6 papers
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…
Kernel Methods for Some Transport Equations with Application to Learning Kernels for the Approximation of Koopman Eigenfunctions: A Unified Approach via Variational Methods, Green's Functions and the Method of Characteristics
Boumediene Hamzi, Houman Owhadi, Umesh Vaidya
We present a unified theoretical and computational framework for constructing reproducing kernels tailored to transport equations and adapted to Koopman eigenfunctions of nonlinear…
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…
Kernel Methods for the Construction of Certified Lyapunov Functions via Approximate Koopman Eigenfunctions
P. Giesl, S. Hafstein, B. Hamzi +4
We present a kernel-based methodology for constructing Lyapunov functions for nonlinear dynamical systems using approximate Koopman eigenfunctions. Our approach decomposes principa…
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…
Extensions of the Path-integral formula for computation of Koopman eigenfunctions
Shankar A. Deka, Umesh Vaidya
Representing nonlinear dynamical systems using the Koopman Operator and its spectrum has distinct advantages in terms of linear interpretability of the model as well as in analysis…