Relevant bibliographies by topics / Stabilité Lipschitz

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Stabilité Lipschitz'

Author: Grafiati
Published: 25 May 2024

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Journal articles on the topic "Stabilité Lipschitz"

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Soliman, A. A. "On eventual stability of impulsive systems of differential equations." International Journal of Mathematics and Mathematical Sciences 27, no. 8 (2001): 485–94. http://dx.doi.org/10.1155/s0161171201005622.

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The notions of Lipschitz stability of impulsive systems of differential equations are extended and the notions of eventual stability are introduced. New notions called eventual and eventual Lipschitz stability. We give some criteria and results.
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Grunert, Katrin, and Matthew Tandy. "Lipschitz stability for the Hunter–Saxton equation." Journal of Hyperbolic Differential Equations 19, no. 02 (June 2022): 275–310. http://dx.doi.org/10.1142/s0219891622500072.

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We study Lipschitz stability in time for [Formula: see text]-dissipative solutions to the Hunter–Saxton equation, where [Formula: see text] is a constant. We define metrics in both Lagrangian and Eulerian coordinates, and establish Lipschitz stability for those metrics.
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Fu, Yu Li. "On Lipschitz stability for F.D.E." Pacific Journal of Mathematics 151, no. 2 (December 1, 1991): 229–35. http://dx.doi.org/10.2140/pjm.1991.151.229.

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Pilyugin, Sergei Yu, and Sergey Tikhomirov. "Lipschitz shadowing implies structural stability." Nonlinearity 23, no. 10 (August 20, 2010): 2509–15. http://dx.doi.org/10.1088/0951-7715/23/10/009.

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Jiang, Zuohai, and Shicheng Xu. "Stability of Pure Nilpotent Structures on Collapsed Manifolds." International Mathematics Research Notices 2020, no. 24 (February 13, 2019): 10317–45. http://dx.doi.org/10.1093/imrn/rnz023.

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Abstract The goal of this paper is to study the stability of pure nilpotent structures on an $n$-manifold for different collapsed metrics. We prove that if two metrics with bounded sectional curvature are $L_0$-bi-Lipschitz equivalent and sufficient collapsed (depending on $L_0$ and $n$), then up to a diffeomorphism, the underlying nilpotent Killing structures coincide with each other, or one is embedded into another as a subsheaf. It improves Cheeger–Fukaya–Gromov’s local compatibility of pure nilpotent Killing structures for one collapsed metric to two Lipschitz equivalent metrics. As an application, we prove that those pure nilpotent Killing structures constructed by various smoothing methods to a Lipschitz equivalent metric with bounded sectional curvature are uniquely determined by the original metric modulo a diffeomorphism.
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Chu, Chin-Ku, Myung-Sun Kim, and Keon-Hee Lee. "Lipschitz stability and Lyapunov stability in dynamical systems." Nonlinear Analysis: Theory, Methods & Applications 19, no. 10 (November 1992): 901–9. http://dx.doi.org/10.1016/0362-546x(92)90102-k.

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Martynyuk, A. A. "On integral stability and Lipschitz stability of motion." Ukrainian Mathematical Journal 49, no. 1 (January 1997): 84–92. http://dx.doi.org/10.1007/bf02486618.

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KLEMENT, ERICH PETER, ANNA KOLESÁROVÁ, RADKO MESIAR, and ANDREA STUPŇANOVÁ. "LIPSCHITZ CONTINUITY OF DISCRETE UNIVERSAL INTEGRALS BASED ON COPULAS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 18, no. 01 (February 2010): 39–52. http://dx.doi.org/10.1142/s0218488510006374.

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The stability of discrete universal integrals based on copulas is discussed and examined, both with respect to the norms L1 (Lipschitz stability) and L∞ (Chebyshev stability). Each of these integrals is shown to be 1-Lipschitz. Exactly the discrete universal integrals based on a copula which is stochastically increasing in its first coordinate turn out to be 1-Chebyshev. A new characterization of stochastically increasing Archimedean copulas is also given.
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Gracia, Juan-Miguel, and Francisco E. Velasco. "Lipschitz stability of controlled invariant subspaces." Linear Algebra and its Applications 434, no. 4 (February 2011): 1137–62. http://dx.doi.org/10.1016/j.laa.2010.10.024.

