[HTML][HTML] Convergent under-approximations of reachable sets and tubes: A piecewise constant approach

M Serry - Journal of the Franklin Institute, 2021 - Elsevier
… It is assumed that the sets X 0 and U are zonotopes with order … of generators of the resulting
zonotopes. On the other hand, the … classes are computationally costly relative to zonotopes. …

Set Invariance Based Localization of Kalman Filter Estimation Error in Automatic Generation Control

D Leko, M Vašak - IECON 2021–47th Annual Conference of …, 2021 - ieeexplore.ieee.org
… set in the G-representation of the zonotope. Since for each estimate it is satisfied that λ∞
≤ 1, it follows that all estimation errors are contained within the set EmRP I. The paper …

[HTML][HTML] Set-Based B-Series

JA dit Sandretto - Mathematics, 2022 - search.proquest.com
… by the intersection of a finite number of zonotopes [47]. Let us … zonotopes—for example,
(14) (y1 wrt y2). Bottom left and right: zoom on a small part computed with intervals or zonotopes

[HTML][HTML] The moment polytope of the abelian polygon space

N Daundkar, P Deshpande - Topology and its Applications, 2021 - Elsevier
… Recall that a zonotope is a polytope all of whose faces are centrally symmetric (see [12, …
cell complex is called zonotopal if every cell is combinatorially isomorphic to a zonotope. …

A Set-Based Prognostics Approach for Wind Turbine Blade Health Monitoring

K Boutrous, V Puig, F Nejjari - IFAC-PapersOnLine, 2022 - Elsevier
… Hypercubes are themselves zonotopes, so the process involves a mapping of a zonotope
to another zonotope that invariably increases conservativeness but for the purposes of …

On the volume of the Minkowski sum of zonoids

M Fradelizi, M Madiman, M Meyer… - arXiv preprint arXiv …, 2022 - arxiv.org
… We note that every zonotope A can be seen as an orthogonal projection of a high di… from
Theorem 5.2 below), indeed such direct generalization requires Theorem 4.2 for all zonotopes

Static analysis of relu neural networks with tropical polyhedra

E Goubault, S Palumby, S Putot, L Rustenholz… - International Static …, 2021 - Springer
… include zonotopes [19, 34], especially considering that feedforward neural nets with one
hidden layer and ReLU activation functions are known to be characterizable by zonotopes, see …

[HTML][HTML] Set-based guaranteed active fault diagnosis for LPV systems with unknown bounded uncertainties

J Tan, S Olaru, MM Seron, F Xu - Automatica, 2021 - Elsevier
This paper focuses on designing, via the minimization of a suitable cost function, an input
sequence to guarantee active fault diagnosis (AFD) of discrete-time linear parameter-varying …

[HTML][HTML] Tractable robust MPC design based on nominal predictions

I Alvarado, P Krupa, D Limon, T Alamo - Journal of Process Control, 2022 - Elsevier
… is a (convex) zonotope, ie, an affine mapping of the unitary box of a certain dimension M (3)
W = H W B M , where H W ∈ R n × M . We note that we consider W as a zonotope to simplify …

Control barrier function meets interval analysis: Safety-critical control with measurement and actuation uncertainties

Y Zhang, S Walters, X Xu - 2022 American Control Conference …, 2022 - ieeexplore.ieee.org
… As in [26], we choose zonotopes or intervals as the representation of reachable tubes for
computational efficiency. We utilize the same algorithms presented in [26] to compute Rlin(xk) …