Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués: Perturbations PDF Download

Author: Jacques Louis Lions
Publisher: Elsevier Masson
ISBN:
Category : Control theory
Languages : fr
Pages : 296

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ISBN:
Category :
Languages : fr
Pages :

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Author: Jacques-Louis Lions
Publisher: Elsevier Masson
ISBN:
Category : Calculus of variations
Languages : fr
Pages : 560

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Author: Jacques-Louis Lions (Mathématicien)
Publisher:
ISBN:
Category :
Languages : fr
Pages :

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Author: Jacques-Louis Lions
Publisher:
ISBN:
Category :
Languages : fr
Pages : 272

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Author: Weijiu Liu
Publisher: Springer Science & Business Media
ISBN: 3642046134
Category : Mathematics
Languages : en
Pages : 303

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Unlike abstract approaches to advanced control theory, this volume presents key concepts through concrete examples. Once the basic fundamentals are established, readers can apply them to solve other control problems of partial differential equations.

Author: Tawfik Masrour
Publisher: Tawfik Masrour
ISBN:
Category :
Languages : fr
Pages : 199

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Cet ouvrage contient une série de contributions consacrées au contrôle des problèmes de mécanique des milieux continus. Les problèmes : On a d'abord observé que l'étude théorique de beaucoup de problèmes de contrôlabilité exacte se ramenait à la preuve d'estimations a priori sur les solutions des problèmes homogènes adjoints. Ces estimations correspondent selon l'intuition à la stabilité de l'observation. Ceci est bien sûr un des résultats et ingrédients essentiels de la méthode d'unicité Hilbertienne «HUM» dûe à J.L. Lions. Bien entendu, la pertinence des équations dépend de la taille des paramètres caractéristiques du problème ; l'exemple le plus fondamental dans notre domaine étant l'équation des plaques bidimensionnelles qui est obtenue comme cas limite de l'élasticité tridimensionnelle lorsque l'épaisseur tend vers zéro ( travaux de Ph.G. Ciarlet et ses collaborateurs pour une étude systématique). Il est alors naturel d'analyser comment les propriétés de contrôle, de stabilisation et d'observation persistent lors des passages à la limite. Cette propriété n'est pas systématique et souvent lorsqu'elle est vraie, difficile à prouver (voir Cioranescu et Saint Jean Paulin et Figueiredo et Zuazua. Les méthodes : Il s'agit d'estimer des quantités qui s'interprètent comme des énergies. Il est donc naturel de s'inspirer des méthodes classiques de contrôle de propagation de l'énergie.

Author: Jacques Simon
Publisher: Springer
ISBN: 3540461817
Category : Technology & Engineering
Languages : en
Pages : 278

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The present proceedings volume is devoted to two subjects. Stabilization with emphasis on exact controllability: considering a physical system, such as a vibrating plate, one can reach a steady state in a finite time by acting on the boundary. Control of boundaries: given a physical system find the geometry of the domain (optimal shape) which minimizes a cost related to the solution of a boundary value problem in this domain, for example find a minimum drag profile. Many lectures included mathematical analysis as well as engineering applications and numerical simulation.

Author: Kaïs Ammari
Publisher: Springer
ISBN: 3319109006
Category : Mathematics
Languages : en
Pages : 189

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By introducing a new stabilization methodology, this book characterizes the stability of a certain class of systems. The stability (exponential, polynomial, or weaker) for the closed loop problem is reduced to an observability estimate for the corresponding uncontrolled system combined with a boundedness property of the transfer function of the associated open loop system. A similar strategy is applied to systems where a delay term is added. The book concludes with many concrete examples. This book is addressed to graduate students in mathematics or engineering and also to researchers with an interest in stabilization and control systems governed by partial differential equations.

Author: Shuping Chen
Publisher: Springer
ISBN: 0387353593
Category : Science
Languages : en
Pages : 334

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Book Description
In the mathematical treatment of many problems which arise in physics, economics, engineering, management, etc., the researcher frequently faces two major difficulties: infinite dimensionality and randomness of the evolution process. Infinite dimensionality occurs when the evolution in time of a process is accompanied by a space-like dependence; for example, spatial distribution of the temperature for a heat-conductor, spatial dependence of the time-varying displacement of a membrane subject to external forces, etc. Randomness is intrinsic to the mathematical formulation of many phenomena, such as fluctuation in the stock market, or noise in communication networks. Control theory of distributed parameter systems and stochastic systems focuses on physical phenomena which are governed by partial differential equations, delay-differential equations, integral differential equations, etc., and stochastic differential equations of various types. This has been a fertile field of research with over 40 years of history, which continues to be very active under the thrust of new emerging applications. Among the subjects covered are: Control of distributed parameter systems; Stochastic control; Applications in finance/insurance/manufacturing; Adapted control; Numerical approximation . It is essential reading for applied mathematicians, control theorists, economic/financial analysts and engineers.