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Journal articles on the topic 'Zonotopic analysis'

Author: Grafiati

Published: 25 May 2024

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1

Trapiello, Carlos, Vicenç Puig, and Damiano Rotondo. "A zonotopic set-invariance analysis of replay attacks affecting the supervisory layer." Systems & Control Letters 157 (November 2021): 105056. http://dx.doi.org/10.1016/j.sysconle.2021.105056.

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2

Harno, Hendra G., and Yoonsoo Kim. "Flight envelope estimation for helicopters under icing conditions via the zonotopic reachability analysis." Aerospace Science and Technology 102 (July 2020): 105859. http://dx.doi.org/10.1016/j.ast.2020.105859.

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3

Sehli, Naima, Kaouther Ibn Taarit, Xubin Ping, Zhenhua Wang, Tarek Raïssi, and Moufida Ksouri. "Fault Detection and Isolation for Linear discrete-time Delayed Systems based on L∞ Observer and Zonotopic Analysis." IFAC-PapersOnLine 55, no. 25 (2022): 169–74. http://dx.doi.org/10.1016/j.ifacol.2022.09.342.

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4

Zhou, Meng, Zhengcai Cao, and Ye Wang. "Robust fault detection and isolation based on finite-frequency H- H unknown input observers and zonotopic threshold analysis." IEEE/CAA Journal of Automatica Sinica 6, no. 3 (May 2019): 750–59. http://dx.doi.org/10.1109/jas.2019.1911492.

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5

Laurel, Jacob, Siyuan Brant Qian, Gagandeep Singh, and Sasa Misailovic. "Synthesizing Precise Static Analyzers for Automatic Differentiation." Proceedings of the ACM on Programming Languages 7, OOPSLA2 (October 16, 2023): 1964–92. http://dx.doi.org/10.1145/3622867.

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We present Pasado, a technique for synthesizing precise static analyzers for Automatic Differentiation. Our technique allows one to automatically construct a static analyzer specialized for the Chain Rule, Product Rule, and Quotient Rule computations for Automatic Differentiation in a way that abstracts all of the nonlinear operations of each respective rule simultaneously. By directly synthesizing an abstract transformer for the composite expressions of these 3 most common rules of AD, we are able to obtain significant precision improvement compared to prior works which compose standard abstract transformers together suboptimally. We prove our synthesized static analyzers sound and additionally demonstrate the generality of our approach by instantiating these AD static analyzers with different nonlinear functions, different abstract domains (both intervals and zonotopes) and both forward-mode and reverse-mode AD. We evaluate Pasado on multiple case studies, namely soundly computing bounds on a neural network’s local Lipschitz constant, soundly bounding the sensitivities of financial models, certifying monotonicity, and lastly, bounding sensitivities of the solutions of differential equations from climate science and chemistry for verified ranges of initial conditions and parameters. The local Lipschitz constants computed by Pasado on our largest CNN are up to 2750× more precise compared to the existing state-of-the-art zonotope analysis. The bounds obtained on the sensitivities of the climate, chemical, and financial differential equation solutions are between 1.31 − 2.81× more precise (on average) compared to a state-of-the-art zonotope analysis.

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6

Henk, Martin, Eva Linke, and Jörg M. Wills. "Minimal zonotopes containing the crosspolytope." Linear Algebra and its Applications 432, no. 11 (June 2010): 2942–52. http://dx.doi.org/10.1016/j.laa.2009.12.041.

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7

TONDU, BERTRAND. "A ZONOTOPE-BASED APPROACH FOR MANIPULABILITY STUDY OF REDUNDANT ROBOT LIMBS." International Journal of Humanoid Robotics 10, no. 03 (September 2013): 1350023. http://dx.doi.org/10.1142/s0219843613500230.

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Kinematic efficiency of robot limbs can be analyzed by means of the manipulability concept defined by Yoshikawa. However, when it is applied to redundant serial chains, that are the most common case in humanoid robotics, Yoshikawa's manipulability measure is not able to take into account the joint velocity range of each robot joint. In order to overcome this difficulty we propose to substitute in the place of the manipulability ellipsoid a manipulability zonotope resulting from the robot Jacobian transform of the joint velocities parallelotope. The proposed manipulability zonotope notion is similar to the well-known manipulability polytope notion, but its associated volume measure can take benefit of the so-called zonotope theory. By means of a famous and powerful theorem about the cubical dissection of any zonotope, an original formula of manipulability measure is proposed from which is also derived a mean manipulability estimate associated to a given joint space working. The proposed tools are applied to a kinematic analysis of a 4R-regional structure model of the upper limb.