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Chu, Chin-Ku, and Keon-Hee Lee. "Embedding of Lipschitz stability in flows." Nonlinear Analysis: Theory, Methods & Applications 26, no. 11 (June 1996): 1749–52. http://dx.doi.org/10.1016/0362-546x(95)00014-m.

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Dissertations / Theses on the topic "Stabilité Lipschitz"

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Neacșu, Ana-Antonia. "Robust Deep learning methods inspired by signal processing algorithms." Electronic Thesis or Diss., université Paris-Saclay, 2023. http://www.theses.fr/2023UPAST212.

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Comprendre l'importance des stratégies de défense contre les attaques adverses est devenu primordial pour garantir la fiabilité et la résilience des réseaux de neurones. Alors que les mesures de sécurité traditionnelles se focalisent sur la protection des données et des logiciels contre les menaces externes, le défi unique posé par les attaques adverses réside dans leur capacité à exploiter les vulnérabilités inhérentes aux algorithmes d'apprentissage automatique.Dans la première partie de la thèse, nous proposons de nouvelles stratégies d'apprentissage contraint qui garantissent la robustesse vis-à-vis des perturbations adverses, en contrôlant la constante de Lipschitz d'un classifeur. Nous concentrons notre attention sur les réseaux de neurones positifs pour lesquels des bornes de Lipschitz précises peuvent être déduites, et nous proposons différentes contraintes de norme spectrale offrant des garanties de robustesse, d'un point de vue théorique. Nous validons notre solution dans le contexte de la reconnaissance de gestes basée sur des signaux électromyographiques de surface (sEMG).Dans la deuxième partie de la thèse, nous proposons une nouvelle classe de réseaux de neurones (ACNN) qui peut être considérée comme un intermédiaire entre les réseaux entièrement connectés et ceux convolutionnels. Nous proposons un algorithme itératif pour contrôler la robustesse pendant l'apprentissage. Ensuite, nous étendons notre solution au plan complexe et abordons le problème de la conception de réseaux de neurones robustes à valeurs complexes, en proposant une nouvelle architecture (RCFF-Net) pour laquelle nous obtenons des bornes fines de la constante de Lipschitz. Les deux solutions sont validées en débruitage audio.Dans la dernière partie, nous introduisons les réseaux ABBA, une nouvelle classe de réseaux de neurones (presque) positifs, dont nous démontrons les propriétés d'approximation universelle.Nous déduisons des bornes fines de Lipschitz pour les couches linéaires ou convolutionnelles, et nous proposons un algorithme pour entraîner des réseaux ABBA robustes.Nous démontrons l'efficacité de l'approche proposée dans le contexte de la classification d'images
Understanding the importance of defense strategies against adversarial attacks has become paramount in ensuring the trustworthiness and resilience of neural networks. While traditional security measures focused on protecting data and software from external threats, the unique challenge posed by adversarial attacks lies in their ability to exploit the inherent vulnerabilities of the underlying machine learning algorithms themselves.The first part of the thesis proposes new constrained learning strategies that ensure robustness against adversarial perturbations by controlling the Lipschitz constant of a classifier. We focus on nonnegative neural networks for which accurate Lipschitz bounds can be derived, and we propose different spectral norm constraints offering robustness guarantees from a theoretical viewpoint. We validate our solution in the context of gesture recognition based on Surface Electromyographic (sEMG) signals.In the second part of the thesis, we propose a new class of neural networks (ACNN) which can be viewed as establishing a link between fully connected and convolutional networks, and we propose an iterative algorithm to control their robustness during training. Next, we extend our solution to the complex plane and address the problem of designing robust complex-valued neural networks by proposing a new architecture (RCFF-Net) for which we derive tight Lipschitz constant bounds. Both solutions are validated for audio denoising.In the last part, we introduce ABBA Networks, a novel class of (almost) non-negative neural networks, which we show to be universal approximators. We derive tight Lipschitz bounds for both linear and convolutional layers, and we propose an algorithm to train robust ABBA networks. We show the effectiveness of the proposed approach in the context of image classification
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Burnet, Steeve. "Méthodes de résolution d’inclusions variationnelles sous hypothèses de stabilité." Thesis, Antilles-Guyane, 2012. http://www.theses.fr/2012AGUY0594/document.

