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Data-Driven Minimum Energy Control for Stochastic Linear Systems with Finite Sample Guarantees

Vaishnavi Sharma, Vaibhav Katewa · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.27599 · cited by 0 works (OpenAlex) · open-access PDF

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在这篇论文中,我们研究了Stochastic linear time-invariant systems(SMEC)的开放循环MEC问题,我们考虑了一系列的Stochastic MEC问题,通过引入新的Stochastic experimental variants of controllability和Gramian matrix,并表明Stochastic MEC(SMEC)问题可以通过增加问题时界线来克服,而不是通过增加问题时界线来克服。我们获得了SMEC的最佳解决方案,并表明它通过使用模拟最高概率的模拟和对基于UEC的最佳量子依赖的定义MEC问题来概括了已知的Stochastic MEC问题。

Machine translation (Meta M2M100); the English original follows.

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 and 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. We then extend the formulation to systems with unknown dynamics using maximum-likelihood estimation and conformal calibration, and compare these approaches with direct sample-based estimation that do not incorporate structural information of SMEC problem into account. Further, with the help of bias-variance analysis, we show when incorporating structural information proves to be better than direct sample based approach. Finally, we establish finite-sample high-probability upper bounds on optimal-cost sub-optimality and original constraint-violation probability under the data-driven controller, quantifying their dependence on the number of experiments, number of samples per experiment, system dimension, input sequence dimension, and noise-to-signal ratio. Using simulations, we validate the theoretical results numerically.

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Topics: Controllability, Mathematical optimization, Upper and lower bounds, Mathematics, Sequence (biology), Optimal control

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