Optimal control of a class of hybrid systems

TLDR

Many manufacturing environments involve discrete jobs processed through workcenters that alter their physical characteristics, with each job possessing a temporal state governed by event-driven dynamics and a physical state governed by time-driven dynamics. The authors present a modeling framework for hybrid systems that captures event-driven and time-driven dynamics and use it to formulate and analyze optimal control problems for single-stage processes. They develop a hybrid system model that integrates event-driven and time-driven dynamics and then formulate and analyze optimal control problems for single-stage processes. They derive first-order optimality conditions and identify properties of optimal state trajectories that simplify obtaining explicit optimal control policies.

Abstract

We present a modeling framework for hybrid systems intended to capture the interaction of event-driven and time-driven dynamics. This is motivated by the structure of many manufacturing environments where discrete entities (termed jobs) are processed through a network of workcenters so as to change their physical characteristics. Associated with each job is a temporal state subject to event-driven dynamics and a physical state subject to time-driven dynamics. Based on this framework, we formulate and analyze a class of optimal control problems for single-stage processes. First-order optimality conditions are derived and several properties of optimal state trajectories (sample paths) are identified which significantly simplify the task of obtaining explicit optimal control policies.