We examine two problems of contemporary interest, both involving the optimal operation of distributed stochastic dynamic systems, one in power systems and another in communication networks. In power systems we address the problem faced by an Independent System Operator which has to optimally utilize a mix of fossil fuel based and renewable generators, controllable and uncontrollable loads, prosumers and storage services, so as to maximize social welfare, without knowing details of any of the entities involved. We revisit general equilibrium theory, addressing the complexity raised by dynamic stochastic agents with privacy concerns. We show how optimality can be attained through stochastic prices discovered by iterative tatonnement mechanisms.
P. R. Kumar obtained his B. Tech. degree in Electrical Engineering (Electronics) from I.I.T. Madras in 1973, and the M.S. and D.Sc. degrees in Systems Science and Mathematics from Washington University, St. Louis, in 1975 and 1977, respectively. From 1977-84 he was a faculty member in the Department of Mathematics at the University of Maryland Baltimore County. From 1985-2011 he was a faculty member in the Department of Electrical and Computer Engineering and the Coordinated Science Laboratory at the University of Illinois. Currently he is at Texas A&M University, where he is a University Distinguished Professor and holds the College of Engineering Chair in Computer Engineering. Kumar is a member of the National Academy of Engineering of the USA, and a Fellow of the World Academy of Sciences. He was awarded an honorary doctorate by the Swiss Federal Institute of Technology (Eidgenossische Technische Hochschule) in Zurich. He received the Outstanding Contribution Award of ACM SIGMOBILE, the IEEE Field Award for Control Systems, the Donald P. Eckman Award of the American Automatic Control Council, and the Fred W. Ellersick Prize of the IEEE Communications Society. He is an ACM Fellow and a Fellow of IEEE. He was a Guest Chair Professor and Leader of the Guest Chair Professor Group on Wireless Communication and Networking at Tsinghua University, Beijing, China. He is an Honorary Professor at IIT Hyderabad. He is a D. J. Gandhi Distinguished Visiting Professor at IIT Bombay. He was awarded the Distinguished Alumnus Award from IIT Madras, the Alumni Achievement Award from Washington University in St. Louis, and the Daniel C. Drucker Eminent Faculty Award from the College of Engineering at the University of Illinois.