الصفحة 1
الصفحة 1
Set-Theoretic Methods in Control
This self-contained monograph describes basic set-theoretic methods for control and provides a discussion of their links to fundamental problems in Lyapunov stability analysis and stabilization, optimal control, control under constraints, persistent disturbance rejection, and uncertain systems analysis and synthesis. New computer technology has catalyzed a resurgence of research in this area, particularly in the development of set-theoretic techniques, many of which are computationally demanding. The work presents several established and potentially new applications, along with numerical examples and case studies. A key theme of the presentation is the trade-off between exact (but computationally intensive) and approximate (but conservative) solutions to problems.
Polynomial Convexity
Devoted to the study of polynomially convex sets, which play an important role in the theory of functions of several complex variables.Presents the general properties of polynomially convex sets with particular attention to the theory of the hulls of one-dimensional sets.Motivates the theory with numerous examples and counterexamples, which serve to illustrate the general theory and to delineate its boundaries.
Notions of Convexity
The first two chapters of this book are devoted to convexity in the classical sense, for functions of one and several real variables respectively. This gives a background for the study in the following chapters of related notions which occur in the theory of linear partial differential equations and complex analysis such as (pluri-)subharmonic functions, pseudoconvex sets, and sets which are convex for supports or singular supports with respect to a differential operator. In addition, the convexity conditions which are relevant for local or global existence of holomorphic differential equations are discussed, leading up to Trépreau’s theorem on sufficiency of condition (capital Greek letter Psi) for microlocal solvability in the analytic category.
Infinite Dimensional Analysis : A Hitchhiker's Guide
This new edition of The Hitchhiker’s Guide has bene?tted from the comments of many individuals, which have resulted in the addition of some new material, and the reorganization of some of the rest. The most obvious change is the creation of a separate Chapter 7 on convex analysis. Parts of this chapter appeared in elsewhere in the second edition, but much of it is new to the third edition. In particular, there is an expanded discussion of support points of convex sets, and a new section on subgradients of convex functions.
Linear Optimization Problems with Inexact Data
Linear programming attracted the interest of mathematicians during and after World War II when the first computers were constructed and methods for solving large linear programming problems were sought in connection with specific practical problems—for example, providing logistical support for the U.S. Armed Forces or modeling national economies. Early attempts to apply linear programming methods to solve practical problems failed to satisfy expectations. There were various reasons for the failure. One of them, which is the central topic of this book, was the inexactness of the data used to create the models. This phenomenon, inherent in most pratical problems, has been dealt with in several ways. At first, linear programming models used "average” values of inherently vague coefficients, but the optimal solutions of these models were not always optimal for the original problem itself. Later researchers developed the stochastic linear programming approach, but this too has its limitations. Recently, interest has been given to linear programming problems with data given as intervals, convex sets and/or fuzzy sets. The individual results of these studies have been promising, but the literature has not presented a unified theory. Linear Optimization Problems with Inexact Data attempts to present a comprehensive treatment of linear optimization with inexact data, summarizing existing results and presenting new ones within a unifying framework.
