On opportunities in distributed control theory
A control problem is considered where several control units are supposed to cooperate, but they all have access to different information about the system state. Considerable progress in the mathematical understanding of such problems has recently been reported from several directions. One example is the analysis of dynamic interaction between routers and sources in the Internet. Another example is synchronization in networks of nonlinearly coupled oscillators.
Versions of the problem have a long history in economic literature as well as in statistical decision theory. Some instances were solved in the 1960-70's, but significant progress has recently been made. In this seminar, we give an introduction to the problem and show how linear matrix inequalities for solution of the classical LQG control problem can be modified to accommodate more complex information patterns. We also discuss how some distributed control laws can be interpreted in economic terms using price mechanisms.