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Dans cette thèse, nous nous intéressons à des inclusions de la forme 0∈ f( x) + F(x), où f est une application univoque et F est une application multivoque à graphe fermé. Ces dernières années, diverses méthodes de résolutions d'inclusions de ce type ont été développées par les chercheurs et, après un bref rappel sur quelques notions d'analyse (univoque et multivoque) nous en présentons quelques unes utilisant l'hypothèse de régularité métrique sur l'application multivoque. Dans la suite de notre travail, plutôt que d'utiliser cette hypothèse de régularité métrique, nous lui préférons des hypothèses directement liées à la solution qui sont la semistabilité et l'hemistabilité. Notons que la semistabilité d'une solution x̅ de l'inclusion 0∈G(x) est en fait équivalente à la sous-régularité métrique forte de l'application multivoque G en x̅ pour 0. Après avoir présenté des méthodes utilisant la semistabilité et l'hemistabilité, nous exposons les nouveaux résultats auxquels nous avons abouti qui consistent essentiellement en des améliorations des méthodes présentées. Ce que nous entendons par améliorations se décline en deux points principaux : soit nous obtenons un meilleur taux de convergence, soit nous utilisons des hypothèses plus faibles qui nous permettent d'obtenir des taux de convergence similaires
In this thesis, we focus on inclusions in the form of 0∈ f( x) + F(x), where f is a single-valued function and F is a set-valued map with closed graph. In the last few years, various methods to solve such inclusions have been developed; after having recalled some notions in analysis (single-valued and set-valued) we present some of them using metric regularity on the set-valued map. Then, instead of considering this metric regularity assumption, we prefer assumptions which are directly connected to the solution, that are semistability and hemistability. One can note that semistabily of a solution x̅ of the inclusion 0∈G(x) is actually equivalent strong metric subregularity on the set-valued map G at x̅ for 0. After having presented some methods using semistability and hemistability, we show the new results we obtained, most of them being improvement of the presented methods. What we mean by improvement is mainly a better convergence rate on the one hand, and weaker assumptions that lead to similar convergence rate, on the other
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Gupta, Kavya. "Stability Quantification of Neural Networks." Electronic Thesis or Diss., université Paris-Saclay, 2023. http://www.theses.fr/2023UPAST004.

