Discrete time schemes for optimal control problems with monotone controls

PHILIPP, E.; ARAGONE, L; PARENTE L.

COMPUTATIONAL AND APPLIED MATHEMATICS

Springer

Año: 2015 vol. 34 p. 847 - 863

Abstract In this article we consider the Hamilton-Jacobi-Bellman (HJB)equation associated to the optimization problem with monotone controls. Theproblem deals with the innite horizon case and costs with update coecients.We study the numerical solution through the discretization in time by nitedierences. Without the classical semiconcavity-like assumptions, we provethat the convergence in this problem is of order h  in contrast with the orderh^1/2 valid for general control problems. This dierence arises from the simpleand precise way the monotone controls can be approximated. We illustrate theresult on a simple example.