A Curse-of-Dimensionality-Free Numerical Method for a Class of HJB PDE's
Abstract
Max-plus methods have been explored for solution of first-order,nonlinear Hamilton-Jacobi-Bellman partial differential equations(HJB PDEs) and corresponding nonlinear control problems.These methods exploit the max-plus linearity of the associated semigroups.Although these methods provide advantages,they still suffer from the curse-of-dimensionality.Here we consider HJB PDEs where the Hamiltonian takes the formof a (pointwise) maximum of linear/quadratic forms.We obtain a numerical method not subject to the curse-of-dimensionality.The method is based on construction of the dual-spacesemigroup corresponding to the HJB PDE.This dual-space semigroup is constructed from thedual-space semigroups corresponding to the constituent Hamiltonians.
