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SUMMARY:Price Mechanisms for Distributed Control Synthesis - Professor And
 ers Rantzer (Department of Automatic Control\, Lund University\, Sweden)
DTSTART:20080502T130000Z
DTEND:20080502T140000Z
UID:TALK10542@talks.cam.ac.uk
CONTACT:Dr Guy-Bart Stan
DESCRIPTION:Many control applications involve several decentralized contro
 l units\, each with access to specific information about the system state.
   Still\, the bulk of control theory is developed in a centralized setting
 \, where all measurements are processed together to compute the control si
 gnals. This paradigm has conceptual advantages\, but also inherent limitat
 ions in terms of complexity and robustness. The purpose of this seminar is
  to sketch how some ideas from economics and game theory may help to go be
 yond the traditional paradigm and support distributed control synthesis fo
 r dynamical systems.\n\nIterative synthesis procedures with provable conve
 rgence to a Nash equilibrium for classes of games are generally hard to ob
 tain. Similar difficulties appear in general equilibrium theory of economi
 cs when it comes to price negotiations aiming for a Walras equilibrium.  H
 owever\, engineering applications often allow us to make the following two
  simplifying assumptions:\n\n1. Every agent has a utility function that is
  ``linear in money''.\n\n2. Agents have no incentive to hide or encode inf
 ormation in their decisions.\n\nUnder the first assumption\, a classical a
 rgument shows that price convergence towards an equilibrium is achieved by
  the gradient algorithm. In this presentation we use the same method for i
 teration of control policies towards a Nash equilibrium. We give discrete 
 time conditions for convergence that can be verified locally without acces
 s to the global model anywhere. Simple examples are discussed.
LOCATION: Cambridge University Engineering Department\, Lecture Room 12
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