Set propagation techniques for reachability analysis

M Althoff, G Frehse, A Girard - Annual Review of Control …, 2021‏ - annualreviews.org
Reachability analysis consists in computing the set of states that are reachable by a
dynamical system from all initial states and for all admissible inputs and parameters. It is a …

Computer-assisted proofs in PDE: a survey

J Gómez-Serrano - SeMA Journal, 2019‏ - Springer
Computer-assisted proofs in PDE: a survey | SeMA Journal Skip to main content Springer
Nature Link Account Menu Find a journal Publish with us Track your research Search Cart 1.Home …

Flow*: An analyzer for non-linear hybrid systems

X Chen, E Ábrahám, S Sankaranarayanan - Computer Aided Verification …, 2013‏ - Springer
Abstract The tool Flow* performs Taylor model-based flowpipe construction for non-linear
(polynomial) hybrid systems. Flow* combines well-known Taylor model arithmetic …

Reachability analysis for neural feedback systems using regressive polynomial rule inference

S Dutta, X Chen, S Sankaranarayanan - Proceedings of the 22nd ACM …, 2019‏ - dl.acm.org
We present an approach to construct reachable set overapproximations for continuous-time
dynamical systems controlled using neural network feedback systems. Feedforward deep …

[ספר][B] Introduction to interval analysis

RE Moore, RB Kearfott, MJ Cloud - 2009‏ - SIAM
This book is intended primarily for those not yet familiar with methods for computing with
intervals of real numbers and what can be done with these methods. Using a pair [a, b] of …

Arb: efficient arbitrary-precision midpoint-radius interval arithmetic

F Johansson - IEEE Transactions on Computers, 2017‏ - ieeexplore.ieee.org
Arb is a C library for arbitrary-precision interval arithmetic using the midpoint-radius
representation, also known as ball arithmetic. It supports real and complex numbers …

The parameterization method for invariant manifolds

A Haro, M Canadell, JL Figueras, A Luque… - Applied mathematical …, 2016‏ - Springer
Poincaré's program for the global analysis of a dynamical system starts by considering
simple solutions, such as equilibria and periodic orbits, together with their corresponding …

[ספר][B] Elementary functions

JM Muller, JM Muller - 2006‏ - Springer
This book is devoted to the computation of the elementary functions. Here, we call
elementary functions the most commonly used mathematical functions: sin, cos, tan, sin− 1 …

Complete search in continuous global optimization and constraint satisfaction

A Neumaier - Acta numerica, 2004‏ - cambridge.org
This survey covers the state of the art of techniques for solving general-purpose constrained
global optimization problems and continuous constraint satisfaction problems, with …

[HTML][HTML] A Chebyshev interval method for nonlinear dynamic systems under uncertainty

J Wu, Y Zhang, L Chen, Z Luo - Applied Mathematical Modelling, 2013‏ - Elsevier
This paper proposes a new interval analysis method for the dynamic response of nonlinear
systems with uncertain-but-bounded parameters using Chebyshev polynomial series …