Design of Optimal Sparse Feedback Gains via the Alternating Direction Method of Multipliers

Prof. Mihailo Jovanovic
Department of Electrical and Computer Engineering
University of Minnesota

Abstract:

This talk is about design of sparse and block sparse feedback gains that minimize the variance of distributed systems. Our approach consists of two steps. First, we identify sparsity patterns of the feedback gains by incorporating sparsity-promoting penalty functions into the optimal control problem, where the added terms penalize the number of communication links in the distributed controller. Second, we optimize the state feedback gains subject to the structural constraints determined by the identified sparsity patterns. This polishing step improves the performance of the distributed controllers. In the first step, we identify sparsity patterns of the feedback gains using the alternating direction method of multipliers, which is a powerful algorithm well-suited to large optimization problems. This method alternates between optimizing the sparsity and optimizing the closed-loop variance, which allows us to exploit the structure of the corresponding objective functions. In particular, we take advantage of the separability of the sparsity-promoting penalty functions to decompose the minimization problem into sub-problems that can be solved analytically. In the second step, we develop Newton's method in conjunction with the conjugate gradient scheme to efficiently compute the optimal sparse feedback matrix. Several examples are provided to illustrate the effectiveness of the developed approach.

Bio:

Mihailo R. Jovanovic (http://www.ece.umn.edu/users/mihailo/) received the Dipl. Ing. and M.S. degrees from the University of Belgrade, Serbia, in 1995 and 1998, respectively, and the Ph.D. degree from the University of California, Santa Barbara, in 2004. Before joining the University of Minnesota, Minneapolis, he was a Visiting Researcher with the Department of Mechanics, the Royal Institute of Technology, Stockholm, Sweden, from September to December 2004. Currently, he is an Associate Professor of Electrical and Computer Engineering at the University of Minnesota, where he serves as the Director of Graduate Studies in the interdisciplinary Ph.D. program in Control Science and Dynamical Systems.

Prof. Jovanovic's expertise is in modeling, dynamics, and control of large-scale and distributed systems and his current research focuses on sparsity-promoting optimal control, dynamics and control of fluid flows, and fundamental limitations in the control of vehicular formations. He is a member of IEEE, APS, and SIAM and has served as an Associate Editor of the IEEE Control Systems Society Conference Editorial Board from July 2006 until December 2010. He received a CAREER Award from the National Science Foundation in 2007, and an Early Career Award from the University of Minnesota Initiative for Renewable Energy and the Environment in 2010.