On the Abstract Structure of the Behavioral Approach to Systems Theory
Elie M. Adam, Munther A. Dahleh

TL;DR
This paper formalizes the abstract pattern underlying the behavioral approach to systems theory, emphasizing the roles of syntax, semantics, and interconnection, to better understand interaction phenomena in systems.
Contribution
It introduces a categorical framework that explicitly captures the structure of the behavioral approach, highlighting the interplay between syntax, semantics, and interconnection.
Findings
Separated behavioral equations and behaviors via syntax and semantics spaces.
Interconnection modeled as a construction similar to topological gluing.
Interpretation map preserves interconnection structure from syntax to semantics.
Abstract
We revisit the behavioral approach to systems theory and make explicit the abstract pattern that governs it. Our end goal is to use that pattern to understand interaction-related phenomena that emerge when systems interact. Rather than thinking of a system as a pair , we begin by thinking of it as an injective map from . This relative perspective naturally brings about the sought structure, which we summarize in three points. First, the separation of behavioral equations and behavior is developed through two spaces, one of syntax and another of semantics, linked by an interpretation map. Second, the notion of interconnection and variable sharing is shown to be a construction of the same nature as that of gluing topological spaces or taking amalgamated sums of algebraic objects. Third, the notion of interconnection…
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Taxonomy
TopicsGene Regulatory Network Analysis · Control and Stability of Dynamical Systems · Complex Systems and Dynamics