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Les réseaux de neurones artificiels sont au cœur des avancées récentes en Intelligence Artificielle. L'un des principaux défis auxquels on est aujourd'hui confronté, notamment au sein d'entreprises comme Thales concevant des systèmes industriels avancés, est d'assurer la sécurité des nouvelles générations de produits utilisant cette technologie. En 2013, une observation clé a révélé que les réseaux de neurones sont sensibles à des perturbations adverses. Ceci soulève de sérieuses inquiétudes quant à leur applicabilité dans des environnements où la sécurité est critique. Au cours des dernières années, des publications ont étudiées les différents aspects de la robustesse des réseaux de neurones, et des questions telles que ``Pourquoi des attaques adverses se produisent?", ``Comment pouvons-nous rendre les réseaux de neurones plus robustes à ces bruits ?", ``Comment générer des attaques plus fortes", etc., se sont posées avec une acuité croissante. Cette thèse vise à apporter des réponses à de telles questions. La communauté s'intéressant aux attaques adverses en apprentissage automatique travaille principalement sur des scénarios de classification, alors que les études portant sur des tâches de régression sont rares. Nos contributions comblent le fossé existant entre les méthodes adverses en apprentissage et les applications de régression.Notre première contribution, dans le chapitre 3, propose un algorithme de type ``boîte blanche" pour attaquer les modèles de régression. L'attaquant adverse présenté est déduit des propriétés algébriques du Jacobien du réseau. Nous montrons que notre attaquant réussit à tromper le réseau de neurones et évaluons son efficacité à réduire les performances d'estimation. Nous présentons nos résultats sur divers ensembles de données tabulaires industriels en libre accès et réels. Notre analyse repose sur la quantification de l'erreur de tromperie ainsi que différentes métriques. Une autre caractéristique remarquable de notre algorithme est qu'il nous permet d'attaquer de manière optimale un sous-ensemble d'entrées, ce qui peut aider à identifier la sensibilité de certaines d'entre elles. La deuxième contribution de cette thèse (Chapitre 4) présente une analyse de la constante de Lipschitz multivariée des réseaux de neurones. La constante de Lipschitz est largement utilisée dans la littérature pour étudier les propriétés intrinsèques des réseaux de neurones. Mais la plupart des travaux font une analyse mono-paramétrique, qui ne permet pas de quantifier l'effet des entrées individuelles sur la sortie. Nous proposons une analyse multivariée de la stabilité des réseaux de neurones entièrement connectés, reposant sur leur propriétés Lipschitziennes. Cette analyse nous permet de saisir l'influence de chaque entrée ou groupe d'entrées sur la stabilité du réseau de neurones. Notre approche repose sur une re-normalisation appropriée de l'espace d'entrée, visant à effectuer une analyse plus précise que celle fournie par une constante de Lipschitz globale. Nous visualisons les résultats de cette analyse par une nouvelle représentation conçue pour les praticiens de l'apprentissage automatique et les ingénieurs en sécurité appelée étoile de Lipschitz. L'utilisation de la normalisation spectrale dans la conception d'une boucle de contrôle de stabilité est abordée au chapitre 5. Une caractéristique essentielle du modèle optimal consiste à satisfaire aux objectifs de performance et de stabilité spécifiés pour le fonctionnement. Cependant, contraindre la constante de Lipschitz lors de l'apprentissage des modèles conduit généralement à une réduction de leur précision. Par conséquent, nous concevons un algorithme permettant de produire des modèles de réseaux de neurones ``stable dès la conception" en utilisant une nouvelle approche de normalisation spectrale, qui optimise le modèle, en tenant compte à la fois des objectifs de performance et de stabilité. Nous nous concentrons sur les petits drones aériens (UAV)
Artificial neural networks are at the core of recent advances in Artificial Intelligence. One of the main challenges faced today, especially by companies likeThales designing advanced industrial systems is to ensure the safety of newgenerations of products using these technologies. In 2013 in a key observation, neural networks were shown to be sensitive to adversarial perturbations, raising serious concerns about their applicability in critically safe environments. In the last years, publications studying the various aspects of this robustness of neural networks, and rising questions such as "Why adversarial attacks occur?", "How can we make the neural network more robust to adversarial noise?", "How to generate stronger attacks?" etc., have grown exponentially. The contributions of this thesis aim to tackle such problems. The adversarial machine learning community concentrates majorly on classification scenarios, whereas studies on regression tasks are scarce. Our contributions bridge this significant gap between adversarial machine learning and regression applications.The first contribution in Chapter 3 proposes a white-box attackers designed to attack regression models. The presented adversarial attacker is derived from the algebraic properties of the Jacobian of the network. We show that our attacker successfully fools the neural network and measure its effectiveness in reducing the estimation performance. We present our results on various open-source and real industrial tabular datasets. Our analysis relies on the quantification of the fooling error as well as different error metrics. Another noteworthy feature of our attacker is that it allows us to optimally attack a subset of inputs, which may help to analyze the sensitivity of some specific inputs. We also, show the effect of this attacker on spectrally normalised trained models which are known to be more robust in handling attacks.The second contribution of this thesis (Chapter 4) presents a multivariate Lipschitz constant analysis of neural networks. The Lipschitz constant is widely used in the literature to study the internal properties of neural networks. But most works do a single parametric analysis, which do not allow to quantify the effect of individual inputs on the output. We propose a multivariate Lipschitz constant-based stability analysis of fully connected neural networks allowing us to capture the influence of each input or group of inputs on the neural network stability. Our approach relies on a suitable re-normalization of the input space, intending to perform a more precise analysis than the one provided by a global Lipschitz constant. We display the results of this analysis by a new representation designed for machine learning practitioners and safety engineers termed as a Lipschitz star. We perform experiments on various open-access tabular datasets and an actual Thales Air Mobility industrial application subject to certification requirements.The use of spectral normalization in designing a stability control loop is discussed in Chapter 5. A critical part of the optimal model is to behave according to specified performance and stability targets while in operation. But imposing tight Lipschitz constant constraints while training the models usually leads to a reduction of their accuracy. Hence, we design an algorithm to train "stable-by-design" neural network models using our spectral normalization approach, which optimizes the model by taking into account both performance and stability targets. We focus on Small Unmanned Aerial Vehicles (UAVs). More specifically, we present a novel application of neural networks to detect in real-time elevon positioning faults to allow the remote pilot to take necessary actions to ensure safety
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Gasmi, Noussaiba. "Observation et commande d'une classe de systèmes non linéaires temps discret." Thesis, Université de Lorraine, 2018. http://www.theses.fr/2018LORR0177/document.

