Stochastic Analysis, Control, Optimization And Applications

Open Mathematics is a challenging notion for theoretical modeling, technical analysis, and numerical simulation in the fields of physics and mathematics, among others, as highly correlated nonlinear phenomena, evolving over a large range of time and length scales, control the underlying systems and processes in their spatiotemporal evolution. Indeed, available data, be they physical, biological, or financial, and technologically complex systems and stochastic systems, such as mechanical or electronic devices, can be managed from the same conceptual approach, both analytically and through computer simulation, using effective nonlinear dynamics methods.

Open Mathematics is a challenging notion for theoretical modeling, technical analysis, and numerical simulation in the fields of physics and mathematics, among others, as highly correlated nonlinear phenomena, evolving over a large range of time and length scales, control the underlying systems and processes in their spatiotemporal evolution. Indeed, available data, be they physical, biological, or financial, and technologically complex systems and stochastic systems, such as mechanical or electronic devices, can be managed from the same conceptual approach, both analytically and through computer simulation, using effective nonlinear dynamics methods.

Complex systems have long been an integral part of modern life and can be encountered everywhere. Undertaking a comprehensive study of such systems is a challenging problem, one which is impossible to solve without the use of contemporary mathematical modeling techniques. Mathematical models form the basis for the optimal design and control of complex systems.

This book is devoted to the development of optimal control theory for finite dimensional systems governed by deterministic and stochastic differential equations driven by vector measures. The book deals with a broad class of controls, including regular controls (vector-valued measurable functions), relaxed controls (measure-valued functions) and controls determined by vector measures, where both fully and partially observed control problems are considered.

Almost all real-world systems are inevitably subject to random structures, parameters, and noises, and stochastic systems have been playing increasingly important roles in all areas of science and engineering.The purpose of this Special Issue is to solicit the recent achievements of control theory and applications of stochastic systems so as to further improve and develop the theoretical methods of stochastic system estimation, fault diagnosis, prognostics, and optimization, among others.

Almost all real-world systems are inevitably subject to random structures, parameters, and noises, and stochastic systems have been playing increasingly important roles in all areas of science and engineering.The purpose of this Special Issue is to solicit the recent achievements of control theory and applications of stochastic systems so as to further improve and develop the theoretical methods of stochastic system estimation, fault diagnosis, prognostics, and optimization, among others.

The 70 revised full papers presented were carefully reviewed and selected from 145 submissions. The papers feature current research on mathematical methods and computing techniques for pattern recognition, computer vision, image analysis, and speech recognition, as well as their applications in such diverse areas as robotics, industry, health, entertainment, space exploration, telecommunications, data mining, document analysis, and natural language processing and recognition to name only few of them.

This book offers a valuable reference guide for researchers in distributed optimization and for senior undergraduate and graduate students alike.