Minimum-Energy Control for Stochastic Linear Systems

Vaishnavi Sharma; Vaibhav Katewa

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arXiv · 2610.13424

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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BibTeX RIS

Vaishnavi Sharma, Vaibhav Katewa. 2026-10-09. Minimum-Energy Control for Stochastic Linear Systems. https://arxiv.org/abs/2610.13424

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