Forward decomposition algorithms for optimal control of a class of hybrid systems

This 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 sufficient conditions that allow us to determine the structure of the optimal sample path and hence decompose a large non‐convex, non‐differentiable problem into a set of smaller convex, constrained optimization problems. Using these conditions, we develop two efficient, low‐complexity, scalable algorithms for explicitly determining the optimal controls. Several numerical examples are included to illustrate the efficacy of the proposed algorithms.