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L’analyse et la synthèse des systèmes dynamiques ont connu un développement important au cours des dernières décennies comme l’atteste le nombre considérable des travaux publiés dans ce domaine, et continuent d’être un axe de recherche régulièrement exploré. Si la plupart des travaux concernent les systèmes linéaires et non linéaires temps continu, peu de résultats ont étaient établis dans le cas temps discret. Les travaux de cette thèse portent sur l’observation et la commande d’une classe de systèmes non linéaires à temps discret. Dans un premier temps, le problème de synthèse d’observateur d’état utilisant une fenêtre de mesures glissante est abordé. Des conditions de stabilité et de robustesse moins restrictives sont déduites. Deux classes de systèmes non linéaires à temps discret sont étudiées : les systèmes de type Lipschitz et les systèmes « one-sided Lipschitz ». Ensuite, une approche duale a été explorée afin de déduire une loi de commande stabilisante basée sur un observateur. Les conditions d’existence d’un observateur et d’un contrôleur stabilisant les systèmes étudiés sont formulées sous forme d’un problème d’optimisation LMI. L’efficacité et la validité des approches présentées sont montrées à travers des exemples académiques
The analysis and synthesis of dynamic systems has undergone significant development in recent decades, as illustrated by the considerable number of published works in this field, and continue to be a research theme regularly explored. While most of the existing work concerns linear and nonlinear continuous-time systems, few results have been established in the discrete-time case. This thesis deals with the observation and control of a class of nonlinear discrete-time systems. First, the problem of state observer synthesis using a sliding window of measurements is discussed. Non-restrictive stability and robustness conditions are deduced. Two classes of discrete time nonlinear systems are studied: Lipschitz systems and one-side Lipschitz systems. Then, a dual approach was explored to derive a stabilizing control law based on observer-based state feedback. The conditions for the existence of an observer and a controller stabilizing the studied classes of nonlinear systems are expressed in term of LMI. The effectiveness and validity of the proposed approaches are shown through numerical examples
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Malanowski, Kazimierz, and Fredi Tröltzsch. "Lipschitz Stability of Solutions to Parametric Optimal Control Problems for Parabolic Equations." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199801001.

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A class of parametric optimal control problems for semilinear parabolic equations is considered. Using recent regularity results for solutions of such equations, sufficient conditions are derived under which the solutions to optimal control problems are locally Lipschitz continuous functions of the parameter in the L1-norm. It is shown that these conditions are also necessary, provided that the dependence of data on the parameter is sufficiently strong.
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Tröltzsch, F. "Lipschitz stability of solutions to linear-quadratic parabolic control problems with respect to perturbations." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199801229.

