Optimal control of hybrid systems in manufacturing

Hybrid systems combine time-driven and event-driven dynamics. This is a natural framework for manufacturing processes: The physical characteristics of production parts undergo changes at various operations described by time-driven models, while the timing control of operations is described by event-driven models. Accordingly, in the framework we propose, manufactured parts are characterized by physical states (e.g., temperature, geometry) subject to time-driven dynamics and by temporal states (e.g., operation start and stop times) subject to event-driven dynamics. We first provide a tutorial introduction to this hybrid system framework and associated optimal control problems through a single-stage manufacturing process model. We then show how th structure of the problem can be exploited to decompose what is a hard nonsmooth, nonconvex optimization problem into a collection of simpler problems. Next, we present extensions to multistage manufacturing processes for which we develop solution algorithms that make use of Bezier approximation techniques. Emphasis is given to the issue of deriving solutions through efficient algorithms, and some explicit numerical results are included.