[PDF][PDF] A comparison of wrench-feasible workspaces using interval analysis and convex linear mapping techniques

JK Pickard, JA Carretero - … of the Canadian Society for Mechanical …, 2014 - researchgate.net
… Since the AF W is also classified as a m-dimensional zonotope, the linear mapping
performed by J yields a ndimensional zonotope. This is due to a well known property of linear …

Time-Varying Tube-Based Output Feedback Robust MPC for T–S Fuzzy Systems

X Ping, J Yao, B Ding, P Wang… - IEEE Transactions on …, 2021 - ieeexplore.ieee.org
… The membership functions errors are bounded within convex sets via the properties of
zonotopes and interval matrices. An offline table stores a series of structures that include nested …

Optimizing cable arrangement in cable-driven parallel robots to improve the range of available wrenches

K Kamali, A Joubair, IA Bonev - … and Information in …, 2018 - asmedigitalcollection.asme.org
… to the definition of a zonotope [11]: “A zonotope is the vector sum of a finite number of closed
line segments in some Euclidean space”. A K-dimensional zonotope is a special case of K-…

The Blackwell relation defines no lattice

N Bertschinger, J Rauh - 2014 IEEE International Symposium …, 2014 - ieeexplore.ieee.org
… Section II we define the zonotope preorder, which is … zonotope preorder does not define a
lattice. In Section III we mention Blackwell’s k-decision orders, which generalize the zonotope

Entropy and boundary conditions in random rhombus tilings

N Destainville - Journal of Physics A: Mathematical and General, 1998 - iopscience.iop.org
… This generic shadow is called a zonotope [16], denoted by Z. When d = 2, the zonotopes
or in other words a function of the side lengths of the zonotope Z. For example, the 3 → 2 tilings …

Set-based active fault diagnosis for discrete-time linear descriptor systems

S Yang, F Xu, X Wang, J Yang… - 2019 American Control …, 2019 - ieeexplore.ieee.org
… order of zonotopes increases quickly. In order to control the order of zonotopes, the order-reduction
method in [24] is used in this paper. More order-reduction methods of zonotopes can …

A tropical approach to neural networks with piecewise linear activations

V Charisopoulos, P Maragos - arXiv preprint arXiv:1805.08749, 2018 - arxiv.org
… By definition, N(hi) is a zonotope since hi is a rank-2 polynomial. Zonotopes are line
segments, so the Minkowski sum of k such zonotopes has at most k nonparallel edges. …

Safe Reinforcement Learning Using Black-Box Reachability Analysis

M Selim, A Alanwar, S Kousik, G Gao… - arXiv preprint arXiv …, 2022 - arxiv.org
… We represent sets using constrained zonotopes, zonotopes, and intervals, because they
enable efficient Minkowski sum computation (a key part of reachability analysis) [30] and …

Scalable Distributed Reachability Analysis for Cyber-Physical Networked Microgrids with Communication Latency

Y Li, Y Zhang, D Zhao, L Du - 2021 IEEE Transportation …, 2021 - ieeexplore.ieee.org
… the dynamic operations of the cyber-physical networked microgrid system, Zonotope
method is adopted in this work. Mathematically, Zonotope is a type of polytope [10], which is a …

[PS][PS] On maximal primitive fixing systems

V Boltyanski, H Martini - Beitrage zur Algebra und Geometrie, 1996 - math.ethz.ch
… Thus, already in the class of zonotopes we have counterexamples to the … zonotopes with
analogous properties, and it is easy to extend this construction to n-dimensional zonotopes with …