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Communication Dans Un Congrès Année : 2022

Operator-valued Kernels and Control of Infinite dimensional Dynamic Systems

Résumé

The Linear Quadratic Regulator (LQR), which is arguably the most classical problem in control theory, was recently related to kernel methods in (Aubin-Frankowski, SICON, 2021) for finite dimensional systems. We show that this result extends to infinite dimensional systems, i.e.\ control of linear partial differential equations. The quadratic objective paired with the linear dynamics encode the relevant kernel, defining a Hilbert space of controlled trajectories, for which we obtain a concise formula based on the solution of the differential Riccati equation. This paves the way to applying representer theorems from kernel methods to solve infinite dimensional optimal control problems.

Dates et versions

hal-03811584 , version 1 (12-10-2022)

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Pierre-Cyril Aubin-Frankowski, Alain Bensoussan. Operator-valued Kernels and Control of Infinite dimensional Dynamic Systems. CDC 2022 - 61st IEEE Conference on Decision and Control, Dec 2022, Cancun, Mexico. ⟨hal-03811584⟩
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