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We consider a class of control problems governed by a linear parabolic initial-boundary value problem with linear-quadratic objective and pointwise constraints on the control. The control system contains different types of perturbations. They appear in the linear part of the objective functional, in the right hand side of the equation, in its boundary condition, and in the initial value. Making use of parabolic regularity in the whole scale of $L^p$ the known Lipschitz stability in the $L^2$-norm is improved to the supremum-norm.
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John, Dominik [Verfasser]. "Uniqueness and Stability near Stationary Solutions for the Thin-Film Equation in Multiple Space Dimensions with Small Initial Lipschitz Perturbations / Dominik John." Bonn : Universitäts- und Landesbibliothek Bonn, 2013. http://d-nb.info/104527626X/34.

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Charabati, Mohamad. "Le problème de Dirichlet pour les équations de Monge-Ampère complexes." Thesis, Toulouse 3, 2016. http://www.theses.fr/2016TOU30001/document.

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Cette thèse est consacrée à l'étude de la régularité des solutions des équations de Monge-Ampère complexes ainsi que des équations hessiennes complexes dans un domaine borné de Cn. Dans le premier chapitre, on donne des rappels sur la théorie du pluripotentiel. Dans le deuxième chapitre, on étudie le module de continuité des solutions du problème de Dirichlet pour les équations de Monge-Ampère lorsque le second membre est une mesure à densité continue par rapport à la mesure de Lebesgue dans un domaine strictement hyperconvexe lipschitzien. Dans le troisième chapitre, on prouve la continuité hölderienne des solutions de ce problème pour certaines mesures générales. Dans le quatrième chapitre, on considère le problème de Dirichlet pour les équations hessiennes complexes plus générales où le second membre dépend de la fonction inconnue. On donne une estimation précise du module de continuité de la solution lorsque la densité est continue. De plus, si la densité est dans Lp , on démontre que la solution est Hölder-continue jusqu'au bord
In this thesis we study the regularity of solutions to the Dirichlet problem for complex Monge-Ampère equations and also for complex Hessian equations in a bounded domain of Cn. In the first chapter, we give basic facts in pluripotential theory. In the second chapter, we study the modulus of continuity of solutions to the Dirichlet problem for complex Monge-Ampère equations when the right hand side is a measure with continuous density with respect to the Lebesgue measure in a bounded strongly hyperconvex Lipschitz domain. In the third chapter, we prove the Hölder continuity of solutions to this problem for some general measures. In the fourth chapter, we consider the Dirichlet problem for complex Hessian equations when the right hand side depends on the unknown function. We give a sharp estimate of the modulus of continuity of the solution as the density is continuous. Moreover, for the case of Lp-density we demonstrate that the solution is Hölder continuous up to the boundary
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Book chapters on the topic "Stabilité Lipschitz"

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Dontchev, Asen L. "Lipschitz Stability in Optimization." In Lectures on Variational Analysis, 103–12. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-79911-3_11.

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Wang, Kelei. "Uniqueness, Stability and Uniform Lipschitz Estimates." In Free Boundary Problems and Asymptotic Behavior of Singularly Perturbed Partial Differential Equations, 17–26. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-33696-6_2.

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Dontchev, A. L. "Characterizations of Lipschitz Stability in Optimization." In Recent Developments in Well-Posed Variational Problems, 95–115. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-015-8472-2_4.

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Pilyugin, Sergei Yu, and Kazuhiro Sakai. "Lipschitz and Hölder Shadowing and Structural Stability." In Lecture Notes in Mathematics, 37–124. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-65184-2_2.

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Guo, Shuli, and Lina Han. "Lipschitz Stability Analysis on a Type of Nonlinear Perturbed System." In Stability and Control of Nonlinear Time-varying Systems, 179–91. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-10-8908-4_9.

