8 research outputs found
Further Constructions of Control-Lyapunov Functions and Stabilizing Feedbacks for Systems Satisfying the Jurdjevic-Quinn Conditions
For a broad class of nonlinear systems, we construct smooth control-Lyapunov
functions whose derivatives along the trajectories of the systems can be made
negative definite by smooth control laws that are arbitrarily small in norm. We
assume our systems satisfy appropriate generalizations of the Jurdjevic-Quinn
conditions. We also design state feedbacks of arbitrarily small norm that
render our systems integral-input-to-state stable to actuator errors.Comment: 15 pages, 0 figures, accepted for publication in IEEE Transactions on
Automatic Control in October 200
Robust Finite-time stability of homogeneous systems with respect tomultiplicative disturbances
International audienceLyapunov characterizations of output finite-time stability are presented for the system which is locally Lipschitz continuous out of the set and continuous on . The definitions are given in the form of and functions. Necessary and sufficient conditions for output finite-time stability are given using Lyapunov functions. The theoretical results are supported by numerical examples
Information-Theoretic Privacy through Chaos Synchronization and Optimal Additive Noise
We study the problem of maximizing privacy of data sets by adding random
vectors generated via synchronized chaotic oscillators. In particular, we
consider the setup where information about data sets, queries, is sent through
public (unsecured) communication channels to a remote station. To hide private
features (specific entries) within the data set, we corrupt the response to
queries by adding random vectors. We send the distorted query (the sum of the
requested query and the random vector) through the public channel. The
distribution of the additive random vector is designed to minimize the mutual
information (our privacy metric) between private entries of the data set and
the distorted query. We cast the synthesis of this distribution as a convex
program in the probabilities of the additive random vector. Once we have the
optimal distribution, we propose an algorithm to generate pseudo-random
realizations from this distribution using trajectories of a chaotic oscillator.
At the other end of the channel, we have a second chaotic oscillator, which we
use to generate realizations from the same distribution. Note that if we obtain
the same realizations on both sides of the channel, we can simply subtract the
realization from the distorted query to recover the requested query. To
generate equal realizations, we need the two chaotic oscillators to be
synchronized, i.e., we need them to generate exactly the same trajectories on
both sides of the channel synchronously in time. We force the two chaotic
oscillators into exponential synchronization using a driving signal.
Simulations are presented to illustrate our results.Comment: arXiv admin note: text overlap with arXiv:1809.03133 by other author
A Unifying Integral Iss Framework For Stability Of Nonlinear Cascades
We analyze nonlinear cascades in which the driven subsystem is integral input-tostate stable (ISS), and we characterize the admissible integral ISS gains for stability. This characterization makes use of the convergence speed of the driving subsystem and allows a larger class of gain functions when the convergence is faster. We show that our integral ISS gain characterization unifies di#erent approaches in the literature which restrict the nonlinear growth of the driven subsystem and the convergence speed of the driving subsystem. The result is used to develop a new observer-based backstepping design in which the growth of the nonlinear damping terms is reduced. Ke words. nonlinear cascades, stabilization, integral input-to-state stability AMS sub je classifications. 93C10, 93D05, 93D15, 93D25 PII. S0363012901387987 1
A stability-theory perspective to synchronisation of heterogeneous networks
Dans ce mémoire, nous faisons une présentation de nos recherches dans le domaine de la synchronisation des systèmes dynamiques interconnectés en réseau. Une des originalités de nos travaux est qu'ils portent sur les réseaux hétérogènes, c'est à dire, des systèmes à dynamiques diverses. Au centre du cadre d'analyse que nous proposons, nous introduisons le concept de dynamique émergente. Il s'agit d'une dynamique "moyennée'' propre au réseau lui-même. Sous l'hypothèse qu'il existe un attracteur pour cette dynamique, nous montrons que le problème de synchronisation se divise en deux problèmes duaux : la stabilité de l'attracteur et la convergence des trajectoires de chaque système vers celles générées par la dynamique émergente. Nous étudions aussi le cas particulier des oscillateurs de Stuart-Landau
Methodik zur Integration von Vorwissen in die Modellbildung
Das Buch zeigt, wie Vorwissen über Eigenschaften dynamischer Systeme und über Funktionen in die mathematische Modellbildung integriert werden kann. Hierzu wird im ersten Teil der Arbeit das verbale Vorwissen mathematisch formuliert. Der zweite Teil beschreibt vier Zugängen, um die entstehenden restringierten Probleme zu lösen. Zahlreiche Beispiele, Tabellen und Zusammenstellungen vervollständigen das Buch