An analytical approximation method for the stabilizing solution of the Hamilton-Jacobi equation based on stable manifold theory

Abstract

Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Abstract-In this paper, an analytical approximation approach for the stabilizing solution of the Hamilton-Jacobi equation using stable manifold theory is proposed. The proposed method gives approximated flows on the stable manifold of the associated Hamiltonian system and provides approximations of the stable Lagrangian submanifold. With this method, the closed loop stability is guaranteed and can be enhanced by taking higher order approximations. A numerical example shows the effectiveness of the method.