Synopses & Reviews
The Festschrift in celebration of John William Helton's pioneering work, Mathematical Methods in Systems, Optimization, and Control comprises a careful selection of articles on systems and control theory, operator theory, and optimization. The book follows Helton's original and long lasting contributions which have shaped control theory and operator theory during the last decades, with specific emphasis on topics aimed at direct applications to current research areas of high impact and interest. The book, by virtue of its diverse contents, strong interdisciplinary contents, and high expertise of its contributors, is one of a kind among all recent publications in the area of mathematical control theory. Mathematicians of all denominations (algebraists, geometers, analysts, numerical and computer scientists) as well as engineers interested in control and optimization will find invaluable references and sources of inspiration in the book.
Review
From the reviews: "A good starting point to learn about Helton's influential work at the edge of Operator theory and systems engineering. ... Many of the main topics in this area are covered by the 19 contributions, all written by the main players in the field. ... brought in the form of a tutorial, a survey, or even a shorter note, but all very readable and up-to-date. ... it can be safely recommended to specialists and to students at an advanced mathematics or engineering level as well." (A. Bultheel, The European Mathematical Society, September, 2012)
Review
From the reviews:"A good starting point to learn about Helton's influential work at the edge of Operator theory and systems engineering. ... Many of the main topics in this area are covered by the 19 contributions, all written by the main players in the field. ... brought in the form of a tutorial, a survey, or even a shorter note, but all very readable and up-to-date. ... it can be safely recommended to specialists and to students at an advanced mathematics or engineering level as well." (A. Bultheel, The European Mathematical Society, September, 2012)
Synopsis
This volume is dedicated to Bill Helton on the occasion of his sixty-fifth birthday. It contains biographical material, a list of Bill's publications, a detailed survey of Bill's contributions to operator theory, optimization and control, and 19 technical articles. Most of the technical articles are expository and should serve as useful introductions to many of the areas which Bill's highly original contributions have helped to shape over the last forty-odd years. These include interpolation, Szegö limit theorems, Nehari problems, trace formulas, systems and control theory, convexity, matrix completion problems, linear matrix inequalities and optimization. The book should be useful to graduate students in mathematics and engineering, as well as to faculty and individuals seeking entry level introductions and references to the indicated topics. It can also serve as a supplementary text to numerous courses in pure and applied
Table of Contents
Preface.- Inroduction (an overview of the contents of the book, from the perspective of Helton's landmark contributions).- Biographical Note and List of Publications of J.W. Helton.- Bounded Analytic Interpolation and H-infinity Control.- Linear Matrix Inequalities and Matrix Convexity.- Optimization and Realization in the Free *-algebra.- Automatic Verification of Matrix Inequalities.- Non-commutative Algebraic Geometry.- Non-Commutative Differential Geometry and Probability.- Modern Trends in Robust Control.- Challenges of Mathematical Biology.- Mathematical Programming and Computer Science.