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8

Xu, Guixiang, Ziyun Wang, and Zhicheng Ji. "A novel zonotopes set membership estimation-based fault diagnosis algorithm." Modern Physics Letters B 32, no. 34n36 (December 30, 2018): 1840092. http://dx.doi.org/10.1142/s0217984918400924.

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For solving the advanced manufacturing fault diagnosis issue, a novel zonotopes estimation-based fault diagnosis algorithm is proposed in this paper. By using the intersection of the convex polytope and the tight strip, the fault diagnosis problem is changed into the analysis of the set membership outer bound computation. If the feasible set is detected empty, the set membership filters are designed. The minimal volume is also calculated and the selected zonotopes can be viewed as the approximate boundary. The simulation results show the effectiveness and practicability of the presented fault diagnosis algorithm.

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9

Alonso-Gutiérrez, David, and Joscha Prochno. "On the geometry of random convex sets between polytopes and zonotopes." Journal of Mathematical Analysis and Applications 450, no. 1 (June 2017): 670–90. http://dx.doi.org/10.1016/j.jmaa.2017.01.042.

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10

Cococcioni, Marco, Marco Grazzi, Le Li, and Federico Ponchio. "A toolbox for measuring heterogeneity and efficiency using zonotopes." Stata Journal: Promoting communications on statistics and Stata 22, no. 1 (March 2022): 25–59. http://dx.doi.org/10.1177/1536867x221083854.

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In this work, we describe the new command zonotope, which, by resorting to a geometry-based approach, provides a measure of productivity that fully accounts for the existing heterogeneity across firms within the same industry. The method we propose also enables assessment of the extent of multidimensional heterogeneity with applications to fields beyond that of production analysis. Finally, we detail the functioning of the software to perform the related empirical analysis, and we discuss the main computational issues encountered in its development.

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11

Bird, Trevor J., Herschel C. Pangborn, Neera Jain, and Justin P. Koeln. "Hybrid zonotopes: A new set representation for reachability analysis of mixed logical dynamical systems." Automatica 154 (August 2023): 111107. http://dx.doi.org/10.1016/j.automatica.2023.111107.

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12

Dbouk, Hani, and Steffen Schön. "Reliable Bounding Zones and Inconsistency Measures for GPS Positioning using Geometrical Constraints." Acta Cybernetica 24, no. 3 (March 19, 2020): 573–91. http://dx.doi.org/10.14232/actacyb.24.3.2020.16.

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Reliable confidence domains for Global Navigation Satellite System (GNSS) positioning and inconsistency measures of the observations are of great importance for any navigation system, especially for safety critical applications. In this work, deterministic error bounds are introduced in form of intervals to assess remaining observation errors. The intervals can be computed based on expert knowledge or based on a sensitivity analysis of the measurement correction process. Using convex optimization, bounding zones are computed for GPS positioning using the geometrical constraints imposed by the observation intervals. The bounding zone is a convex polytope, where exploiting only the navigation geometry, confidence domain is computed in form of zonotope. We show that the relative volume between the polytopes and the zonotope is an inconsistency measures. Small polytope volume indicates bad consistency of the observations. In extreme cases empty sets are obtained which indicates large outliers. We determine the observation intervals via sensitivity analysis of the Klobuchar ionospheric model and Saastamoinen tropospheric model. The remaining errors are treated as white noise. We explain how the shape and the volume of the polytope are related to the positioning geometry. We show that this assignment has to be interpreted with care. Furthermore, we propose a new concept of Minimum Detectable Biases (MDB). Taking GPS data from simulations and real experiments, a comparison analysis between the proposed deterministic bounding method and the classical least-squares adjustment has been conduct in terms of accuracy and reliability. This helps validating that our proposed deterministic bound methods shows high internal and external reliability compared to the probabilistic approaches and that it provides rigorous inconsistency measures.

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13

Rauh, Andreas, and Luc Jaulin. "Novel Techniques for a Verified Simulation of Fractional-Order Differential Equations." Fractal and Fractional 5, no. 1 (February 21, 2021): 17. http://dx.doi.org/10.3390/fractalfract5010017.

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Verified simulation techniques have been investigated intensively by researchers who are dealing with ordinary and partial differential equations. Tasks that have been considered in this context are the solution to initial value problems and boundary value problems, parameter identification, as well as the solution of optimal control problems in cases in which bounded uncertainty in parameters and initial conditions are present. In contrast to system models with integer-order derivatives, fractional-order models have not yet gained the same attention if verified solution techniques are desired. 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. As such, not only the influence of uncertain but bounded parameters can be accounted for in a guaranteed way. In addition, also round-off and (temporal) truncation errors that inevitably occur in numerical software implementations can be considered in a rigorous manner. This paper presents novel iterative and series-based solution approaches for the case of initial value problems to fractional-order system models, which will form the basic building block for implementing state estimation schemes in continuous-discrete settings, where the system dynamics is assumed as being continuous but measurements are only available at specific discrete sampling instants.

