75 research outputs found
Model checking polygonal differential inclusions using invariance kernels
Polygonal hybrid systems are a subclass of planar hybrid
automata which can be represented by piecewise constant differential
inclusions. Here, we identify and compute an important object of such
systems’ phase portrait, namely invariance kernels. An invariant set is a
set of initial points of trajectories which keep rotating in a cycle forever
and the invariance kernel is the largest of such sets. We show that this
kernel is a non-convex polygon and we give a non-iterative algorithm for
computing the coordinates of its vertices and edges. Moreover, we present
a breadth-first search algorithm for solving the reachability problem for
such systems. Invariance kernels play an important role in the algorithm.peer-reviewe
Static analysis of SPDIs for state-space reduction
Polygonal hybrid systems (SPDI) are a subclass of planar hybrid
automata which can be represented by piecewise constant differential
inclusions. The reachability problem as well as the computation of certain objects of the phase portrait, namely the viability, controllability
and invariance kernels, for such systems is decidable. In this paper
we show how to compute another object of an SPDI phase portrait,
namely semi-separatrix curves and show how the phase portrait can
be used for reducing the state-space for optimizing the reachability
analysis.peer-reviewe
Computer-aided verification : how to trust a machine with your life
Mathematical predictive analysis of the behaviour of circuits and computer pro- grams is a core problem in computer science. Research in formal verification and semantics of programming languages has been an active field for a number of decades, but it was only through techniques developed over these past twenty years that they have been scaled up to work on non-trivial case-studies. This report gives an overview of a number of computer- aided formal verification areas I have been working on over these past couple of years in such a way to be accessible to computer scientists in other disciplines. Brief mention is made of problems in these areas I am actively working on. It does not purport to be an overview of the whole field of computer-aided formal verification or a detailed technical account of my research.peer-reviewe
The method of characteristics revisited. A viability approach
This mini-course provides a presentation of the method of characteristics to
initial/boundary-value problems for systems of first-order partial differential
equations and to Hamilton-Jacobi variational inequalities. In particular, these
results are indeed useful for the treatment of hybrid systems of control
theory.
We rely on tools forged by set-valued analysis and viability theory, which
happen to be both efficient and versatile to cover many problems. They find
here unexpected relevance
Extracting discontinuity using the probe and enclosure methods
This is a review article on the development of the probe and enclosure
methods from past to present, focused on their central ideas together with
various applications.Comment: 121 pages, minor modificatio
Quantum isometries and noncommutative geometry
The space has no free analogue, but we can talk instead about
the free sphere , as the manifold defined by the
equations . We discuss here the structure and
hierarchy of the submanifolds , with particular
attention to the manifolds having an integration functional .Comment: 400 pages. arXiv admin note: text overlap with arXiv:1909.0815
Gratings: Theory and Numeric Applications, Second Revisited Edition
International audienceThe second Edition of the Book contains 13 chapters, written by an international team of specialist in electromagnetic theory, numerical methods for modelling of light diffraction by periodic structures having one-, two-, or three-dimensional periodicity, and aiming numerous applications in many classical domains like optical engineering, spectroscopy, and optical telecommunications, together with newly born fields such as photonics, plasmonics, photovoltaics, metamaterials studies, cloaking, negative refraction, and super-lensing. Each chapter presents in detail a specific theoretical method aiming to a direct numerical application by university and industrial researchers and engineers.In comparison with the First Edition, we have added two more chapters (ch.12 and ch.13), and revised four other chapters (ch.6, ch.7, ch.10, and ch.11
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