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: Max-Plus Methods for Nonlinear Control and Estimation
  name:
    name part: McEneaney, William M.
    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: 2006
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIV, 246 p. online resource.
  abstract: The central focus of this book is the control of continuous-time/continuous-space nonlinear systems. Using new techniques that employ the max-plus algebra, the author addresses several classes of nonlinear control problems, including nonlinear optimal control problems and nonlinear robust/H-infinity control and estimation problems. Several numerical techniques are employed, including a max-plus eigenvector approach and an approach that avoids the curse-of-dimensionality. Well-known dynamic programming arguments show there is a direct relationship between the solution of a control problem and the solution of a corresponding Hamilton–Jacobi–Bellman (HJB) partial differential equation (PDE). The max-plus-based methods examined in this monograph belong to an entirely new class of numerical methods for the solution of nonlinear control problems and their associated HJB PDEs; they are not equivalent to either of the more commonly used finite element or characteristic approaches. The potential advantages of the max-plus-based approaches lie in the fact that solution operators for nonlinear HJB problems are linear over the max-plus algebra, and this linearity is exploited in the construction of algorithms. The book will be of interest to applied mathematicians, engineers, and graduate students interested in the control of nonlinear systems through the implementation of recently developed numerical methods. Researchers and practitioners tangentially interested in this area will also find a readable, concise discussion of the subject through a careful selection of specific chapters and sections. Basic knowledge of control theory for systems with dynamics governed by differential equations is required.
  table of contents: Max-Plus Analysis -- Dynamic Programming and Viscosity Solutions -- Max-Plus Eigenvector Method for the Infinite Time-Horizon Problem -- Max-Plus Eigenvector Method Error Analysis -- A Semigroup Construction Method -- Curse-of-Dimensionality-Free Method -- Finite Time-Horizon Application: Nonlinear Filtering -- Mixed L?/L2 Criteria.
  note: by William M. McEneaney.
  subject:
    topic: Mathematics
  subject:
    topic: Algebra
  subject:
    topic: Mathematical analysis
  subject:
    topic: Analysis (Mathematics)
  subject:
    topic: Partial differential equations
  subject:
    topic: Applied mathematics
  subject:
    topic: Engineering mathematics
  subject:
    topic: System theory
  subject:
    topic: Control engineering
  subject:
    topic: Robotics
  subject:
    topic: Mechatronics
  subject:
    topic: Mathematics
  subject:
    topic: Analysis
  subject:
    topic: Applications of Mathematics
  subject:
    topic: Algebra
  subject:
    topic: Systems Theory, Control
  subject:
    topic: Control, Robotics, Mechatronics
  subject:
    topic: Partial Differential Equations
  classification: QA299.6-433
  classification: 515
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Systems & Control: Foundations & Applications
  identifier: 9780817644536
  identifier: http://dx.doi.org/10.1007/0-8176-4453-9
  record info:
    record creation date: 100301
    record change date: 20151204164817.0
    record identifier: 978-0-8176-4453-6