Papers › Linear quadratic control of nonlinear systems with Koopman operator learning and the...

Linear quadratic control of nonlinear systems with Koopman operator learning and the Nyström method

5 Mar 2024arXiv:2403.02811archive 2025-07-28

Edoardo Caldarelli, Antoine Chatalic, Adrià Colomé, Cesare Molinari, Carlos Ocampo-Martinez, Carme Torras, Lorenzo Rosasco

In this paper, we study how the Koopman operator framework can be combined with kernel methods to effectively control nonlinear dynamical systems. While kernel methods have typically large computational requirements, we show how random subspaces (Nystr\"om approximation) can be used to achieve huge computational savings while preserving accuracy. Our main technical contribution is deriving theoretical guarantees on the effect of the Nystr\"om approximation. More precisely, we study the linear quadratic regulator problem, showing that the approximated Riccati operator converges at the rate m^(-1/2), and the regulator objective, for the associated solution of the optimal control problem, converges at the rate m⁻¹, where m is the random subspace size. Theoretical findings are complemented by numerical experiments corroborating our results.

PaperPDFCode

Code

lcsl/nys-koop-lqr officialmentioned in paper report

Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.

Code Syntology ran Syntology

Not run by Syntology. Nothing on this page verifies that the listed code works.

Tasks

Operator learning

Results from the paper archive 2025-07-28

No leaderboard rows for this paper in the archive.

Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections