William M. McEneaney - Böcker

The central focus of this work is the control of nonlinear systems. Using new techniques that employ the max-plus algebra, the author addresses several classes of nonlinear control problems, including nonlinear optimal control problems, nonlinear robust H-infinity control problems, and nonlinear risk-sensitive stochastic control problems.Well-known dynamic programming arguments show there is a direct relationship between the solution of a control problem, and the solution of a corresponding Hamilton--Jacobi--Bellman (HJB) partial differential equation (PDE). The max-plus-based methods examined in this monograph belong to an entirely new class of methods for the solution of nonlinear control problems and their associated HJB PDEs; they are not equivalent to either of the more commonly used finite element or characteristic approaches. The potential advantages of max-plus-based approaches lie in the fact that solution operators for nonlinear HJB problems are linear over the max-plus algebra, and this linearity is exploited in the construction of algorithms.The book will be of interest to applied mathematicians, engineers, and graduate students interested in the control of nonlinear systems through the implementation of recently developed numerical methods.Researchers and practitioners tangentially interested in this area will also find a readable, concise discussion of the subject through a careful selection of specific chapters and sections. Basic knowledge of control theory for systems with dynamics governed by differential equations is required; the material on risk-sensitive stochastic control requires knowledge of systems governed by stochastic differential equations.

In view of Professor Wendell Fleming's many fundamental contributions, his profound influence on the mathematical and systems theory communi­ ties, his service to the profession, and his dedication to mathematics, we have invited a number of leading experts in the fields of control, optimiza­ tion, and stochastic systems to contribute to this volume in his honor on the occasion of his 70th birthday. These papers focus on various aspects of stochastic analysis, control theory and optimization, and applications. They include authoritative expositions and surveys as well as research papers on recent and important issues. The papers are grouped according to the following four major themes: (1) large deviations, risk sensitive and Hoc control, (2) partial differential equations and viscosity solutions, (3) stochastic control, filtering and parameter esti­ mation, and (4) mathematical finance and other applications. We express our deep gratitude to all of the authors for their invaluable contributions, and to the referees for their careful and timely reviews. We thank Harold Kushner for having graciously agreed to undertake the task of writing the foreword. Particular thanks go to H. Thomas Banks for his help, advice and suggestions during the entire preparation process, as well as for the generous support of the Center for Research in Scientific Computation. The assistance from the Birkhauser professional staff is also greatly appreciated.

In view of Professor Wendell Fleming's many fundamental contributions, his profound influence on the mathematical and systems theory communi­ ties, his service to the profession, and his dedication to mathematics, we have invited a number of leading experts in the fields of control, optimiza­ tion, and stochastic systems to contribute to this volume in his honor on the occasion of his 70th birthday. These papers focus on various aspects of stochastic analysis, control theory and optimization, and applications. They include authoritative expositions and surveys as well as research papers on recent and important issues. The papers are grouped according to the following four major themes: (1) large deviations, risk sensitive and Hoc control, (2) partial differential equations and viscosity solutions, (3) stochastic control, filtering and parameter esti­ mation, and (4) mathematical finance and other applications. We express our deep gratitude to all of the authors for their invaluable contributions, and to the referees for their careful and timely reviews. We thank Harold Kushner for having graciously agreed to undertake the task of writing the foreword. Particular thanks go to H. Thomas Banks for his help, advice and suggestions during the entire preparation process, as well as for the generous support of the Center for Research in Scientific Computation. The assistance from the Birkhauser professional staff is also greatly appreciated.

The rising tide of threats, from financial cybercrime to asymmetric military conflicts, demands greater sophistication in tools and techniques of law enforcement, commercial and domestic security professionals, and terrorism prevention. Concentrating on computational solutions to determine or anticipate an adversary's intent, Adversarial Reasoning: Computational Approaches to Reading the Opponent's Mind discusses the technologies for opponent strategy prediction, plan recognition, deception discovery and planning, and strategy formulation that not only applies to security issues but also to game industry and business transactions.Addressing a broad range of practical problems, including military planning and command, military and foreign intelligence, antiterrorism, network security, as well as simulation and training systems, this reference presents an overview of each problem and then explores various approaches and applications to understand the minds and negate the actions of your opponents. The techniques discussed originate from a variety of disciplines such as stochastic processes, artificial intelligence planning, cognitive modeling, robotics and agent theory, robust control, game theory, and machine learning, among others. The beginning chapters outline the key concepts related to discovering the opponent's intent and plans while the later chapters journey into mathematical methods for counterdeception. The final chapters employ a range of techniques, including reinforcement learning within a stochastic dynamic games context to devise strategies that combat opponents.By answering specific questions on how to create practical applications that require elements of adversarial reasoning while also exploring theoretical developments, Adversarial Reasoning: Computational Approaches to Reading the Opponent's Mind is beneficial for practitioners as well as researchers.