On the receding horizon hierarchical optimal control of manufacturing systems

This paper concerns the development of a hierarchical framework for the integrated planning and scheduling of a class of manufacturing systems. In this framework, dynamic optimization plays an important role in order to de®ne control strategies that, by taking into account the dynamic nature of these systems, minimize customized cost functionals subject to state and control constraints. The proposed architecture is composed of a set of hierarchical levels where a two-way information ̄ow, assuming the form of a state feedback control, is obtained through a receding horizon control scheme. The averaging e€ect of the receding horizon control scheme enables this deterministic approach to handle random and unexpected events at all levels of the hierarchy. At a given level, production targets to the subsystems immediately below are de®ned by solving appropriate optimal control problems. Ecient iterative algorithms based on optimality conditions are used to yield control strategies in the form of production rates for the various subsystems. At the lower level, this control strategy is further re®ned in such a way that all sequences of operations are fully speci®ed. The minimum cost sensitivity information provided in the optimal control formulation supports a mechanism, based on the notion of a critical machine, which plays an important role in the exploitation of the available ̄exibility. Finally, an important point to note is that our approach is particularly suited to further integration of the production system into a larger supply chain management framework, which is well supported by recent developments in hybrid systems theory.