Hamilton-Jacobi-Bellman equations on time scales

Abstract

In this paper, we consider a class of optimal control problems on time scales without state constraints, target conditions or the fixed terminal time. We first present and show a time scale version of the Bellman optimality principle. On this basis, using a chain rule of multivariables on time scales, we will derive Hamilton-Jacobi-Bellman equations on a time scale for these kind of optimal control problems. Finally, the quantum time scale is considered as an example to illustrate our results. © 2009 Elsevier Ltd. All rights reserved.