Numerical methods for HJB equations of optimization problems for piecewise deterministic systems

This paper deals with numerical methods for the optimization of piecewise, stationary and deterministic systems. It mainly extends the methods used by Kushner and by Gonzales and Roffman to deal with a different kind of optimization problem and provides a comparison between these extended methods. The basic idea behind the numerical approximation methods is to build a discrete Markov decision process with finite state space and finite control space which is readily solvable and approximates the optimization problem for the class of piecewise deterministic systems. To illustrate the usefulness of the proposed methods, a numerical example in the field of production systems is presented.