Advances in Observability for Nonlinear Networks: Theory and Application

Abstract

Large-scale dynamic systems model a wide range of systems with great societal relevance. This includes the internet, power grids, water systems, river networks, and transportation systems. Interestingly, these systems share so much in common---their mathematical models are nearly identical, they are all nonlinear and high-dimensional, and are riddled with malicious or benign uncertainty. At its core this field can be segmented into four branches: (i) The first is concerned with physics-based modeling (differential equations modeling various processes, ranging from power flow to water quality dynamics); (ii) the second branch studies improved sensing and system monitoring (algorithms that essentially infer overall system state from limited sensor data, e.g., inferring chlorine concentrations in the network from only a few sensors); (iii) the third branch investigates realtime regulation and control to improve system behavior in the fast timescale (methods that determine optimal, varying schedules for controllers, e.g., determining ramp meter signals on highways); (iv) the fourth is concerned with network analysis and design, resource allocation, and uncertainty propagation in the long timescale (methods to improve system control, reliability, and resilience through adding or removing new nodes, edges, and sensors). This dissertation starts with utilizing well-known, nonlinear models of various systems---models that have been developed and calibrated for decades in power, water, and combustion networks. It presents contributions in branches (ii)-(iv) involving the following. First, it revisits two related classical problems in transmission power networks and water quality in drinking systems: where to place sensors to maximize information gain. In contrast to the literature, more realistic models under significant variability from uncertainty are considered. The second contribution is a new way to assess measures of observability in large-scale systems. This introduces algorithms that quantify observability while building connections with other methods in the literature. The third contribution studies uncertainty propagation in power networks at scale, yielding an understanding of system weaknesses. The final contribution designs partitioning algorithms to dissect networks into smaller ones, thereby ensuring that a wide host of methods can be applied locally without resorting to a full system analysis.