June 07, 2013, Webb 1100

In this talk, we consider a fully decentralized cooperative control problem with two dynamically decoupled agents. The objective is to design a state-feedback controller for each agent such that a global quadratic cost is minimized. No communication, explicit or implicit, is permitted between the agents or their controllers. The agents are coupled through the cost function and the process noise alone. Our main result is an explicit and generically minimal state-space construction of the optimal controller. Surprisingly, the optimal controller is dynamic, and it has a number of states that scales with the rank of the covariance between the process noise of each agent. The key step in the solution is a special decomposition of the noise covariance that splits the associated convex program into simpler fundamental problems that can be solved separately. This insight leads to a physical interpretation for the states of the optimal controller as well as a new separation principle for decentralized control.

Laurent Lessard received the B.A.Sc. degree in Engineering Science from the University of Toronto in 2003, and the M.S. and Ph.D. degrees in Aeronautics and Astronautics from Stanford University in 2005 and 2011 respectively. He is currently a postdoctoral scholar in Mechanical Engineering at the University of California, Berkeley. Prior to coming to Berkeley, he was a postdoctoral scholar for one year in the Department of Automatic Control at Lund University, Sweden. His research interests include optimization and control, with an emphasis on large or complex applications such as adaptive optics, power grids, and distributed safety validation.