November 02, 2011, ESB 2001

Stabilization and disturbance attenuation are two classical problems in Control. A re-formulation of these problems in the context of networked systems is presented. Stabilization is discussed in the framework of cooperative distributed control. Disturbance attenuation in the framework of non-cooperative decentralized control. In the cooperative case agents exchange information over a consensus network. By freezing inputs over time-intervals of proper length, their values can be propagated over the network in real time. Two observer-based results are presented for the case of sampled-data systems and discrete-time systems. In the non-cooperative case the disturbance attenuation problem is discussed from the viewpoint of Equilibrium Invariance, a set theoretic notion akin to the notion of Nash equilibrium in games. It is assumed that agents have convex bounded constraints on their control variable and face a convex bounded exogenous disturbance. An invariant equilibrium obtains when each agent succeeds in keeping its own output inside a convex bounded domain irrespective of the action of other agents and of disturbance. Invariant equilibria and corresponding strategies can be obtained via a LMI formulation. Potential application in Finance is discussed.

The author is associate professor at the Electrical and Information Engineering Department of the University of L'Aquila, Italy. His interests are in the area of constrained control, dynamic games, learning automata, optimization and applications in Economics.