Morphisms of networks of hybrid open systems

This dissertation develops a theory of networks of hybrid open systems and morphisms. This theory 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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2020

Author dc:creator

• Schmidt, Arnold James

Contributors dc:contributor

• Lerman, Eugene
• DeVille, Lee
• Berwick-Evans, Dan
• Nijholt, Eddie

• networks of open systems, hybrid systems, category theory, control systems, dynamical systems

Statement dc:rights

• Copyright 2019 by Arnold James Schmidt. All rights reserved.

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/106210

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/106210