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Felgenhauer, Ursula. "Lipschitz Stability of Broken Extremals in Bang-Bang Control Problems." In Large-Scale Scientific Computing, 317–25. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-78827-0_35.

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Fu, Chaojin, and Ailong Wu. "Global Exponential Stability of Delayed Neural Networks with Non-lipschitz Neuron Activations and Impulses." In Advances in Computation and Intelligence, 92–100. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-04843-2_11.

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Di Ferdinando, Mario, Pierdomenico Pepe, and Emilia Fridman. "Practical Stability Preservation Under Sampling, Actuation Disturbance and Measurement Noise, for Globally Lipschitz Time-Delay Systems." In Advances in Delays and Dynamics, 109–24. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-89014-8_6.

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Hashimoto, Hiroya. "Approximation and Stability of Solutions of SDEs Driven by a Symmetric α Stable Process with Non-Lipschitz Coefficients." In Lecture Notes in Mathematics, 181–99. Heidelberg: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-00321-4_7.

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"Stability in the Lipschitz norms." In Functional Equations and Inequalities in Several Variables, 235–43. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812778116_0025.

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Conference papers on the topic "Stabilité Lipschitz"

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Doostmohammadian, Mohammad Reza, and Hassan Sayyaadi. "Finite-Time Consensus in Undirected/Directed Network Topologies." In ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2010. http://dx.doi.org/10.1115/esda2010-24012.

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The main contribution of this paper is to introduce a novel non-Lipschitz protocol that guarantees consensus in finite-time domain. Its convergence in networks with both unidirectional and bidirectional links is investigated via Lyapunov Theorem approach. It is also proved that final agreement value is equal to average of agents’ states for the bidirectional communication case. In addition effects of communication time-delay on stability are assessed and two other continuous Lipschitz protocols are also analyzed.
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Kokolakis, Nick-Marios T., Kyriakos G. Vamvoudakis, and Wassim M. Haddad. "Fixed-Time Learning for Optimal Feedback Control." In ASME 2023 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2023. http://dx.doi.org/10.1115/detc2023-117007.

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Abstract In this paper, we introduce the problem of fixed-time optimal stabilization to construct feedback controllers that guarantee closed-loop system fixed-time stability while optimizing a given performance measure. Specifically, fixed-time stability of the closed-loop system is established via a Lyapunov function satisfying a differential inequality while simultaneously serving as a solution to the steady-state Hamilton-Jacobi-Bellman equation ensuring optimality. Given that the Hamilton-Jacobi-Bellman equation is generally difficult to solve, we develop a critic-only reinforcement learning-based algorithm for learning the solution to the steady-state Hamilton-Jacobi-Bellman equation in fixed-time. In particular, a non-Lipschitz experience replay-based learning law utilizing recorded and current data is introduced for updating the critic weights to learn the value function. The non-Lipschitz property of the dynamics gives rise to fixed-time stability, while the experience replay-based approach eliminates the need to satisfy the persistence of excitation condition as long as the recorded data is sufficiently rich. Simulation results demonstrate the efficacy of the proposed approach.
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Puerta, Ferran, and Xavier Puerta. "On the Lipschitz stability of (A,B)-invariant subspaces." In 2009 17th Mediterranean Conference on Control and Automation (MED). IEEE, 2009. http://dx.doi.org/10.1109/med.2009.5164649.

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BELLASSOUED, M., and M. YAMAMOTO. "LIPSCHITZ STABILITY IN AN INVERSE HYPERBOLIC PROBLEM BY BOUNDARY OBSERVATIONS." In Proceedings of the 5th International ISAAC Congress. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789812835635_0130.

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Ozcan, Neyir. "New results for global stability of neutral-type delayed neural networks." In The 11th International Conference on Integrated Modeling and Analysis in Applied Control and Automation. CAL-TEK srl, 2018. http://dx.doi.org/10.46354/i3m.2018.imaaca.004.

