UTRC CDS Lecture: Ashutosh Nayyar, "Sufficient Statistics for Linear Control Strategies"
Friday, September 11, 2015
1146 A V Williams
301 405 6576
UTRC Control and Dynamical Systems Invited Lecture
Sufficient Statistics for Linear Control Strategies in Decentralized LQG Problems
Department of Electrical Engineering
University of Southern California
We consider two classes of decentralized control problems with linear dynamics, quadratic costs and Gaussian disturbances (also called decentralized LQG problems). In the first class, the coupling of dynamics among subsystems and the inter-controller communication are characterized by the same directed graph. If this graph is a multitree, we show that each controller need only estimate the states of the sub-systems it affects (its descendants) as well as the sub-systems it observes (its ancestors). The optimal control action for each controller is a linear function of the estimate it computes and the estimates computed by its ancestors. Moreover, all state estimates may be updated recursively, much like a Kalman filter.
The second class of problems involves a decentralized LQG system with partial history sharing information structure where linear control strategies are not always optimal. Nonetheless, linear control strategies are appealing due to their analytic and implementation simplicity. We identify finite-dimensional and recursively updatable sufficient statistics for the best linear control strategies in these problems.
Ashutosh Nayyar is an assistant professor in the electrical engineering department at the University of Southern California. He received the B.Tech. degree in Electrical Engineering from the Indian Institute of Technology, Delhi, India. He received the MS and PhD degree in Electrical Engineering and Computer Science from the University of Michigan, Ann Arbor. He worked as a post-doctoral researcher at the University of Illinois at Urbana-Champaign and at the University of California, Berkeley. His research focuses on the theory and applications of decentralized decision-making in a wide array of decentralized systems such as: sensing and communication systems, decentralized control systems, cyber-physical systems and electric energy systems.