NUMERICAL-METHODS FOR HJB EQUATIONS OF OPTIMIZATION PROBLEMS FOR PIECEWISE DETERMINISTIC SYSTEMS

This paper deals with numerical methods for the optimization of piecew ise, stationary and deterministic systems. We mainly extend the method s used by Kushner and by Gonzales and Roffman to deal with a different kind of optimization problem and provide a comparison between these e xtended methods. The basic idea behind the numerical approximation met hods is to build a discrete Markov decision process with finite state space and finite control space which is readily solvable and approxima tes the optimization problem for the class of piecewise deterministic systems. To illustrate the usefulness of the proposed methods, a numer ical example in the field of production systems is presented.