Abstract

We revisit the Bang-Bang principle, established for deterministic dynamics with affine control, in a stochastic setting where the dynamics are subject to Brownian motion. We show that such a principle does not generally apply in this context. However, we demonstrate that it does apply under certain conditions with deterministic controls. With stochastic controls, we obtain, under certain conditions, that Mayer's problems with an expectation criterion and a compact control set are equivalent to the same problems with controls taking values in the closed convex hull of the control set. This result is illustrated by a linearized dynamics of the SIR epidemiological model.

Author information

Contact details are reproduced from the original publication and may be historical.

Dan Goreac

(1) École d'Actuariat, Université Laval Québec, Canada
(2) LAMA, Université Gustave Eiffel, UPEM,
Univ. Paris Est Creteil, CNRS, Marne-la-Vallée, France
(3) School of Mathematics and Statistics, Shandong University, Weihai, P. R. China

dan.goreac@act.ulaval.ca

Keywords

  • Bang-Bang principle
  • optimal control
  • stochastic differential equations
  • convexity

Mathematics Subject Classification

93E20, 60H10, 49J30

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Suggested citation

R. Chenevat, D. Goreac, Q. Li, A. Rapaport. “About the Bang-Bang Principle for Controlled Affine Dynamics with Brownian Noise.” Journal of Convex Analysis 33 (2026), No. 3&4, 801–816. https://doi.org/10.68381/jca33045

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Published by Heldermann Verlag, 2026. Rights now held by Banach Press LLC.