rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Viability Theory
  name:
    name part: Aubin, Jean-Pierre.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2009
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XXV, 545 p. online resource.
  abstract: This work examines viability theory and its applications to control theory and differential games. The emphasis is on the construction of feedbacks and dynamical systems by myopic optimization methods. Systems of first-order partial differential inclusions, whose solutions are feedbacks, are constructed and investigated. Basic results are then extended to the case of fuzzy control problems, distributed control problems, and control systems with delays and memory. Aimed at graduate students and research mathematicians, both pure and applied, this book offers specialists in control and nonlinear systems tools to take into account general state constraints. Viability theory also allows researchers in other disciplines—artificial intelligence, economics, game theory, theoretical biology, population genetics, cognitive sciences—to go beyond deterministic models by studying them in a dynamical or evolutionary perspective in an uncertain environment. The book is a compendium of the state of knowledge about viability...Mathematically, the book should be accessible to anyone who has had basic graduate courses in modern analysis and functional analysis…The concepts are defined and many proofs of the requisite results are reproduced here, making the present book essentially self-contained. —Bulletin of the AMS Because of the wide scope, the book is an ideal reference for people encountering problems related to viability theory in their research…It gives a very thorough mathematical presentation. Very useful for anybody confronted with viability constraints. —Mededelingen van het Wiskundig Genootschap.
  table of contents: Outline of the Book -- Viability Theorems for Ordinary and Stochastic Differential Equations -- Set-Valued Maps -- Viability Theorems for Differential Inclusions -- Viability Kernels and Exit Tubes -- Invariance Theorems for Differential Inclusions -- Regulation of Control Systems -- Smooth and Heavy Viable Solutions -- Partial Differential Inclusions of Tracking Problems -- Lyapunov Functions -- Miscellaneous Viability Issues -- Viability Tubes -- Functional Viability -- Viability Theorems for Partial Differential Inclusions -- Differential Games.
  note: by Jean-Pierre Aubin.
  subject:
    topic: Mathematics
  subject:
    topic: Artificial intelligence
  subject:
    topic: Game theory
  subject:
    topic: System theory
  subject:
    topic: Biomathematics
  subject:
    topic: Control engineering
  subject:
    topic: Robotics
  subject:
    topic: Mechatronics
  subject:
    topic: Mathematics
  subject:
    topic: Systems Theory, Control
  subject:
    topic: Control, Robotics, Mechatronics
  subject:
    topic: Game Theory, Economics, Social and Behav. Sciences
  subject:
    topic: Mathematical and Computational Biology
  subject:
    topic: Artificial Intelligence (incl. Robotics)
  classification: Q295
  classification: QA402.3-402.37
  classification: 519
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Systems & Control: Foundations & Applications
  identifier: 9780817649104
  identifier: http://dx.doi.org/10.1007/978-0-8176-4910-4
  record info:
    record creation date: 100301
    record change date: 20151204150016.0
    record identifier: 978-0-8176-4910-4