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.

Provides the reader with up-to-date coverage of the control of the important partial-differential-equation class of systems Examples applied in biological systems are of growing interest to control theorists and engineers Mathematical level provided allows the book to be accessible to the non-control-specialist Includes supplementary material: sn.pub/extras

Klappentext

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.

Inhalt
General Introduction.- General Introduction.- Convex Analysis and Duality Principles.- Convexity and Topology.- A Brief Overview of Sobolev Spaces.- LegendreFenchel Transformation and Duality.- Lagrange Duality Theory.- General Results and Concepts on Robust and Optimal Control Theory for Evolutive Systems.- Studied Systems and General Results.- Optimal Control Problems.- Stabilization and Robust Control Problem.- Remarks on Numerical Techniques.- Applications in the Biological and Physical Sciences: Modeling and Stabilization.- Vortex Dynamics in Superconductors and GinzburgLandau-type Models.- Multi-scale Modeling of Alloy Solidification and Phase-field Model.- Large-scale Ocean in the Climate System.- Heat Transfer Laws on Temperature Distribution in Biological Tissues.- LotkaVolterra-type Systems with Logistic Time-varying Delays.- Other Systems.