Optimization and Control in Dynamical Network Systems

Abstract: Dynamical network systems are complex interconnected systems useful to describe many real world problems. The advances in information technology has led the current trend towards connecting more and more systems, creating "intelligent" systems, where the intelligence originates in the scale and complexity of the network. With the growing scale of networked systems comes also higher demands on performance and continuous availability and this creates the need for optimization and control of network systems. This thesis makes four important contributions in this area.In the first contribution, we consider a collaborative road freight transportation system. An efficiency measure for the road utilization in collaborative transportation scenarios is introduced, which evaluates the performance of collaboration strategies in comparison to an optimal central planner. The efficiency measure is used to study a freight transport simulation in Germany and taxi trips using real data from New York City. This is followed by a study of the optimal idling locations for trucks, and the optimal locations for distribution centers. These locations are then exploited in a simulation of a realistic collaborative freight transport system.The second contribution studies the important problem of gathering data that are distributed among the nodes in an anonymous network, i.e., a network where the nodes are not endowed with unique identifies. Two specific tasks are considered: to estimate the size of the network, and to aggregate the distribution of local measurements generated by the nodes. We consider a framework where the nodes require anonymity and have restricted computational resources. We propose probabilistic algorithms with low resource requirements, that quickly generate arbitrarily accurate estimates. For dynamical networks, we improve the accuracy through a regularization term which captures the trade-off between the reliability of the gathered data and a-priori assumptions for the dynamics.In the third contribution, a peer-to-peer network is utilized to improve a live-streaming media application. In particular, we study how an overlay network, constructed from simple preference functions, can be used to build efficient topologies that reduce both network latency and interruptions. We present necessary and sufficient convergence conditions, as well as convergence rate estimates, and demonstrate the improvements for a real peer-to-peer video streaming application.The final contribution is a distributed optimization algorithm. We consider a distributed multi-agent optimization problem of minimizing the sum of convex objective functions. A decentralized optimization algorithm is introduced, based on dual decomposition, together with the subgradient method for finding the optimal solution. The convergence rate is analyzed for different step size rules, constant and time-varying communication delays, and noisy communication channels.