Dynamic Optimization of
Hybrid Systems and Applications
Complex dynamic systems are
often decomposed into 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). This gives rise to a “Hybrid
System.” Examples of such hybrid system settings naturally arise in manufacturing,
networks of Unmanned Autonomous Vehicles (UAVs)
or sensors, and in flow models of computer networks. Trade offs between the
higher and lower level components of hybrid systems lead to optimization problems
which are typically nondifferentiable and nonconvex.
In this presentation, problems of this type will be considered, aimed at jointly
optimizing the performance of both time-driven and event-driven system components.
It will be shown that the structure of certain problems can be exploited to
establish the uniqueness of a solution (despite the lack of convexity) and
to decompose what is at first sight a hard nonsmooth,
nonconvex optimization problem into a collection of simpler
problems, thus reducing computational complexity from exponential to linear.
An efficient solution methodology will be described and illustrated with some
interactive java applet examples of manufacturing system applications.