Discrete time schemes for optimal control problems with monotone controls

L.S. ARAGONE; L.A. PARENTE; E.A. PHILIPP

COMPUTATIONAL AND APPLIED MATHEMATICS

SPRINGER

Lugar: Sao Paulo; Año: 2015 vol. 34 p. 847 - 863

In this article we consider the Hamilton-Jacobi-Bellman (HJB) equation associated to the optimization problem with monotone controls. The problem deals with the infinite horizon case and costs with update coeficients. We study the numerical solution through the discretization in time by finite dierences. Without the classical semiconcavity-like assumptions, we prove that the convergence in this problem is of order $h^gamma$ in contrast with the order $h^{gamma/2}$ valid for general control problems. This diference arises from the simple and precise way the monotone controls can be approximated. We illustrate the result on a simple example.