A splitting algorithm for Hamilton-Jacobi-Bellman equations
The dynamic programming approach to the solution of deterministic optimal control problems gives the characterization of the value function in terms of a partial differential equation of the first order, the Hamilton-Jacobi-Bellman equation. This approach permits to compute controls in feedback form and, as a consequence, approximate optimal trajectories. The goal of this paper is to split up a problem given over a domain \(\Omega\) into a sequence of problems set in subdomains of manageable size \(\Omega_ r\), \(r= 1,\dots, d\). Roughly speaking, instead of one problem in dimension \(N\) the solutions of \(d\) problems in dimensions \(N_ r\), \(r= 1,\dots, d\) with \(N= N_ 1+\cdots+ N_ d\) are computed. In the last section results of some numerical experiments in \(\mathbb{R}^ 2\) are discussed.
scientific article; zbMATH DE number 699069
scientific article