Synthesizing Structure: Patterned Control of Distributed Systems

Nature provides fabulous proofs-of-concept for distributed systems, such as flocks of starlings that perform stunning aerial displays without the direction of a single leader. Autonomous engineering systems (such as groups of robots) are often architected in the same fashion, with a control action split among several independent parts rather than being centralized. In these instances, a system's parts interact with a distinct interconnection structure - a pattern - that must be adhered to by the system's controller. This thesis explores a method for preserving patterns in control design: for several common control problems, we show how to check whether a pattern-preserving controller exists, and we provide a method by which to find one. To do so, we encode patterns through algebraic commuting relationships, and we carry those commuting relationships through the standard controller design steps of system decomposition and feedback synthesis (among others). We also discover how these patterns alter a systemâ s basic properties such as controllability and observability. Our results apply in a variety of fields, ranging from formation flying to distributed power generation and from coupled chemical tanks to self-driving cars. Though we take our initial cues from nature, we hope that our work is not just "for the birds".Ph.D