Games and Price Mechanisms for Distributed Control

Anders Rantzer, Lund University


Many control applications have a decentralized structure,
where each subunit has 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 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.