[HTML][HTML] Set-membership-based distributed moving horizon estimation of large-scale systems

P Segovia, V Puig, E Duviella - ISA transactions, 2022 - Elsevier
This work is concerned with the design of a two-step distributed state estimation scheme for
large-scale systems in the presence of unknown-but-bounded disturbances and noise. The …

[HTML][HTML] On extensions of the Loomis-Whitney inequality and Ball's inequality for concave, homogeneous measures

J Hosle - Advances in Applied Mathematics, 2020 - Elsevier
… For the proof of our theorem, we will recall the definition of a zonotope. A zonotope is simply
a Minkowski sum of line segments Z = ∑ i = 1 m [ − x i , x i ] . By linearity (1.3), if Z = ∑ i = 1 …

GLIR: A Practical Global-local Integrated Reactive Planner towards Safe Human-Robot Collaboration

M El-Shamouty, J Titze, S Kortik, W Kraus… - Center for Cyber … - ieeexplore.ieee.org
… ARMTD [19] approximates ˆRs using zonotopes and integrates them into trajectory … It must
be noted that ARMTD can also accept octrees if zonotopes over-approximate octrees [19]. Neo…

Concrete polytopes may not tile the space

A Garber, I Pak - Mathematika, 2020 - Wiley Online Library
… that in R 3 all such polytopes must be zonotopes (polytopes with centrally symmetric faces of
all … In particular, all lattice zonotopes multitile the space [12], and they are concrete because …

[PDF][PDF] Certified Deep Learning: Verification and Training

M Mirman - 2022 - research-collection.ethz.ch
… AI2 first creates an abstract element A1 capturing all perturbed images (Here, we use a 2-bounded
set of zonotopes). It then propagates A1 through the abstract transformer of each layer…

Novel techniques for a verified simulation of fractional-order differential equations

A Rauh, L Jaulin - Fractal and Fractional, 2021 - mdpi.com
… In general, verified simulation techniques rely on interval methods, zonotopes, or Taylor
model arithmetic and allow for computing guaranteed outer enclosures of the sets of solutions. …

[HTML][HTML] The equivariant volumes of the permutahedron

F Ardila, A Schindler, AR Vindas-Meléndez - Discrete & Computational …, 2021 - Springer
… To compute the volume of the fixed polytope \(\Pi _n^\sigma \) we will use its description as
a zonotope, recalling that a zonotope can be tiled by parallelotopes as follows. If A is a set of …

Guaranteed SLAM-A pure interval approach

A Codreş, B Codreş, A Stancu - 2022 26th International …, 2022 - ieeexplore.ieee.org
This paper presents a new Simultaneous Localisation And Mapping (SLAM) method which
takes into account all measurements provided by a 2D LiDAR sensor and generates a …

Safety verification and robustness analysis of neural networks via quadratic constraints and semidefinite programming

M Fazlyab, M Morari, GJ Pappas - IEEE Transactions on …, 2020 - ieeexplore.ieee.org
… We can adapt the result of Proposition 1 to other sets such as polytopes, zonotopes, and
ellipsoids, as outlined below. The derivation of the corresponding QCs can be found in …

[HTML][HTML] Impact of energy communities on the European electricity and heating system decarbonization pathway: Comparing local and global flexibility responses

S Backe, S Zwickl-Bernhard, D Schwabeneder, H Auer… - Applied Energy, 2022 - Elsevier
This paper investigates how the European electricity and heating system is impacted when
medium-scale energy communities (ECs) are developed widely across Europe. We study the …