Morphisms of Networks of Hybrid Open Systems

TL;DR

This thesis develops a categorical framework for networks of hybrid open systems, defining morphisms and relations that preserve system interconnections and generalize the concept of networks as collections of interconnected systems.

Contribution

It introduces a formal categorical approach to hybrid open systems and networks, establishing morphisms and relations that preserve system interconnections and generalize existing frameworks.

Findings

Relations among system pairs induce relations among interconnected systems

The formalism preserves morphisms when building networks

Provides a categorical foundation for hybrid open systems

Abstract

This thesis (defended 10/07/2019) develops a theory of networks of hybrid open systems and morphisms. It builds upon a framework of networks of continuous-time open systems as product and interconnection. We work out categorical notions for hybrid systems, deterministic hybrid systems, hybrid open systems, networks of hybrid open systems, and morphisms of networks of hybrid open systems. We also develop categorical notions for abstract systems, abstract open systems, networks of abstract open systems, and morphisms of networks of abstract open systems. We show that a collection of relations holding among pairs of systems induces a relation between interconnected systems. We use this result for abstract systems to prove a corresponding result for networks of hybrid systems. This result translates as saying that our procedure for building networks preserves morphisms of open systems: a collection of morphisms of (sub)systems is sent to a morphism of networked systems. We thus both justify our formalism and concretize the intuition that a network is a collection of systems pieced together in a certain way.