One considers a class of systems described by a set of state equations indexed over a finite set E. A random jump process with value in E represents the perturbations affecting the system. We assume that this process if a Markov chain whose transition rates depend on the system state and control. a state discontinuity is triggered by any jump of the perturbation process. A discounted expected cost accumulated over an infinite time horizon is to be minimized. A set of optimality conditions are derived for this problem. It is shown how this theory permits the modeling of production and preventive maintenance scheduling in a flexible manufacturing system.
Published May 1987 , 31 pages