Fundamental Issues in the Control of Complex Systems

The advent of complex interconnected systems has caused several longstanding open mathematical problems to become pertinent practical problems as well. This includes the design of the smart grid, control of multi-vehicle formations, structural control of buildings to mitigate the effects of earthquakes, and many of the technologies increasingly referred to as cyber-physical systems. We will discuss the fundamental, underlying, unifying issues that arise in the control of these systems.

The main issue discussed is the design of decentralized controllers, as conventional controls analysis breaks down when multiple controllers have access to different information. It is shown that when a simple condition holds, then optimal controllers may be found via convex optimization. This condition unifies the few previously identified tractable problems, and elucidates many new ones. Subsequent work studying the synthesis of controllers for the remaining problems is then addressed.

We also discuss how the need to reduce model complexity in these systems is related to the problems of sparse estimation and compressed sensing. The need to develop parsimonious models in a dynamic fashion gives rise to the problem of sparse signal processing, and we discuss recent progress toward developing such a filter.
Michael Rotkowitz is the Queen Elizabeth II Fellow in the Department of Electrical and Electronic Engineering at the University of Melbourne, as well as an Honorary Fellow in the Department of Mathematics and Statistics. He obtained his PhD from Stanford University in 2005, and has also held positions at the Royal Institute of Technology in Stockholm and the Australian National University in Canberra. His awards include the 2005 CDC Best Student-Paper Award, the 2008 IFAC World Congress Young Author Prize, and the 2007 George Axelby Outstanding Paper Award.