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IEEE Conference on Decision and Control

作者： Epiphane Loko Antoine Chaillet Yuan Wang Iasson Karafyllis Pierdomenico Pepe Laboratoire des signaux et systèmes Université Paris-Saclay CNRS CentraleSupélec Gif-sur-Yvette France Mathematical Sciences Department Florida Atlantic University Boca Raton FL USA Mathematics Department National Technical University of Athens Athens Greece Information Engineering Computer Science and Mathematics Department University of L’Aquila Italy

ISBN: (数字)9798350316339

ISBN: (纸本)9798350316346

We propose relaxed Lyapunov-based conditions to ensure input-to-state stability (ISS) of nonlinear time-delay systems. Their strength lies in the fact that the dissipation rate of the Lyapunov-Krasovskii functional (LKF) involves only the current value of solution’s norm rather than the LKF itself. The additional requirement takes the form of a growth condition between the dissipation rate and its maximal increase along the system’s solutions. We show through examples that the obtained conditions are more general than existing techniques, including the strictification method through the addition of an exponential term in the integral kernel of the LKF, whose limitations are highlighted through a counter-example.

关键词： Kernel

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Confidence intervals of survival predictions with neural networks trained on molecular data

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Informatics in Medicine Unlocked 2024年 44卷

作者： Roblin, Elvire Cournède, Paul-Henry Michiels, Stefan MICS - Laboratory of Mathematics and Computer Science CentraleSupélec Paris-Saclay Unversity France Oncostat U1018 Inserm Paris-Saclay University labeled Ligue Contre le Cancer Villejuif France Department of Biostatistics and Epidemiology Gustave Roussy Paris-Saclay University France

In medicine, an important objective is predicting patients’ survival based on their molecular and clinical characteristics. In this context, neural networks have recently been used for their ability to capture complex interactions in the data. Measuring the uncertainty associated with survival estimates obtained by neural networks is essential to enhance predictions’ reliability. We compared four methods adapted to multilayer perceptrons (MLPs) for building confidence intervals at the patient level. The methods were based either on bootstrap with Boot (Efron, 1979), ensembling with DeepEns (Lakshminarayanan et al., 2016), or Monte-Carlo Dropout with MCDrop and BMask (Gal and Ghahramani, 2016;Mancini et al., 2020). A comparison was made through MLP-based survival models: CoxCC and CoxTime (Kvamme et al., 2019) in a continuous time framework, DeepHit (Lee et al., 2018) and PLANN (Biganzoli et al., 1998) in a discrete time framework. We applied the methods to a simulation study, enabling us to estimate a coverage rate of the estimated confidence intervals. We also applied them to real-world datasets, and predicted the survival probability for patients with breast cancer and patients with lung cancer. In the simulation study, CoxCC and CoxTime obtained the mean C-indices numerically closest to those from the Oracle model (mean C-index of 0.723 for CoxCC, 0.726 for CoxTime, versus 0.743 for the Oracle model). Regarding the confidence intervals of survival probabilities, Boot with CoxCC obtained a coverage rate of 96.5%, the closest to the nominal value of 95%. MCDrop was slightly anticonservative and obtained a coverage rate of 89.8% with CoxTime. This method may represent a reasonable compromise in terms of coverage with regards of computational time. In the breast cancer cohort, MLPs had difficulty capturing additional prognostic information from the molecular data. In contrast, in the lung cancer cohort, the models led to substantially stronger discrimination values w

关键词： Confidence intervals Machine learning Multi-layer perceptrons Survival prediction Uncertainty

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Scalable Stability of Nonlinear Interconnected Systems in case of amplifying Perturbations

Scalable Stability of Nonlinear Interconnected Systems in ca...

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American Control Conference (ACC)

作者： Marco Mirabilio Alessio Iovine Department of Information Engineering Computer Science and Mathematics Center of Excellence DEWS University of L’Aquila Laboratory of Signal and Systems (L2S) Centre National de la Recherche Scientifique (CNRS) CentraleSupélec Paris-Saclay University Gif-sur-Yvette France

This paper investigates the stability of large-scale systems (LSSs) in the presence of subsystems that amplify the perturbations propagated by their neighborhood, possibly leading to undesired behaviors of the overall interconnected system. Then, sufficient conditions ensuring the system trajectories boundedness and the subsequent LSS asymptotic stability in the sense of scalable Mesh Stability are proven to exist. The theoretical results show that there exists a dependence between the stability and the topology of the interconnected system. The obtained framework is then exploited for the stability analysis of a network of electrical microgrids, showing the effectiveness of the theoretical results.

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SIMD-based exact parallel fuzzy dilation operator for fast computing of fuzzy spatial relations 6

SIMD-based exact parallel fuzzy dilation operator for fast c...

