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Title:Morphisms of networks of hybrid open systems
Author(s):Schmidt, Arnold James
Director of Research:Lerman, Eugene
Doctoral Committee Chair(s):DeVille, Lee
Doctoral Committee Member(s):Berwick-Evans, Dan; Nijholt, Eddie
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(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.
Issue Date:2019-12-06
Type:Text
URI:http://hdl.handle.net/2142/106210
Rights Information:Copyright 2019 by Arnold James Schmidt. All rights reserved.
Date Available in IDEALS:2020-03-02
Date Deposited:2019-12


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