[HTML][HTML] Verification of deep convolutional neural networks using imagestars

HD Tran, S Bak, W Xiang, TT Johnson - International conference on …, 2020 - Springer
… We compare our approach with the zonotope and polytope methods in two aspects including
verification time and conservativeness of the results. To do that, we train 3 CNNs in small, …

Using Intersection of Unions to Minimize Multi-directional Linearization Error in Reachability Analysis

A Adimoolam, I Saha - 25th ACM International Conference on Hybrid …, 2022 - dl.acm.org
… as a union zonotope because it represents a union of zonotopes without intersection. Given
two IoU zonotopes Z and Z′, we represent the IoU zonotope resulting from their intersection …

A Polynomial Case of Nonconvex Quadratic Optimization

M Černý, M Rada, M Hladík - BOOK OF ABSTRACTS - odam.upol.cz
We consider the following case of quadratic optimization: given Q∈ Rn× n with rank r and
given p∈ Rn and x≤ x∈ Rp (where inequalities between vectors are understood …

[HTML][HTML] Fault detection for uncertain LPV systems using probabilistic set-membership parity relation

Y Wan, V Puig, C Ocampo-Martinez, Y Wang… - Journal of Process …, 2020 - Elsevier
This paper considers fault detection of uncertain linear parameter varying systems that have
polynomial dependence on parametric uncertainties. A conventional set-membership (SM) …

The Image Containment Problem and Some Classes of Polynomial Instances

R Pesenti, F Rinaldi - SIAM Journal on Optimization, 2007 - SIAM
… a minimum total length zonotope containing k assigned … zonotopes in R2 centered in the
origin are considered and a method to approximate a given zonotope by means of zonotopes

[PDF][PDF] Réarrangements convexes des marches aléatoires

Y Davydov, AM Vershik - Annales de l'IHP Probabilités et statistiques, 1998 - numdam.org
… Nous étudions donc ici le comportement asymptotique des courbes des zonotopes Zn/bn …
On va considérer d’abord les zonotopes Zn engendrés par une suite de variables aléatoires …

Fault Detection and Isolation for Linear discrete-time Delayed Systems based on L∞ Observer and Zonotopic Analysis

N Sehli, KI Taarit, X Ping, Z Wang, T Raïssi, M Ksouri - IFAC-PapersOnLine, 2022 - Elsevier
This paper considers actuator fault detection and isolation (FDI) problem for a class of linear
discrete-time systems with constant time-delay. Based on delay-free representation, a novel …

A provable defense for deep residual networks

M Mirman, G Singh, M Vechev - arXiv preprint arXiv:1903.12519, 2019 - arxiv.org
… the analysis with the Hybrid Zonotope domain. For all abstract layers, we describe their
effect on a given hybrid zonotope h with m correlated error coefficients, producing a new hybrid …

Model predictive real-time monitoring of linear systems

X Chen, S Sankaranarayanan - 2017 IEEE Real-Time Systems …, 2017 - ieeexplore.ieee.org
… T x ≤ bu}, we may only need to evaluate the range of the transformed zonotope a T Z, the
range has no intersection with [bl,bu] if and only if the zonotope has no intersection with the …

Set propagation techniques for reachability analysis

M Althoff, G Frehse, A Girard - Annual Review of Control …, 2021 - hal.archives-ouvertes.fr
… An alternative to zonotope bundles are constrained zonotopes, which are computationally
more demanding, but operations on them are exact for Minkowski sum and convex hull [18]. …