A continuous-time fundamental lemma and its application in data-driven optimal control

Data-driven control of discrete-time and continuous-time systems is of tremendous research interest. In this paper, we explore data-driven optimal control of continuous-time linear systems using input–output data. Based on a density result, we rigorously derive error bounds for finite-order polynomial approximations of elements of the system behavior. To this end, we leverage a link between latent variables and flat outputs of controllable systems. Combined with a continuous-time counterpart of Willems et al.’s fundamental lemma, we characterize the suboptimality resulting from polynomial approximations in data-driven linear–quadratic optimal control. Finally, we draw upon a numerical example to illustrate our results.

Subjects

Continuous time

Data-driven control

Differential flatness

Identifiable

Persistency of excitation

Polynomial approximation

DDC Class

620: Engineering

515: Analysis

003: Systems Theory

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publishedVersion

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https://creativecommons.org/licenses/by/4.0/

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1-s2.0-S016769112400238X-main.pdf

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Main Article

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707.04 KB

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A continuous-time fundamental lemma and its application in data-driven optimal control