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

Kousik, Shreyas; Dai, Adam; Gao, Grace Xingxin

doi:10.1109/tac.2022.3191750

Cited by 21 publications

(3 citation statements)

References 40 publications

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“…Currently, there are several geometric sets that can be considered. One prominent example is zonotopes (Kousik et al, 2023), which are symmetric, convex polyhedra that are widely used for their ability to provide efficient numerical implementations of affine plots and exact Minkowski summations. However, it is important to note that zonotopes are not suitable for representing shapes with smooth boundaries, such as ellipsoids.…”

Section: System Modelingmentioning

confidence: 99%

Distributed set-membership estimation for automated straddle carriers using smart sensors

Chen,

Zhang,

Xia

et al. 2024

Transactions of the Institute of Measurement and Control

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Considering the harsh environment of the port, automated straddle carriers, characterized by their large size, tall frame, and high center of gravity, may experience instability during steering and transportation due to inaccurate state estimation. Thus, this paper explores state estimation techniques for automated straddle carriers utilizing smart sensors which are capable of data measurement and processing. First, using the steering principles and lateral characteristics of automated straddle carriers, a dynamic linear model is established based on Newton’s second law of motion. Then, in order to enhance the reliability and flexibility of state estimation, a distributed smart sensor network structure is introduced. In addition, considering the challenge of unknown-but-bounded noise and the precision demands of the considered automated straddle carrier, a modified distributed set-membership estimation algorithm is proposed and is derived sufficient conditions for the existence of the estimation set for the considered automated straddle carriers. Finally, the effectiveness and superiority of the proposed method are demonstrated by performance analyses.

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Section: System Modelingmentioning

confidence: 99%

Distributed set-membership estimation for automated straddle carriers using smart sensors

Chen,

Zhang,

Xia

et al. 2024

Transactions of the Institute of Measurement and Control

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“…Our reachability and verification algorithms support arbitrary convex sets, where we only require that the support function can be evaluated. While the set S can also be defined by a symbolic equation returning its support function, the uncertain sets in verification tasks are often defined using common convex set representations such as intervals, zonotopes, polytopes, zonotope bundles [6], constrained zonotopes [52], ellipsoids, ellipsotopes [36], or capsules [49]. Hence, we now provide the support functions and support vectors for some of these set representations, where we focus on the most commonly-used ones.…”

Section: Set Representations and Operationsmentioning

confidence: 99%

Fully-Automated Verification of Linear Systems Using Reachability Analysis with Support Functions

Wetzlinger

Kochdumper

Bak

et al. 2023

Proceedings of the 26th ACM International Conference on Hybrid Systems: Computation and Control

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While reachability analysis is one of the major techniques for formal verification of dynamical systems, the requirement to adequately tune algorithm parameters often prevents its widespread use in practical applications. In this work, we fully automate the verification process for linear time-invariant systems: Based on the computation of tight upper and lower bounds for the support function of the reachable set along a given direction, we present a fully-automated verification algorithm, which is based on iterative refinement of the upper and lower bounds and thus always returns the correct result in decidable cases. While this verification algorithm is particularly well suited for cases where the specifications are represented by halfspace constraints, we extend it to arbitrary convex unsafe sets using the Gilbert-Johnson-Keerthi algorithm. In summary, our automated verifier is applicable to arbitrary convex initial sets, input sets, as well as unsafe sets, can handle time-varying inputs, automatically returns a counterexample in case of a safety violation, and scales to previously unanalyzable high-dimensional state spaces. Our evaluation on several challenging benchmarks shows significant improvements in computational efficiency compared to verification using other state-of-the-art reachability tools.

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“…When there are no uncertainties, proposals using intervals (Thabet et al (2014)), zonotopes (Combastel (2003)) and ellipsoids (Chernousko (2005)) suffer from approximations during the intersection phase. Additionally, one can use ellipsotopes (Kousik et al (2022)) and AH-polytopes (Sadraddini and Tedrake (2019)) but not with uncertainties since there are currently no proposal of explicit formulas for the convex hull operation. Using polytopes in hyperplane representation (Silvestre et al (2017a)) or in Constrained Zonotopes (CZs) (Scott et al (2016)) are the most predominant approaches.…”

Section: Introductionmentioning

confidence: 99%

Set-valued estimators for Uncertain Linear Parameter-Varying systems

Silvestre

2022

Systems & Control Letters

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

Cited by 21 publications

References 40 publications

Distributed set-membership estimation for automated straddle carriers using smart sensors

Distributed set-membership estimation for automated straddle carriers using smart sensors

Fully-Automated Verification of Linear Systems Using Reachability Analysis with Support Functions

Set-valued estimators for Uncertain Linear Parameter-Varying systems

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