Uncertainty And Optimality

This text deals with different modern topics in probability, statistics and operations research. Wherever necessary, the theory is explained in great detail, with illustrations. Numerous references are given, in order to help young researchers who want to start their work in a particular area. The contributors are distinguished statisticians and operations research experts from all over the world.

This book introduces the theory and applications of uncertain optimal control, and establishes two types of models including expected value uncertain optimal control and optimistic value uncertain optimal control. These models, which have continuous-time forms and discrete-time forms, make use of dynamic programming. The uncertain optimal control theory relates to equations of optimality, uncertain bang-bang optimal control, optimal control with switched uncertain system, and optimal control for uncertain system with time-delay. Uncertain optimal control has applications in portfolio selection, engineering, and games. The book is a useful resource for researchers, engineers, and students in the fields of mathematics, cybernetics, operations research, industrial engineering, artificial intelligence, economics, and management science.

An examination of how the rational expectations revolution and game theory have enhanced the understanding of how an economy functions.

Here, two highly experienced authors present an alternative approach to optimal stopping problems. The basic ideas and techniques of the approach can be explained much simpler than the standard methods in the literature on optimal stopping problems. The monograph will teach the reader to apply the technique to many problems in economics and finance, including new ones. From the technical point of view, the method can be characterized as option pricing via the Wiener-Hopf factorization.

The theory of optimal decisions in a stochastic environment has seen many new developments in recent years. The implications of such theory for empirical and policy applications are several. This book attempts to analyze some of the impor tant applied aspects of this theory and its recent developments. The stochastic environment is considered here in specific form, e.g., (a) linear programs (LP) with parameters subject to a probabilistic mechanism, (b) decision models with risk aversion, (c) resource allocation in a team, and (d) national economic planning. The book attempts to provide new research insights into several areas, e.g., (a) mixed strategy solutions and econometric tests of hypotheses of LP models, (b) the dual problems of efficient estimation and optimal regulation, (c) input-output planning under imperfect competition, and (d) linear programs viewed as constrained statistical games. Methods of optimal decision rules developed here for quadratic and linear decision problems are applicable in three broad areas: (a) applied economic models in resource allocation, planning and team decision, (b) operations research models in management decisions involving portfolio analysis and stochastic programming, and (c) systems science models in stochastic control and adaptive behavior. Some results reported here have been published in professional journals be-. fore, and I would like to thank the following journals in particular: Inter national Journal of Systems Science, Journal of Optimization Theory and Applica tions and Journal of Mathematical Analysis and Applications.

This monograph provides the reader with a systematic treatment of robust filter design, a key issue in systems, control and signal processing, because of the fact that the inevitable presence of uncertainty in system and signal models often degrades the filtering performance and may even cause instability. The methods described are therefore not subject to the rigorous assumptions of traditional Kalman filtering. The monograph is concerned with robust filtering for various dynamical systems with parametric uncertainties and focuses on parameter-dependent approaches to filter design. Classical filtering schemes, like H2 filtering and H¥ filtering, are addressed and emerging issues such as robust filtering with constraints on communication channels and signal frequency characteristics are discussed. The text features: · design approaches to robust filters arranged according to varying complexity level and emphasizing robust filtering in the parameter-dependent framework for the first time; · guidance on the use of special realistic phenomena or factors to describe problems more accurately and to improve filtering performance; · a unified linear matrix inequality formulation of design approaches for easy and effective filter design; · demonstration of the techniques of matrix decoupling technique, the generalized Kalman‒Yakubovich‒Popov lemma, the free weighting matrix technique and the delay modelling approach, in robust filtering; · numerous easy-to-follow simulation examples, graphical and tabular illustrations to help the reader understand the filter design approaches developed; and · an account of emerging issues on robust filtering for research to inspire future investigation. Robust Filtering for Uncertain Systems will be of interest to academic researchers specializing in linear, robust and optimal control and estimation and to practitioners working in tracking and network control or signal filtering, detection and estimation. Graduate students learning control and systems theory, signal processing or applied mathematics will also find the book to be a valuable resource.