Open Access
Fundamental Study Bisimulation relations for dynamical, control, and hybrid systems
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TLDR
In this article, the notion of bisimulation equivalence for dynamical systems as well as control systems has been introduced, inspired by the categorical framework of Joyal, Nielsen and Winskel.Abstract:
The fundamental notion of bisimulation equivalence for concurrent processes, has escaped the world of continuous, and subsequently, hybrid systems. Inspired by the categorical framework of Joyal, Nielsen and Winskel, we develop novel notions of bisimulation equivalence for dynamical systems as well as control systems. We prove that these notions can be captured by the abstract notion of bisimulation as developed by Joyal, Nielsen and Winskel. This is the first unified notion of system equivalence that transcends discrete and continuous systems. Furthermore, this enables the development of a novel and natural notion of bisimulation for hybrid systems, which is the final goal of this paper. © 2005 Elsevier B.V. All rights reserved.read more
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Book
Communication and Concurrency
TL;DR: This chapter discusses Bisimulation and Observation Equivalence as a Modelling Communication, a Programming Language, and its application to Equational laws.
Book
Nonlinear Control Systems
Alberto Isidori,M. Thoma,Eduardo D. Sontag,B. W. Dickinson,A. Fettweis,J. L. Massey,J. W. Modestino +6 more
TL;DR: In this paper, a systematic feedback design theory for solving the problems of asymptotic tracking and disturbance rejection for linear distributed parameter systems is presented, which is intended to support the development of flight controllers for increasing the high angle of attack or high agility capabilities of existing and future generations of aircraft.
Book
A comprehensive introduction to differential geometry
TL;DR: Spivak's comprehensive introduction to differential geometry as discussed by the authors takes as its theme the classical roots of contemporary differential geometry, and explains why it is absurdly inefficient to eschew the modern language of manifolds, bundles, forms, etc., which was developed precisely to rigorize the concepts of classical differential geometry.
Book
An introduction to differentiable manifolds and Riemannian geometry
TL;DR: In this article, the authors present a revised edition of one of the classic mathematics texts published in the last 25 years, which includes updated references and indexes and error corrections and will continue to serve as the standard text for students and professionals in the field.
Journal ArticleDOI
Bisimulation through probabilistic testing
Kim Guldstrand Larsen,Arne Skou +1 more
TL;DR: By using probabilistic transition systems as the underlying semantic model, it is shown how a testing algorithm can distinguish, with a probability arbitrarily close to one, between processes that are not bisimulation equivalent.