[HTML][HTML] Improved geometric path enumeration for verifying relu neural networks

S Bak, HD Tran, K Hobbs, TT Johnson - International Conference on …, 2020 - Springer
… Beyond memory savings, with offset zonotopes we can consider ways to reduce the
zonotope’s overapproximation error when adding constraints to \(\theta \). The proposed …

Unknown input observer design for linear parameter-varying systems in a bounded error context

J Li, Z Wang, T Raïssi, Y Shen - IEEE Transactions on …, 2020 - ieeexplore.ieee.org
… , the center of zonotopes should be bounded and the size of zonotopes should be minimized.
… characterize the size of zonotopes. Note that the zonotope Xk shares the same size withZe …

A polynomial time algorithm for solving the closest vector problem in zonotopal lattices

ST McCormick, B Peis, R Scheidweiler… - SIAM Journal on Discrete …, 2021 - SIAM
… cell is a zonotope. Zonotopes are defined as projections of cubes; all of their faces (of any
dimension) are centrally symmetric. All lattices up to dimension three have a zonotope as their …

Sizing the White Whale

A Deza, M Hao, L Pournin - arXiv preprint arXiv:2205.13309, 2022 - arxiv.org
… properties of a highly structured zonotope—the White Whale [4]—… This zonotope appears
in a number of contexts as for … case of the primitive zonotopes, a family of zonotopes originally …

Interval Estimation for Discrete-time Descriptor System Based on Zonotopic Kalman Filter

A Chen, M Sun, Y Shen, Y Liu - International Journal of Control …, 2022 - Springer
zonotopes are adopted in this paper to characterize uncertainties. Furthermore, by effectively
handling wrapping effects, zonotope-… the successful implementation of zonotope in different …

Reachable dynamics of networked microgrids with large disturbances

Y Zhou, P Zhang, M Yue - IEEE Transactions on Power …, 2020 - ieeexplore.ieee.org
zonotopes and zonotope bundles in the ODE-enabled formal analysis. Simulation shows that
zonotope… load-shedding disturbance, while zonotope-bundle still catches the fast nonlinear …

Further results on the design of a class of discrete‐time set‐valued state estimators

N Meslem, T Raïssi, G Besançon - International Journal of …, 2022 - Wiley Online Library
… Second, to obtain tighter state enclosures, we propose to apply zonotope set computation
instead of interval analysis to design a new set-valued state estimation algorithm. Through …

[HTML][HTML] Upper bounds for the analytic complexity of puiseux polynomial solutions to bivariate hypergeometric systems

VA Krasikov - 2020 - cyberleninka.ru
… In Section 2 we investigate particular cases of hy-pergeometric systems defined by zonotopes
and analyze the analytic complexity of their solutions. We formulate and prove an estimate …

Conservatism Comparison of SUIO and Luenberger Observer in Invariant Set-Based Robust Fault Detection for LPV Systems

B Min, J Yang, J Tan, C Wang… - 2021 IEEE International …, 2021 - ieeexplore.ieee.org
This paper concentrates on analyzing and comparing the invariant set-based fault detection
(FD) performance of the set-theoretic unknown input observer (SUIO)-based method and the …

Computing non-convex inner-approximations of reachable sets for nonlinear continuous systems

N Kochdumper, M Althoff - 2020 59th IEEE Conference on …, 2020 - ieeexplore.ieee.org
… We use the sparse representation of polynomial zonotopes introduced in [19] to represent …
Since C is a polynomial zonotope and all polynomial zonotopes are connected, it holds that C …