Stabilization, Optimal and Robust Control: Theory and Applications in Biological and Physical Sciences / Edition 1

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Stabilization, Optimal and Robust Control develops robust control of infinite-dimensional dynamical systems derived from time-dependent coupled PDEs associated with boundary-value problems. Rigorous analysis takes into account nonlinear system dynamics, evolutionary and coupled PDE behaviour and the selection of function spaces in terms of solvability and model quality. Mathematical foundations are provided so that the book remains accessible to the non-control-specialist. Following chapters giving a general view of convex analysis and optimization and robust and optimal control, problems arising in fluid mechanical, biological and materials scientific systems are laid out in detail. The combination of mathematical fundamentals with application of current interest will make this book of much interest to researchers and graduate students looking at complex problems in mathematics, physics and biology as well as to control theorists.
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Editorial Reviews

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“The focus of the book is stabilization, control and fluctuation of systems governed by Partial Differential Equations (PDE), and their applications to biological and physical sciences. The techniques used are the ones of robust control theory based around game theory. … The book is of interest both for control theorist than for researchers involved in complex problems in fluid mechanics, biological systems and material sciences.” (Rosa Maria Bianchini, Zentralblatt MATH, Vol. 1169, 2009)

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Product Details

  • ISBN-13: 9781848003439
  • Publisher: Springer London
  • Publication date: 9/25/2008
  • Series: Communications and Control Engineering Series
  • Edition description: 2008
  • Edition number: 1
  • Pages: 502
  • Product dimensions: 6.30 (w) x 9.40 (h) x 1.40 (d)

Table of Contents

General Introduction.- Part I: Convex Analysis and Duality Principles.- Convexity and Topology.- A Brief Overview of Sobolev Spaces.- Legendre-Fenchel Transformation and Duality.- Lagrange Duality Theory.- Part II: General Results and Concepts in Robust and Optimal Control Theory for Evolutive Systems.- Studied Systems and General Results.- Optimal Control Problem.- Stabilization and Robust Control Problem.- Remarks on Numerical Techniques.- Part III: Applications in the Biological and Physical Sciences: Modelling and Stabilization.- Vortex Dynamics in Superconductors and Ginzburg-Landau-type Models.- Multiscale Modeling Solidification of Binary Alloys and Phase-filed Model.- Large-scale Ocean in the Climate System.- Heat Transfer Laws on Temperature Distribution in Biological Tissues.- Lotka-Volterra-type Systems with Logistic Time-varying Delays.- Other Systems.

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