An improved forward algorithm for optimal control of a class of hybrid systems

This note 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 a new property of the optimal state trajectory structure which holds under a modified condition on the cost function. This allows us to develop a low-complexity, scalable algorithm for explicitly determining the optimal controls, which can be more efficient than the best algorithm to date, known as the Forward Algorithm. A numerical example is included to illustrate the efficacy of the proposed algorithm, and to compare it with the Forward Algorithm.