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14

Harno, Hendra G., Yoonsoo Kim, Jun Moon, and Hyochoong Bang. "Zonotopic Kalman filtering for stability augmentation and flight envelope estimation." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, April 9, 2021, 095441002199538. http://dx.doi.org/10.1177/0954410021995389.

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This article introduces a novel methodology based on zonotopic Kalman filtering for stabilizing attitude dynamics and estimating flight envelopes of an unmanned helicopter via an observer-based (output) feedback control law and a reachability analysis, respectively. The helicopter dynamics is represented by a linear state-space model, based on which the feedback control law is designed. Since not all state variables are measurable, state information is acquired by applying a zonotopic Kalman filter to yield sets of state-variable estimates of the helicopter in terms of zonotopes. Not only are the resulting zonotopes used for the observer-based feedback control, but also for estimating the flight envelopes of the helicopter based on the reachability analysis. This approach is useful for enhancing pilot’s awareness about dynamic responses of the helicopter, which may undergo unsafe flight conditions due to actuator faults triggered by undesirable perturbations. The efficacy of the proposed methodology is demonstrated via an example, where we also expose the benefits of applying the zonotopic Kalman filter as compared with an ordinary stochastic Kalman filter.

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15

Wan, Jian, and Luc Jaulin. "Reducing the wrapping effect of set computation via Delaunay triangulation for guaranteed state estimation of nonlinear discrete-time systems." Computing, March 15, 2024. http://dx.doi.org/10.1007/s00607-024-01275-0.

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AbstractSet computation methods have been widely used to compute reachable sets, design invariant sets and estimate system state for dynamic systems. The wrapping effect of such set computation methods plays an essential role in the accuracy of their solutions. This paper studies the wrapping effect of existing interval, zonotopic and polytopic set computation methods and proposes novel approaches to reduce the wrapping effect for these set computation methods based on the task of computing the dynamic evolution of a nonlinear uncertain discrete-time system with a set as the initial state. The proposed novel approaches include the partition of a polytopic set via Delaunay triangulation and also the representation of a polytopic set by the union of small zonotopes for the following set propagation. The proposed novel approaches with the reduced wrapping effect has been further applied to state estimation of a nonlinear uncertain discrete-time system with improved accuracy. Similar to bisection for interval and zonotopic sets, Delaunay triangulation has been introduced as a set partition tool for polytopic sets, which has opened new research directions in terms of novel set partition, set representation and set propagation for reducing the wrapping effect of set computation.

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16

Wang, Jing, Zhenlin Wang, and Meng Zhou. "Adaptive Event-Triggered Finite-Frequency Fault Detection With Zonotopic Threshold Analysis for LPV Systems." IEEE Transactions on Cybernetics, 2021, 1–11. http://dx.doi.org/10.1109/tcyb.2021.3054633.

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17

Meslem, Nacim. "Tight set-valued state estimation by combining reachability analysis and set-filtering approaches." Transactions of the Institute of Measurement and Control, September 8, 2023. http://dx.doi.org/10.1177/01423312231190193.

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In this work, a new approach to design set-valued state estimator for linear discrete-time systems subject to additive and bounded process and measurement uncertainties is proposed. First, the system state equation is rewritten to obtain a stable numerical scheme on which an explicit reachability method is developed, based on zonotopic set computation and a re-initialization procedure. Then, to enhance the accuracy of the computed reachable set, a set-filtering technique is designed based on the system output equation and its intrinsic invariant relationships. The implementation of this filtering method is based on interval analysis coupled to contractor algorithms. The convergence property of the proposed set-valued state estimator is shown under the classical detectability assumption of linear systems. Some simulation results are presented to show the merit of the proposed new set-membership state estimation approach.

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18

Lamouchi, Rihab, Nacim Meslem, and Tarek Raïssi. "Tight interval state estimate for discrete‐time descriptor linear systems." International Journal of Robust and Nonlinear Control, February 16, 2024. http://dx.doi.org/10.1002/rnc.7265.

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SummaryIn this work, two state estimation methods are proposed for a class of discrete‐time descriptor linear systems subject to bounded uncertainties. First, we propose set‐valued estimator algorithm using symmetric boxes to compute rigorous bounds of the system states. The observer gains are calculated using norm to attenuate the effects of the uncertainties and to improve the accuracy of the proposed estimator. Second, to obtain tighter state enclosures, zonotopic set computation are developed instead of interval analysis to design a new set‐valued state estimation algorithm. The performances of the proposed state estimation approaches are highlighted on different illustrative examples.

