 |
Center for Nonlinear Studies |
The rapid development of mobile computers, smart sensors, and communication networks has brought a new reality into our world – large-scale complex networks with massive amounts of data. This new reality has had broad affects in various fields of engineering; prominent examples include power systems, machine learning, and autonomous vehicles. Among potential approaches for handling the vast quantities of information in such emerging systems, distributed algorithms have several potential advantages over centralized approaches. In particular, distributed algorithms can improve cybersecurity, reduce the expense of communication infrastructure, and stimulate parallel and local computations. The focus of this talk has two parts. In the first part, I will present the most popular and well-studied algorithms in the literature, namely distributed gradient methods, while explicitly accounting for network delays, one of the most critical issues in distributed systems. In particular, I show the convergence of such algorithms in the presence of uniform, but possibly arbitrarily large, communication delays between the agents. Moreover, I provide an upper bound on the rate of convergence of the algorithm as a function of the network size, topology, and the delays. In the second part, I will talk about network resource allocation problems, which have numerous applications in many areas including power systems. I will introduce distributed Lagrangian methods in solving these problems. I then apply such methods to solve multi-area optimal power flow problems under uncertainty in power systems and show some simulations on the IEEE test systems. Finally, I conclude my talk with some directions for my future research.
Host: Carleton Coffrin