Perturbation analysis: A framework for data-driven control and optimization of discrete event and hybrid systems

The history of Perturbation Analysis (PA) is intimately related to that of Discrete Event Dynamic Systems (DEDS), starting with a solution of a long-standing problem in the late 1970s and continuing today with the control and optimization of Hybrid Systems and the emergence of event-driven control methods. We review the origins of the PA theory and how it became part of a broader framework for modelling, control and optimization of DEDS. We then discuss the theoretical underpinnings of Infinitesimal Perturbation Analysis (IPA) as a data-driven stochastic gradient estimation method and how it has been applied over the past few decades. We explain how IPA offers a basis for general-purpose stochastic optimization of Markovian systems through the notion of the performance potential and how it has evolved beyond DEDS and now provides a framework for control and optimization of Hybrid Systems and, more generally, event-driven methodologies.