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"This paper deals with the stability analysis of the class of neutral-type neural networks with constant time delay. By using a suitable Lyapunov functional, some delay independent sufficient conditions are derived, which ensure the global asymptotic stability of the equilibrium point for this this class of neutral-type neural networks with time delays with respect to the Lipschitz activation functions. The presented stability results rely on checking some certain properties of matrices. Therefore, it is easy to verify the validation of the constraint conditions on the network parameters of neural system by simply using some basic information of the matrix theory."
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Mukherjee, Arunima, and Aparajita Sengupta. "Input tracking of Lipschitz nonlinear systems using input-state-stability approach." In 2016 2nd International Conference on Control, Instrumentation, Energy & Communication (CIEC). IEEE, 2016. http://dx.doi.org/10.1109/ciec.2016.7513814.

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Hristova, S., A. Dobreva, and K. Ivanova. "Lipschitz stability of differential equations with supremum and non-instantaneous impulses." In SEVENTH INTERNATIONAL CONFERENCE ON NEW TRENDS IN THE APPLICATIONS OF DIFFERENTIAL EQUATIONS IN SCIENCES (NTADES 2020). AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0040099.

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Barucq, H., H. Calandra, M. V. De Hoop, F. Faucher, and J. Shi. "Full waveform inversion for elastic medium using quantitative Lipschitz stability estimates." In 7th EAGE Saint Petersburg International Conference and Exhibition. Netherlands: EAGE Publications BV, 2016. http://dx.doi.org/10.3997/2214-4609.201600240.

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Yuan, Zhecheng, Guozheng Ma, Yao Mu, Bo Xia, Bo Yuan, Xueqian Wang, Ping Luo, and Huazhe Xu. "Don’t Touch What Matters: Task-Aware Lipschitz Data Augmentation for Visual Reinforcement Learning." In Thirty-First International Joint Conference on Artificial Intelligence {IJCAI-22}. California: International Joint Conferences on Artificial Intelligence Organization, 2022. http://dx.doi.org/10.24963/ijcai.2022/514.

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One of the key challenges in visual Reinforcement Learning (RL) is to learn policies that can generalize to unseen environments. Recently, data augmentation techniques aiming at enhancing data diversity have demonstrated proven performance in improving the generalization ability of learned policies. However, due to the sensitivity of RL training, naively applying data augmentation, which transforms each pixel in a task-agnostic manner, may suffer from instability and damage the sample efficiency, thus further exacerbating the generalization performance. At the heart of this phenomenon is the diverged action distribution and high-variance value estimation in the face of augmented images. To alleviate this issue, we propose Task-aware Lipschitz Data Augmentation (TLDA) for visual RL, which explicitly identifies the task-correlated pixels with large Lipschitz constants, and only augments the task-irrelevant pixels for stability. We verify the effectiveness of our approach on DeepMind Control suite, CARLA and DeepMind Manipulation tasks. The extensive empirical results show that TLDA improves both sample efficiency and generalization; it outperforms previous state-of-the-art methods across 3 different visual control benchmarks.
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Wang, Yan, and David M. Bevly. "Robust Observer Design for Lipschitz Nonlinear Systems With Parametric Uncertainty." In ASME 2013 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/dscc2013-4104.

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This paper discusses optimal and robust observer design for the Lipschitz nonlinear systems. The stability analysis for the Lure problem is first reviewed. Then, a two-DOF nonlinear observer is proposed so that the observer error dynamic model can be transformed to an equivalent Lure system. In this framework, the difference of the nonlinear parts in the vector fields of the original system and observer is modeled as a nonlinear memoryless block that is covered by a multivariable sector condition or an equivalent semi-algebraic set defined by a quadratic polynomial inequality. Then, a sufficient condition for asymptotic stability of the observer error dynamics is formulated in terms of the feasibility of polynomial matrix inequalities (PMIs), which can be solved by Lasserre’s moment relaxation. Furthermore, various quadratic performance criteria, such as H2 and H∞, can be easily incorporated in this framework. Finally, a parameter adaptation algorithm is introduced to cope with the parameter uncertainty.
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