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6th Workshop on Programming Models for SIMD/Vector Processing, WPMVP 2020, co-located with PPoPP 2020

作者： Pierrard, Régis Cabaret, Laurent Poli, Jean-Philippe Hudelot, Céline CEA LIST Gif-sur-Yvette cedex91191 France Paris-Saclay University CentraleSupélec Mathematics Interacting with Computer Science Gif-sur-Yvette91190 France

ISBN: (纸本)9781450375207

For decades, fuzzy spatial relations have demonstrated their utility and effectiveness for visual reasoning, including semantic annotation and object recognition. However, a major issue is that they often involve fuzzy morphological operators that are compute-intensive leading to long latency in the relation evaluation. As a result, approximate methods have been proposed to compute some relations in an acceptable time, but they are not as generic as the fuzzy dilation or do not make the most of modern computing architectures. In this paper, we introduce the Reverse and the Parallel Reverse (PR) algorithms. Reverse is an exact and efficient algorithm for the fuzzy dilation operator and PR combines the Reverse algorithm exactness with efficient usage of modern-processor multiple cores using OpenMP. Using SIMD extensions to enhance Parallel Reverse, PR128 (AVX), PR256 (AVX2), and PR512 (AVX512) are faster than the state-of-the-art approximate methods while remaining generic and exact. To demonstrate the performance of PR and highlight the contribution of the SIMD instructions, an extensive benchmark was carried out on two datasets of natural and artificial images. © 2020 Association for Computing Machinery.

关键词： Object recognition

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Path generation based on convex lifting: optimization of the corridors

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IFAC-PapersOnLine 2022年第16期55卷 260-265页

作者： Marco Mirabilio Sorin Olaru Carlos E.T. Dórea Alessio Iovine Maria Domenica Di Benedetto Department of Information Engineering Computer Science and Mathematics Center of Excellence DEWS University of L'Aquila Université Paris-Saclay CNRS CentraleSupélec Laboratoire des signaux et systèmes 91190 Gif-sur-Yvette France Department of Computer Engineering and Automation Universidade Federal do Rio Grande do Norte UFRN-CT-DCA 59078-900 Natal RN Brazil

The capability to compute a partition of a cluttered environment starting from the obstacles that lie in it enables the construction of a route connecting an initial point to a desired final one. In this paper, we revisit the convex lifting method for the computation of a suitable partition of the cluttered environment with the objective to propose a systematic procedure of reorganization of the cells within the partition in order to repel their boundaries from the obstacles. The ultimate goal is the construction of a connecting-path between an initial point and a final point characterized by a corridor with improved width guaranteeing the collision avoidance. The qualities of the corridors will impact the constraints on the motion of the controlled agent and consequently the real-time performance and robustness of the navigation in a cluttered environment.

关键词： obstacle avoidance linear systems optimization

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Uniform Global Asymptotic Stability for Time-Invariant Delay Systems

Uniform Global Asymptotic Stability for Time-Invariant Delay...

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IEEE Conference on Decision and Control

作者： Iasson Karafyllis Pierdomenico Pepe Antoine Chaillet Yuan Wang Mathematics Department National Technical University of Athens Athens Greece Information Engineering Computer Science and Mathematics Department University of L’Aquila L’Aquila Italy L2S-CentraleSupélec and Université Paris-Saclay France Mathematical Sciences Department Florida Atlantic University Boca Raton FL USA

ISBN: (数字)9781665467612

ISBN: (纸本)9781665467629

For time-invariant finite-dimensional systems, it is known that global asymptotic stability (GAS) is equivalent to uniform global asymptotic stability (UGAS), in which the decay rate and transient overshoot of solutions are requested to be uniform on bounded sets of initial states. This paper investigates this relationship for time-invariant delay systems. We show that UGAS and GAS are equivalent for this class of systems under the assumption of robust forward completeness, i.e. under the assumption that the reachable set from any bounded set of initial states on any finite time horizon is bounded. We also show that, if the state space is a space in a particular family of Sobolev or Hölder spaces, then GAS is equivalent to UGAS and that robust forward completeness holds. Based on these equivalences, we provide a novel Lyapunov characterization of GAS (and UGAS) in the aforementioned spaces.

