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 …
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 …
be embedded within the hybrid zonotope set definition. A numerical example using hybrid …
Efficient Backward Reachability using the Minkowski Difference of Constrained Zonotopes
… 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 …
… 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 …
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 …
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 …
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 …
systems with generally uncertain transition probabilities and unknown-but-bounded …
Zonotope Domains for Lagrangian Neural Network Verification
… 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 …
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
… , constrained zonotopes and constrained polynomial zonotopes … zonotopes can not represent
shapes with smooth boundaries such as ellipsoids, and constrained polynomial zonotopes …
shapes with smooth boundaries such as ellipsoids, and constrained polynomial zonotopes …
Fast zonotope‐tube‐based LPV‐MPC for autonomous vehicles
… 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 …
to implement the proposed robust MPC approach. The main reason for the use of zonotopes …