Summary
International Symposium on Nonlinear Theory and Its Applications
2022
Session Number:B1L-B
Session:
Number:B1L-B-04
Spectral Analysis of Koopman Operator and Hamilton Jacobi Equation
Umesh Vaidya,
pp.217-218
Publication Date:12/12/2022
Online ISSN:2188-5079
Summary:
We present an approach based on the spectral analysis of Koopman operator for the approximate solution of the Hamilton Jacobi equation. It is well-known that one can associate an Hamiltonian dynamical system with the Hamilton Jacobi equation. Furthermore, Lagrangian submanifold plays of the Hamiltonian dynamical system plays a fundamental role in the solution of Hamilton Jacobi equation. We show that the principal eigenfunctions of the Koopman operator associated with the Hamiltonian dynamical system can be used in the construction of Lagrangian submanifold thereby approximating the solution of the Hamiltonian Jacobi equation. The construction procedure for the approximate solution of Hamiltonian Jacobi equation is convex and data-driven. The application of the developed framework is demonstrated on solving the optimal control and robust control problems. Simulation results are presented to validate the main findings of the paper.