Presents and demonstrates stabilizer design techniques that can be used to solve stabilization problems with constraints. These methods have their origins in convex programming and stability theory. However, to provide a practical capability in stabilizer design, the methods are tailored to the special features and needs of this field. Hence, the main emphasis of this book is on the methods of stabilization, rather than optimization and stability theory. The text is divided into three parts. Part I contains some background material. Part II is devoted to behavior of control systems, taking examples from mechanics to illustrate the theory. Finally, Part III deals with nonlocal stabilization problems, including a study of the global stabilization problem.
Since the volume may be of interest to a broad variety of people, it is arranged in parts that require different levels of mathematical background. Part I can be assessed by those interested in the application of visualization methods in decision making. In Part II computational methods are introduced in a relatively simple form. Part III is written for readers in applied mathematics interested in the theoretical basis of modern optimization.
The book offers a simultaneous presentation of the theory and numerical treatment of inverse problems for Maxwell's equations. The inverse problems are central to many areas of science and technology such as geophysical exploration, remote sensing, near-surface radar-location, dielectric logging, medical imaging, etc. The basic idea. of inverse methods is to extract from the evaluation of measured electromagnetic field the details of the medium considered. The inverse problems are investigated not only for Maxwell's equations but also for their guasistationary approximation and in the case of harmonic dependence in time. Starting with the simplest one-dimensional inverse problems, the book leads its readers to more complicated multidimensional ones studied for media of various kinds. The unique solvability of a number of the considered problems is shown as well as the stability of their solutions. The numerical analysis ranges from the finite-difference scheme inversion to the linearization method and finally the dynamic variant of the Gel'fand-Levitan method. Computational results are presented. The book is intended to provide graduate students in applied mathematics and geophysics, as well as the researches in the field, with an understanding of inverse problem theory. Although the main part of the book is rather theoretical in nature, it is also of practical value to experimentalists and engineers.
This book focuses on the issues of decision-making with several numerical criteria. It introduces an original general approach to solving multicriteria problems given quantitative information about the preference relation of a decision-maker. It considers the problems with crisp as well as fuzzy preference relations, accepting the four axioms of “reasonable choice”. Further, it defines the notion of an information quantum about the preference relation of a decision-maker and studies the reduction of the Pareto set using a finite collection of information quanta, demonstrating that the original approach yields a good approximation for the set of nondominated alternatives in a multicriteria problem. Lastly, it analyzes a possible combination of the axiomatic approach with other well-known methods. Intended for a wide range of professionals involved in solving multicriteria problems, including researchers, design engineers, product engineers, developers and analysts, the book is also a valuable resource for undergraduate and postgraduate students of mathematics, economics, and engineering.
Since the volume may be of interest to a broad variety of people, it is arranged in parts that require different levels of mathematical background. Part I can be assessed by those interested in the application of visualization methods in decision making. In Part II computational methods are introduced in a relatively simple form. Part III is written for readers in applied mathematics interested in the theoretical basis of modern optimization.
Presents and demonstrates stabilizer design techniques that can be used to solve stabilization problems with constraints. These methods have their origins in convex programming and stability theory. However, to provide a practical capability in stabilizer design, the methods are tailored to the special features and needs of this field. Hence, the main emphasis of this book is on the methods of stabilization, rather than optimization and stability theory. The text is divided into three parts. Part I contains some background material. Part II is devoted to behavior of control systems, taking examples from mechanics to illustrate the theory. Finally, Part III deals with nonlocal stabilization problems, including a study of the global stabilization problem.
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