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Learning Minimum-Energy Controls from Heterogeneous Data

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Document pages: 6 pages

Abstract: In this paper we study the problem of learning minimum-energy controls forlinear systems from heterogeneous data. Specifically, we consider datasetscomprising input, initial and final state measurements collected usingexperiments with different time horizons and arbitrary initial conditions. Inthis setting, we first establish a general representation of input and sampledstate trajectories of the system based on the available data. Then, we leveragethis data-based representation to derive closed-form data-driven expressions ofminimum-energy controls for a wide range of control horizons. Further, wecharacterize the minimum number of data required to reconstruct theminimum-energy inputs, and discuss the numerical properties of our expressions.Finally, we investigate the effect of noise on our data-driven formulas, and,in the case of noise with known second-order statistics, we provide correctedexpressions that converge asymptotically to the true optimal control inputs.

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