A collocation-based approach to solve the finite horizon Hamilton-Jacobi-Bellman equation

Abstract

This paper presents an approach to derive the optimal feedback control laws by solving the finite time Hamilton Jacobi Ballman equation. Conventional methods to solve the HJB equation suffer from curse of dimensionality as the number of spatial variables is equal to the state dimension, which is twice the number of degrees of freedom of a mechanical system. The presented approach exploits the recently developed non-product quadrature method known as Conjugate Unscented Transformation (CUT) in conjunction with sparse approximation tools to devise a collocation method to solve the HJB equation in a computationally efficient manner. Numerical simulation results are presented to assess the efficacy of the proposed ideas.