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19

He, Yikang, Wenhan Zhang, Zhenhua Wang, and Wen He. "Indirect measurement of solar array rotation angle for satellite emergency rescue." Transactions of the Institute of Measurement and Control, November 23, 2022, 014233122211249. http://dx.doi.org/10.1177/01423312221124989.

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In the emergency rescue mission, the primary task is to achieve the satellite’s orientation to the sun and ensure the energy supply. For this purpose, it is necessary to determine the rotation angle of solar array relative to satellite body. However, the rotation angle cannot be measured directly by the angle sensor in case of satellite emergency. To handle this issue, an indirect measurement method of solar array rotation angle is proposed in this paper. First, the indirect point measurement value of solar array rotation angle is given via the relationship between satellite body coordinate frame and solar array coordinate frame and the Rodrigues’ rotation formula. Then, the interval analysis technique is used to determine the upper and lower bounds of rotation angle and evaluate the influence of measurement noises. Based on the determined point measurement value and the interval analysis results, a zonotopic Kalman filter-based strategy is further proposed to improve the measurement accuracy. Finally, the effectiveness and validity of the proposed approach are demonstrated by numerical simulations, which illustrate its engineering application value.

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20

Chen, Ye, Chunyan Zhang, and Yinya Li. "An event‐triggered zonotopic Gaussian state estimator for discrete‐time stochastic multiplicative systems with zonotopic set‐membership and stochastic uncertainties." International Journal of Robust and Nonlinear Control, April 18, 2024. http://dx.doi.org/10.1002/rnc.7388.

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SummaryThis article addresses the challenge of estimating the state of a discrete‐time stochastic multiplicative system with zonotopic set‐membership and stochastic uncertainties. The stochastic system model incorporates additive and multiplicative Gaussian and zonotopic set‐membership uncertainties, posing challenges in accurately managing these sources of uncertainty. In practical scenarios with limited communication resources, it is crucial to reduce communication overhead, save resources, and prevent unnecessary information transmission. To achieve these objectives, this article proposes an event‐triggered mechanism and a corresponding state estimator. The optimal gain matrix of the state estimator is derived to minimize the estimation uncertainty represented by the size of zonotope and Gaussian confidence ellipsoid regions. Conditions are established to guarantee the mean square stability of the estimation error, ensuring reliable estimation performance. The configuration of the triggering condition parameters, which play a vital role in determining the event‐triggered updates, is presented. is presented. The effectiveness of the proposed event‐triggered mechanism and the corresponding estimator is demonstrated through simulation results and analyses, using specific metrics and evaluation criteria.

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21

Li, Yi, and Jiuxiang Dong. "Fault Detection for Discrete-Time Interval Type-2 Takagi--Sugeno Fuzzy Systems using $H_{-}/L_{\infty }$ Unknown Input Observer and Zonotopic Analysis." IEEE Transactions on Fuzzy Systems, 2023, 1–12. http://dx.doi.org/10.1109/tfuzz.2023.3305456.

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22

Bouchard, Samuel, Clément Gosselin, and Brian Moore. "On the Ability of a Cable-Driven Robot to Generate a Prescribed Set of Wrenches." Journal of Mechanisms and Robotics 2, no. 1 (December 18, 2009). http://dx.doi.org/10.1115/1.4000558.

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This paper presents a new geometry-based method to determine if a cable-driven robot operating in a d-degree-of-freedom workspace (2≤d≤6) with n≥d cables can generate a given set of wrenches in a given pose, considering acceptable minimum and maximum tensions in the cables. To this end, the fundamental nature of the available wrench set is studied. The latter concept, defined here, is closely related to similar sets introduced by Ebert-Uphoff and co-workers (2004, “Force-Feasible Workspace Analysis for Underconstrained, Point-Mass Cable Robots,” IEEE Trans. Rob. Autom., 5, pp. 4956–4962; 2007, “Workspace Optimization of a Very Large Cable-Driven Parallel Mechanism for a Radiotelescope Application,” Proceedings of the ASME IDETC/CIE Mechanics and Robotics Conference, Las Vegas, NV). It is shown that the available wrench set can be represented mathematically by a zonotope, a special class of convex polytopes. Using the properties of zonotopes, two methods to construct the available wrench set are discussed. From the representation of the available wrench set, computationally efficient and noniterative tests are presented to verify if this set includes the task wrench set, the set of wrenches needed for a given task.

