Together with Bruno Gaujal and Arie Hordijk, we layed some foundations for non Markovian control of discrete event dynamic systems in a series of papers. The theory is related to multimodularity properties of the immediate cost functions. As applications, we consider admission control, and control of polling, service and vacations, into quite general systems (those that can be described as linear in the max-plus algebra). We pursue our research in non-Markovian closed-loop control as well, and we currently study new applications of our theory.
Another paper on non Markovian control is
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