关键词： Asymptotic stability Delay systems Aerospace electronics Transient analysis

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Growth Conditions for Global Exponential Stability and Exp-Iss of Time-Delay Systems Under Point-Wise Dissipation

SSRN

引用

SSRN 2022年

作者： Chaillet, Antoine Karafyllis, Iasson Pepe, Pierdomenico Wang, Yuan Mathematics Department National Technical University of Athens Athens15780 Greece Université Paris-Saclay CNRS CentraleSupélec Laboratoire des signaux et systèmes Gif-sur-Yvette 91190 France Information Engineering Computer Science and Mathematics Department University of L’Aquila L’Aquila67100 Italy Mathematical Sciences Department Florida Atlantic University Boca RatonFL33431 United States

For time-delay systems, it is known that global asymptotic stability is guaranteed by the existence of a Lyapunov-Krasovskii functional that dissipates in a point-wise manner along solutions, namely whose dissipation rate involves only the current value of the solution's norm. So far, the extension of this result to global exponential stability (GES) holds only for systems ruled by a globally Lipschitz vector field and remains largely open for the input-to-state stability (ISS) property. In this paper, we rely on the notion of exponential ISS to extend the class of systems for which GES or ISS can be concluded from a point-wise dissipation. Our results in turn show that these properties still hold in the presence of a sufficiently small additional term involving the whole state history norm. We provide explicit estimates of the tolerable magnitude of this extra term and show through an example how it can be used to assess robustness with respect to modeling uncertainties. © 2022, The Authors. All rights reserved.

关键词： Delay control systems

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Growth conditions for global exponential stability and exp-ISS of time-delay systems under point-wise dissipation

arXiv

引用

arXiv 2022年

作者： Chaillet, Antoine Karafyllis, Iasson Pepe, Pierdomenico Wang, Yuan Mathematics Department National Technical University of Athens Athens15780 Greece Université Paris-Saclay CNRS CentraleSupélec Laboratoire des Signaux et Systèmes Gif-Sur-Yvette 91190 France Information Engineering Computer Science and Mathematics Department University of L’Aquila L’Aquila67100 Italy Mathematical Sciences Department Florida Atlantic University Boca RatonFL33431 United States

For time-delay systems, it is known that global asymptotic stability is guaranteed by the existence of a Lyapunov-Krasovskii functional that dissipates in a point-wise manner along solutions, namely whose dissipation rate involves only the current value of the solution’s norm. So far, the extension of this result to global exponential stability (GES) holds only for systems ruled by a globally Lipschitz vector field and remains largely open for the input-to-state stability (ISS) property. In this paper, we rely on the notion of exponential ISS to extend the class of systems for which GES or ISS can be concluded from a point-wise dissipation. Our results in turn show that these properties still hold in the presence of a sufficiently small additional term involving the whole state history norm. We provide explicit estimates of the tolerable magnitude of this extra term and show through an example how it can be used to assess robustness with respect to modeling uncertainties. Copyright © 2022, The Authors. All rights reserved.

关键词： Delay control systems

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Is Global Asymptotic Stability Necessarily Uniform for Time-Delay Systems?

arXiv

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arXiv 2022年

作者： Karafyllis, Iasson Pepe, Pierdomenico Chaillet, Antoine Wang, Yuan Dept. of Mathematics National Technical University of Athens Zografou Campus Athens15780 Greece Dept. of Information Engineering Computer Science and Mathematics University of L'Aquila L'Aquila67100 Italy L2S-CentraleSupélec and Université Paris-Saclay Institut Universitaire de France France Dept. of Mathematical Sciences Florida Atlantic University Boca RatonFL33431 United States

关键词： Equivalence classes

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Majorization-Minimization for sparse SVMs

arXiv

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arXiv 2023年

作者： Benfenati, A. Chouzenoux, E. Franchini, G. Latva–Äijö, S. Narnhofer, D. Pesquet, J.-C. Scott, S.J. Yousefi, M. Environmental and Science Department Via Celoria 2 Milano20133 Italy CVN Inria CentraleSupélec University Paris Saclay 9 rue Joliot Curie Gif-sur-Yvette91190 France Department of Physics Informatics and Mathematics Via Campi 213/B Modena41125 Italy Department of Mathematics and Statistics Pietari Kalmin katu 5 Helsinki00014 Finland Institute for Computer Graphic and Vision Graz University of Technology Inffeldgasse 16 Graz8010 Austria Department of Mathematical Sciences University of Bath BA2 7AY United Kingdom Department of Mathematics and Geosciences University of Trieste via Valerio 12/1 34127 Italy

Several decades ago, Support Vector Machines (SVMs) were introduced for performing binary classification tasks, under a supervised framework. Nowadays, they often outperform other supervised methods and remain one of the most popular approaches in the machine learning arena. In this work, we investigate the training of SVMs through a smooth sparse-promoting-regularized squared hinge loss minimization. This choice paves the way to the application of quick training methods built on majorization-minimization approaches, benefiting from the Lipschitz differentiabililty of the loss function. Moreover, the proposed approach allows us to handle sparsity-preserving regularizers promoting the selection of the most significant features, so enhancing the performance. Numerical tests and comparisons conducted on three different datasets demonstrate the good performance of the proposed methodology in terms of qualitative metrics (accuracy, precision, recall, and F1 score) as well as computational cost. © 2023, CC BY.

关键词： Support vector machines

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