed by random events. We assume that the control has to be decided prior to observing the outcome of the perturbed state equations. We investigate the use of probability functions in the objective function or constraints to define optimal or feasible controls. We provide an extension of differentiability results for probability functions in infinite dimensions usable in this context. These results are subsequently combined with the optimal control setting to derive a novel Pontryagin's optimality principle.

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