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23

Andreoli, Francesco, and Claudio Zoli. "Robust dissimilarity comparisons with categorical outcomes." Social Choice and Welfare, August 16, 2022. http://dx.doi.org/10.1007/s00355-022-01419-1.

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AbstractThe analysis of many phenomena requires partitioning societies into groups and studying the extent at which these groups are distributed with different intensities across relevant non-ordered categorical outcomes. When the groups are similarly distributed, their members have equal chances to achieve any of the attainable outcomes. Otherwise, a form of dissimilarity between groups distributions prevails. We characterize axiomatically the dissimilarity partial order of multi-group distributions defined over categorical outcomes. The main result provides an equivalent representation of this partial order by the ranking of multi-group distributions originating from the inclusion of their zonotope representations. The zonotope inclusion criterion refines (that is, is implied by) majorization conditions that are largely adopted in mainstream approaches to multi-group segregation or univariate and multivariate inequality analysis.

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24

Kochdumper, Niklas, and Matthias Althoff. "Sparse Polynomial Zonotopes: A Novel Set Representation for Reachability Analysis." IEEE Transactions on Automatic Control, 2020, 1. http://dx.doi.org/10.1109/tac.2020.3024348.

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25

Zhang, Yuhao, Hang Zhang, and Xiangru Xu. "Backward Reachability Analysis of Neural Feedback Systems Using Hybrid Zonotopes." IEEE Control Systems Letters, 2023, 1. http://dx.doi.org/10.1109/lcsys.2023.3289572.

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26

Kousik, Shreyas, Adam Dai, and Grace X. Gao. "Ellipsotopes: Uniting Ellipsoids and Zonotopes for Reachability Analysis and Fault Detection." IEEE Transactions on Automatic Control, 2022, 1–13. http://dx.doi.org/10.1109/tac.2022.3191750.

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27

Kochdumper, Niklas, Hanna Krasowski, Xiao Wang, Stanley Bak, and Matthias Althoff. "Provably Safe Reinforcement Learning via Action Projection using Reachability Analysis and Polynomial Zonotopes." IEEE Open Journal of Control Systems, 2023, 1–14. http://dx.doi.org/10.1109/ojcsys.2023.3256305.

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28

Zhu, Fanglai, Yuyan Tang, and Zhenhua Wang. "Interval-Observer-based Fault Detection and Isolation Design for T-S Fuzzy System Based on Zonotope Analysis." IEEE Transactions on Fuzzy Systems, 2021, 1. http://dx.doi.org/10.1109/tfuzz.2021.3050854.

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29

Abdelaziz, S., L. Esteveny, L. Barbé, P. Renaud, B. Bayle, and M. de Mathelin. "Design of a Magnetic Resonance Imaging-Compatible Cable-Driven Manipulator With New Instrumentation and Synthesis Methods." Journal of Mechanical Design 136, no. 9 (June 19, 2014). http://dx.doi.org/10.1115/1.4027783.

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This paper deals with the design of a cable-driven manipulator (CDM) with instrumented structure for magnetic resonance imaging (MRI)-guided interventions. The strong magnetic field and the limited space inside the scanner constitute two severe design constraints. To handle them, a new synthesis approach for CDM is proposed in order to optimize the device compactness. This approach is based on the use of the zonotope properties to optimize the robot geometry, and the interval analysis tools for its validation. Remote actuation with Bowden cables is considered for MRI-compatibility. High friction along the line transmissions can then be expected which leads to a new instrumentation for cable tension evaluation. A prototype is manufactured and assessed. The principle of the instrumentation is validated as well as the user requirements in terms of workspace and ability to resist to external forces applied by the physician.

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30

Fassina, Nicolò, Francesco Ranzato, and Marco Zanella. "Robustness verification of k-nearest neighbors by abstract interpretation." Knowledge and Information Systems, April 26, 2024. http://dx.doi.org/10.1007/s10115-024-02108-4.

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AbstractWe study the certification of stability properties, such as robustness and individual fairness, of the k-nearest neighbor algorithm (kNN). Our approach leverages abstract interpretation, a well-established program analysis technique that has been proven successful in verifying several machine learning algorithms, notably, neural networks, decision trees, and support vector machines. In this work, we put forward an abstract interpretation-based framework for designing a sound approximate version of the kNN algorithm, which is instantiated to the interval and zonotope abstractions for approximating the range of numerical features. We show how this abstraction-based method can be used for stability, robustness, and individual fairness certification of kNN. Our certification technique has been implemented and experimentally evaluated on several benchmark datasets. These experimental results show that our tool can formally prove the stability of kNN classifiers in a precise and efficient way, thus expanding the range of machine learning models amenable to robustness certification.

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