Control of stochastically interacting systems on networks

Abstract

The goal of this thesis is to develop control theoretic analysis and algorithms for characterizing and controlling stochastically interacting systems on networks. Such systems have three essential features - (i) they are stochastic processes, (ii) they are made up several individual components connected through a network, and (iii) the connected components influence one another through local interactions. This thesis presents analysis and control of three representative examples of such systems from the fields of spreading processes, smart manufacturing, and transport phenomena. In the first part of the thesis, control of spreading processes on lattices is considered. Analysis and control of spreading processes is difficult because the dimensionality of state space is often large. A common approach to this issue is to use mean field approximations which completely average out the stochasticity inherent to these systems. Instead this thesis, using recently developed tools from nonequilibrium statistical physics, accurately characterizes open loop behavior of spreading processes in its stable, neutral and unstable regimes. Such a characterization is not possible using approximate models. Furthermore, for an unstable spreading process, a randomized control policy is proposed that is optimal in both resource allocation and control effort. In the second part of the thesis, control of smart manufacturing processes is considered. Due to increased product customization and rapidly changing demands, the recent trend in manufacturing is to shift towards modular architectures. Such a shift presents scheduling challenges in a rapidly and dynamically changing environment. This thesis presents a queuing theory framework for modeling job flow, and a stochastic scheduling algorithm. Such an approach is amenable for fast implementation while achieving balanced load among operating agents. In the last part of the thesis, control of transport phenomena is considered. Transport phenomena are systems that are in nonequilibrium. Even though study and analysis of systems exhibiting nonequilibrium phenomena have been considered in the past, there is no effective way to control or modify the behavior of these systems. This thesis presents control theoretic formulations for systems in nonequilibrium. Starting from a paradigmatic model for traffic flow known as totally asymmetric simple exclusion process (TASEP), thesis presents routing policies to achieve maximum flow rate of traffic for all set of input traffic conditions. Extensions are also made to TASEP models on intersections and generic road networks.