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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

Spanish

El problema de control de la energía mínima de probabilidad (MEC) sin validez de circuito abierto requiere de entradas de control que minimicen la energía de control mientras se asegura que el estado terminal alcanza un valor deseado. En este artículo, estudiamos el problema de MEC de circuito abierto para sistemas lineales lineales de tiempo invariante. Consideramos una variedad de restricciones estocásticas que imponen que el error terminal sea \emph{small}, y demuestran que el problema de MEC estocástico directo (SMEC) puede ser formulado como un QCQP. Obtendemos la solución óptima para SMEC y mostramos que generaliza el conocido problema de MEC determinista utilizando la estimación de la máxima probabilidad-probabilidad y la simulación de la estimación de la máxima probabilidad de calib

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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