Morphisms of networks of hybrid open systems

Schmidt, Arnold James

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https://hdl.handle.net/2142/106210 Copy

Description

Title

Morphisms of networks of hybrid open systems

Author(s)

Schmidt, Arnold James

Issue Date

2019-12-06

Director of Research (if dissertation) or Advisor (if thesis)

Lerman, Eugene

Doctoral Committee Chair(s)

DeVille, Lee

Committee Member(s)

• Berwick-Evans, Dan
• Nijholt, Eddie

Department of Study

Mathematics

Discipline

Mathematics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

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

Abstract

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.

Graduation Semester

2019-12

Type of Resource

text

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

Copyright and License Information

Copyright 2019 by Arnold James Schmidt. All rights reserved.

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