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PreprintCC BY 4.0arXiv

Risk-Sensitive Stochastic Optimal Control on Positive Cones

  • Mohamad Al Ahdab
  • John-Josef Leth
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Abstract

We consider stochastic optimal control problems in which the state is constrained to a proper cone. Specifically, we consider risk-neutral, risk-averse, and risk-seeking formulations within a single entropic-risk framework. We investigate classes of problems whose Bellman operator preserves affine functions and characterize their optimal value functions and feedback policies for both finite-horizon and time-average infinite-horizon problems. Additionally, we establish convergence and state-bound results under finite-step cost observability. Moreover, we demonstrate an exact connection between entropic-risk optimal control on proper cones and deterministic infsup control for systems whose dynamics and stage costs are affine in the disturbances. In addition, we provide examples of classes of systems for which explicit solutions can be obtained.

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Cite

BibTeXRIS
BibTeX
@misc{ahdab2026risksensitive,
  title = {{Risk-Sensitive Stochastic Optimal Control on Positive Cones}},
  author = {Mohamad Al Ahdab and John-Josef Leth},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.06887},
  eprint = {2611.06887},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.06887},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Risk-Sensitive Stochastic Optimal Control on Positive Cones
AU  - Mohamad Al Ahdab
AU  - John-Josef Leth
PY  - 2026
DA  - 2026/11/04
PB  - arXiv
DO  - 10.48550/arxiv.2611.06887
UR  - https://arxiv.org/abs/2611.06887
AB  - We consider stochastic optimal control problems in which the state is constrained to a proper cone. Specifically, we consider risk-neutral, risk-averse, and risk-seeking formulations within a single entropic-risk framework. We investigate classes of problems whose Bellman operator preserves affine functions and characterize their optimal value functions and feedback policies for both finite-horizon and time-average infinite-horizon problems. Additionally, we establish convergence and state-bound results under finite-step cost observability. Moreover, we demonstrate an exact connection between entropic-risk optimal control on proper cones and deterministic infsup control for systems whose dynamics and stage costs are affine in the disturbances. In addition, we provide examples of classes of systems for which explicit solutions can be obtained.
ER  -