A hierarchical decomposition method for optimal control of hybrid systems

We consider optimal control problems for hybrid systems with a separable cost structure allowing us to decompose them into two components: a lower-level component with time-driven dynamics (describing the physical state of the system) interacting with a higher-level component with event-driven dynamics (describing the changes in the operating modes of the system). We develop a hybrid controller which aims at jointly optimizing the performance of both hierarchical components. We demonstrate this approach on two problems: a linear system switching from one operating mode to another and a multistage manufacturing system. In the first problem, the main difficulty is due to the coupling of the physical states across modes, whereas in the second it is due to the nondifferentiable event-driven dynamics.