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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 timedriven 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.

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SUMMARYThis paper considers optimal control problems for a class of hybrid systems motivated by the structure of manufacturing environments that integrate process and operations control. We derive new necessary and su$cient conditions that allow us to determine the structure of the optimal sample path and hence decompose a large non-convex, non-di!erentiable problem into a set of smaller convex, constrained optimization problems. Using these conditions, we develop two e$cient, low-complexity, scalable algorithms for explicitly determining the optimal controls. Several numerical examples are included to illustrate the e$cacy of the proposed algorithms.

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 timedriven 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.