Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userNetworks of hybrid open systems
100
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We generalize the results of Networks of open systems by the first author to the setting of hybrid systems. In particular we introduce the notions of hybrid open systems, their networks and maps between networks. A network of systems is a blueprint for building a larger system out of smaller subsystems by specifying a pattern of interactions between subsystems --- an interconnection map. Maps between networks allow us to produce maps between complex hybrid dynamical systems by specifying maps between their subsystems
rate research
Read More
Many systems of interest in science and engineering are made up of interacting subsystems. These subsystems, in turn, could be made up of collections of smaller interacting subsystems and so on. In a series of papers David Spivak with collaborators formalized these kinds of structures (systems of systems) as algebras over presentable colored operads. It is also very useful to consider maps between dynamical systems. This amounts to viewing dynamical systems as objects in an appropriate category. This is the point taken by DeVille and Lerman in the study of dynamics on networks. The goal of this paper is to describe an algebraic structure that encompasses both approaches to systems of systems. To this end we replace the monoidal category of wiring diagrams by a monoidal double category whose objects are surjective submersions. This allows us, on one hand, build new large open systems out of collections of smaller open subsystems and on the other keep track of maps between open systems. As a special case we recover the results of DeVille and Lerman on fibrations of networks of manifolds.
We propose a definition of the category of hybrid systems in which executions are special types of morphisms. Consequently morphisms of hybrid systems send executions to executions. We plan to use this result to define and study networks of hybrid systems.
Many systems of interest in science and engineering are made up of interacting subsystems. These subsystems, in turn, could be made up of collections of smaller interacting subsystems and so on. In a series of papers David Spivak with collaborators formalized these kinds of structures (systems of systems) as algebras over presentable colored operads. It is also very useful to consider maps between dynamical systems, which in effect amounts to viewing dynamical systems as objects in an appropriate category. This is the point of view taken by DeVille and Lerman in the study of dynamics on networks. The goal of this paper is to describe an algebraic structure that encompasses both approaches to systems of systems. This allows us, on one hand, build new large open systems out of collections of smaller open subsystems and on the other keep track of maps between open systems. Consequently we obtain synchrony results for open systems which generalize the synchrony results of Golubitsky, Stewart and their collaborators for groupoid invariant vector fields on coupled cell networks.
We establi
We propose a new framework for the study of continuous time dynamical systems on networks. We view such dynamical systems as collections of interacting control systems. We show that a class of maps between graphs called graph fibrations give rise to maps between dynamical systems on networks. This allows us to produce conjugacy between dynamical systems out of combinatorial data. In particular we show that surjective graph fibrations lead to synchrony subspaces in networks. The injective graph fibrations, on the other hand, give rise to surjective maps from large dynamical systems to smaller ones. One can view these surjections as a kind of fast/slow variable decompositions or as abstractions in the computer science sense of the word.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
