Anders Rantzer, LTH
Many control applications have a decentralized structure, where each subunit as access to different information about the system state. Still, most control theory has been developed in a centralized setting, where all measurements are processed together to compute the control signals. This paradigm has conceptual advantages, but also inherent limitations in terms of complexity and integrity. The purpose of this lecture is to show how ideas from convex optimization and game theory may help to go beyond the traditional paradigm to support analysis and synthesis of distributed controllers.
In particular, we will reconsider well established methods for decomposition of large scale optimization problems by introduction of dual variables. These can be interpreted as prices in a market mechanism serving to achieve mutual agreement between different subproblems. The same idea can be used for decomposition of large scale control systems, with dynamics in both decision variables and prices. The dynamics bring interesting new phenomena. For example, expected future prices could be highly relevant for todays decisions.