Decentralized Stackelberg Strategies for Interconnected Stochastic Dynamic Systems *

Abstract

A two-level sequential decision formulation for the control of interconnected stochastic linear discrete-time systems is investigated.A n interconnection of several systems is considered, whereby each subsystem has a decision maker and an associated quadratic cost function. One of the decision makers is designated as leader or coordinator and his control strategies are to be chosen prior to those of the others. The information available to each decision maker may be different from those of the others.The second level decision makers are regarded as followers in the context of Stackelberg strategies. Their strategies are in accordance with the Nash equilibrium concept except that the coordinator's strategy is known to all of them. The coordinator chooses his strategy under the assumption that the followers will fully exploit the prior announcement of his strategy.Recursive equations for determining the control laws for each subsystem are derived for various types of information structures. Centralized information is considered first. Finally feedback Stackelberg strategies are derived for the more realistic but more complicated (from a design computation viewpoint) situation where the subsystem control laws are based only on local subsystem measurements.