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math.DS2026
Kernel-Based LMI Approaches to Solving the Hamilton-Jacobi-Bellman Equation and Nonlinear Optimal Control
Boumediene Hamzi, Umesh Vaidya
We present a kernel-based linear matrix inequality (LMI) approach for the approximate solution of Hamilton--Jacobi--Bellman (HJB) equations arising in nonlinear optimal control. Th…
math.DS2026
Kernel Methods for Stochastic Dynamical Systems with Application to Koopman Eigenfunctions: Feynman-Kac Representations and RKHS Approximation
Boumediene Hamzi, Houman Owhadi, Umesh Vaidya
We extend the unified kernel framework for transport equations and Koopman eigenfunctions, developed in previous work by the authors for deterministic systems, to stochastic differ…
math.DS2024
Kernel Methods for the Approximation of the Eigenfunctions of the Koopman Operator
Jonghyeon Lee, Boumediene Hamzi, Boya Hou +3
The Koopman operator provides a linear framework to study nonlinear dynamical systems. Its spectra offer valuable insights into system dynamics, but the operator can exhibit both d…