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Article | REF: AF1374 V1

Optimal Control

Author: J. Frédéric BONNANS

Publication date: April 10, 2015

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10. Numerical diagrams for the HJB equation

In this section, we assume that the cost and dynamics functions are Lipschitzian and bounded. We begin by discretizing the finite-horizon problem (121) .

10.1 Finite differences, scalar state

We are given a number of time steps N and therefore a time step h 0 := T/N; the discretization instants are t k := kh 0 , k = 0 to N. The space step is h 1 > 0, and the spatial grid points are x ...

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