Theory Constraints

This book provides a broad overview of the current problems, challenges and solutions in the field of control theory, communication theory and computational resources management. Recent results on dynamical systems, which open new opportunities for research and challenges to be addressed in the future, are proposed in the context of computational and communication constraints. In order to take into the account complex phenomena, such as nonlinearities, time-varying parameters and limited availability of information, the book proposes new approaches for open problems with both theoretical and practical significance.

Frequency Domain Criteria for Absolute Stability focuses on recently-developed methods of delay-integral-quadratic constraints to provide criteria for absolute stability of nonlinear control systems. The known or assumed properties of the system are the basis from which stability criteria are developed. Through these methods, many classical results are naturally extended, particularly to time-periodic but also to nonstationary systems. Mathematical prerequisites including Lebesgue-Stieltjes measures and integration are first explained in an informal style with technically more difficult proofs presented in separate sections that can be omitted without loss of continuity.

Everything should be made as simple as possible, but not simpler. (Albert Einstein, Readers Digest, 1977) The modern practice of creating technical systems and technological processes of high effi.ciency besides the employment of new principles, new materials, new physical effects and other new solutions ( which is very traditional and plays the key role in the selection of the general structure of the object to be designed) also includes the choice of the best combination for the set of parameters (geometrical sizes, electrical and strength characteristics, etc.) concretizing this general structure, because the Variation of these parameters ( with the structure or linkage being already set defined) can essentially affect the objective performance indexes.

Control of Complex Systems: Structural Constraints and Uncertainty focuses on control design under information structure constraints, with a particular emphasis on large-scale systems. The complexity of such systems poses serious computational challenges and severely restricts the types of feedback laws that can be used in practice.

This book shows, on numerous examples, how to make decisions in realistic situations when we have both uncertainty and constraints. In most these situations, the book's emphasis is on the why-question, i.e., on a theoretical explanation for empirical formulas and techniques. Such explanations are important: they help understand why these techniques work well in some cases and not so well in others, and thus, help practitioners decide whether a technique is appropriate for a given situation.

Two-stage stochastic programming models are considered as attractive tools for making optimal decisions under uncertainty. Traditionally, optimality is formalized by applying statistical parameters such as the expectation or the conditional value at risk to the distributions of objective values.

Data mining essentially relies on several mathematical disciplines, many of which are presented in this second edition of this book. Topics include partially ordered sets, combinatorics, general topology, metric spaces, linear spaces, graph theory. To motivate the reader a significant number of applications of these mathematical tools are included ranging from association rules, clustering algorithms, classification, data constraints, logical data analysis, etc.

In economics agents are assumed to choose on the basis of rational calculations aimed at the maximization of their pleasure or profit. Formally, agents are said to manifest transitive and consistent preferences in attempting to maximize their utility in the presence of several constraints.