, Volume 15, Issue 1, pp 1-13

A numerical approach to the infinite horizon problem of deterministic control theory

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Abstract

We are concerned with the Hamilton-Jacobi equation related to the infinite horizon problem of deterministic control theory. Approximate solutions are constructed by means of a discretization in time as well as in the state variable and we prove that their rate of convergence to the viscosity solution is of order 1, provided a semiconcavity assumption is satisfied. A computational algorithm, originally due to R. Gonzales and E. Rofman, is adapted and reformulated for the problem at hand in order to obtain an error estimate for the numerical approximate solutions.

This work has been partially supported by CNR-GNAFA.
Communicated by W. Fleming