# The reproducing kernel Hilbert spaces underlying linear SDE Estimation, Kalman filtering and their relation to optimal control

@inproceedings{AubinFrankowski2022TheRK, title={The reproducing kernel Hilbert spaces underlying linear SDE Estimation, Kalman filtering and their relation to optimal control}, author={Pierre-Cyril Aubin-Frankowski and Alain Bensoussan}, year={2022} }

It is often said that control and estimation problems are in duality. Recently, in Aubin-Frankowski (2021a), we found new reproducing kernels in Linear-Quadratic optimal control by focusing on the Hilbert space of controlled trajectories, allowing for an elegant handling of state constraints and meeting points. We now extend this view to estimation problems where it is known that kernels are the covariances of stochastic processes. Here, the Markovian Gaussian processes stem from the linear…

## One Citation

### Operator-valued Kernels and Control of Infinite dimensional Dynamic Systems

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— The Linear Quadratic Regulator (LQR), which is arguably the most classical problem in control theory, was recently related to kernel methods in [1] for ﬁnite dimensional systems. We show that this…

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