• Corpus ID: 251564640

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… 

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References

SHOWING 1-10 OF 35 REFERENCES

Linearly Constrained Linear Quadratic Regulator from the Viewpoint of Kernel Methods

This study presents how matrix-valued reproducing kernels allow for an alternative viewpoint in the linear quadratic regulator problem, and introduces a strengthened continuous-time convex optimization problem which can be tackled exactly with finite dimensional solvers, and which solution is interior to the constraints.

Operator-valued Kernels and Control of Infinite dimensional Dynamic Systems

— 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

Interpreting the dual Riccati equation through the LQ reproducing kernel

It is shown that LQ optimal control can be seen as a regression problem over the space of controlled trajectories, and that the latter has a very natural structure as a reproducing kernel Hilbert space (RKHS).

General duality between optimal control and estimation

  • E. Todorov
  • Mathematics
    2008 47th IEEE Conference on Decision and Control
  • 2008
This work obtains a more natural form of LQG duality by replacing the Kalman-Bucy filter with the information filter and generalizes this result to non-linear stochastic systems, discrete stochastics systems, and deterministic systems.

New Results in Linear Filtering and Prediction Theory

The Duality Principle relating stochastic estimation and deterministic control problems plays an important role in the proof of theoretical results and properties of the variance equation are of great interest in the theory of adaptive systems.

Duality for Nonlinear Filtering

Nearly 60 years ago, in a celebrated paper of Kalman and Bucy, it was established that optimal estimation for linear Gaussian systems is dual to a linear-quadratic optimal control problem. In this

Tropical reproducing kernels and optimization

. Hilbertian kernel methods and their positive semidefinite kernels have been extensively used in various fields of applied mathematics and ma- chine learning, owing to their several equivalent

An Introduction to Infinite-Dimensional Analysis

In this revised and extended version of his course notes from a 1-year course at Scuola Normale Superiore, Pisa, the author provides an introduction – for an audience knowing basic functional