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PreprintCC BY 4.0arXiv

Minimum-Energy Control for Stochastic Linear Systems

  • Vaishnavi Sharma
  • Vaibhav Katewa
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Abstract

The open-loop minimum-energy control (MEC) problem asks for control inputs that minimize the control energy while ensuring the terminal state reaches a desired value. In this paper, we study the open-loop MEC problem for stochastic linear time-invariant systems. We consider a variety of stochastic constraints that enforce the terminal error to be \emph{small}, and show that Stochastic MEC (SMEC) problem can be formulated as a QCQP. We obtain the optimal solution for SMEC and show that it generalizes the well-known Deterministic MEC problem by introducing novel stochastic variants of controllability and Gramian matrices. Finally, we show that there exists a fundamental lower bound on the optimal control energy which cannot be overcome by increasing the time horizon of the problem.

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Cite

BibTeXRIS
BibTeX
@misc{sharma2026minimumenergy,
  title = {{Minimum-Energy Control for Stochastic Linear Systems}},
  author = {Vaishnavi Sharma and Vaibhav Katewa},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.13424},
  eprint = {2610.13424},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.13424},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Minimum-Energy Control for Stochastic Linear Systems
AU  - Vaishnavi Sharma
AU  - Vaibhav Katewa
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2610.13424
UR  - https://arxiv.org/abs/2610.13424
AB  - The open-loop minimum-energy control (MEC) problem asks for control inputs that minimize the control energy while ensuring the terminal state reaches a desired value. In this paper, we study the open-loop MEC problem for stochastic linear time-invariant systems. We consider a variety of stochastic constraints that enforce the terminal error to be \emph{small}, and show that Stochastic MEC (SMEC) problem can be formulated as a QCQP. We obtain the optimal solution for SMEC and show that it generalizes the well-known Deterministic MEC problem by introducing novel stochastic variants of controllability and Gramian matrices. Finally, we show that there exists a fundamental lower bound on the optimal control energy which cannot be overcome by increasing the time horizon of the problem.
ER  -