Linear quadratic control of nonlinear systems with Koopman operator learning and the Nyström method
arxiv(2024)
摘要
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 (Nyström 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 Nyström
approximation. More precisely, we study the linear quadratic regulator problem,
showing that both the approximated Riccati operator and the regulator
objective, for the associated solution of the optimal control problem, converge
at the rate m^-1/2, where m is the random subspace size. Theoretical
findings are complemented by numerical experiments corroborating our results.
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