Hybrid Zonotopes: A Mixed-Integer Set Representation for the Analysis of Hybrid Systems

TJ Bird - 2022 - hammer.purdue.edu
… representation named the hybrid zonotope. The hybrid zonotope builds upon a combination
of … It is shown that the hybrid zonotope is equivalent to the union of an exponential number of …

Unions and Complements of Hybrid Zonotopes

TJ Bird, N Jain - IEEE Control Systems Letters, 2021 - ieeexplore.ieee.org
… of hybrid zonotopes. The addition of these set operations proves the hybrid zonotope’s …
be embedded within the hybrid zonotope set definition. A numerical example using hybrid …

Efficient Backward Reachability using the Minkowski Difference of Constrained Zonotopes

L Yang, H Zhang, JB Jeannin… - IEEE Transactions on …, 2022 - ieeexplore.ieee.org
… Our algorithm sequentially linearizes the dynamics, and uses constrained zonotopes for set
… This Minkowski difference needs to be represented as a constrained zonotope to enable …

The Vector Balancing Constant for Zonotopes

L Heck, V Reis, T Rothvoss - arXiv preprint arXiv:2210.16460, 2022 - arxiv.org
… We prove that for any zonotope K ⊆ Rd one has vb(K,K) % d logloglogd. … zonotope,
generalizing Vaaler’s Theorem for cubes. We also prove that for two different normalized zonotopes

Neural Network Approximation based on Hausdorff distance of Tropical Zonotopes

P Misiakos, G Smyrnis, G Retsinas… - … Conference on Learning …, 2021 - openreview.net
… or negative zonotope. We thus call these line segments generators of the zonotope. The
generators further receive the characterization positive or negative depending on the zonotope

Fault detection and isolation for discrete-time Markovian jump systems with generally bounded transition probabilities: A zonotope-based method

D Lu, X Zhang, Y Lan, X Wang - Transactions of the Institute …, 2021 - journals.sagepub.com
This paper addresses the fault detection and isolation for a class of discrete-time Markovian
jump system with generally bounded transition probabilities. The proposed method is mainly …

[HTML][HTML] Zonotope-based interval estimation for discrete-time Markovian jump systems with complex transition probabilities and quantization

Q Tang, W Chen, L Yang - Journal of the Franklin Institute, 2022 - Elsevier
This paper investigates the interval estimation for a class of discrete-time Markovian jump
systems with generally uncertain transition probabilities and unknown-but-bounded …

Zonotope Domains for Lagrangian Neural Network Verification

M Jordan, J Hayase, AG Dimakis, S Oh - arXiv preprint arXiv:2210.08069, 2022 - arxiv.org
… DeepZ zonotopes, the DeepZ zonotopes augmented with IBP bounds, and zonotopes
Then we perform dual ascent over 2-d zonotopes, before merging the zonotopes of the final …

Ellipsotopes: Combining Ellipsoids and Zonotopes for Reachability Analysis and Fault Detection

S Kousik, A Dai, G Gao - arXiv preprint arXiv:2108.01750, 2021 - arxiv.org
… , constrained zonotopes and constrained polynomial zonotopeszonotopes can not represent
shapes with smooth boundaries such as ellipsoids, and constrained polynomial zonotopes

Fast zonotope‐tube‐based LPV‐MPC for autonomous vehicles

E Alcalá, V Puig, J Quevedo… - IET Control Theory & …, 2020 - Wiley Online Library
… Using zonotope … , zonotopes are used to compute reachable sets and therefore, the tube
to implement the proposed robust MPC approach. The main reason for the use of zonotopes