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Beginning with a tutorial guide to MATLAB®, the text thereafter is divided into two main areas. In Part I, both real and complex discrete dynamical systems are considered, with examples presented from population dynamics, nonlinear optics, and materials science. Part II includes examples from mechanical systems, chemical kinetics, electric circuits, economics, population dynamics, epidemiology, and neural networks. Common themes such as bifurcation, bistability, chaos, fractals, instability, multistability, periodicity, and quasiperiodicity run through several chapters. Chaos control and multifractal theories are also included along with an example of chaos synchronization. Some material deals with cutting-edge published research articles and provides a useful resource for open problems in nonlinear dynamical systems. Readers are guided through theory via example, and the graphical MATLAB® interface. The Simulink® accessory is used to simulate real-world dynamical processes. Examples from: mechanics, electric circuits, economics, population dynamics, epidemiology, nonlinear optics, materials science, and neural networks. Over 330 illustrations, 300 examples, and exercises with solutions. Aimed at senior undergraduates, graduate students, and working scientists in various branches of engineering, applied mathematics, and the natural sciences.

Both refining and extending previous publications by the authors, the material in this monograph has been class-tested in mathematical institutions throughout the world. Covering some of the key areas of optimal control theory (OCT)—a rapidly expanding field that has developed to analyze the optimal behavior of a constrained process over time—the authors use new methods to set out a version of OCT's more refined ‘maximum principle'designed to solve the problem of constructing optimal control strategies for uncertain systems where some parameters are unknown. Known as a ‘min-max'problem, this type of difficulty occurs frequently when dealing with finite uncertain sets.The text begins with a standalone section that reviews classical optimal control theory. Moving on to examine the tent method in detail, the book then presents its core material, which is a more robust maximum principle for both deterministic and stochastic systems. The results obtained have applications in production planning, reinsurance-dividend management, multi-model sliding mode control, and multi-model differential games. Using powerful new tools in optimal control theory, this book explores material that will be of great interest to post-graduate students, researchers, and practitioners in applied mathematics and engineering, particularly in the area of systems and control.

This monograph is a self-contained, coherent presentation of the background and progress of the stability of time-delay systems. Focusing on techniques, tools, and advances in numerical methods and optimization algorithms, the authors developed material which, up until now, has been scattered in technical journals and conference proceedings. Special emphasis is placed on systems with uncertainty and stability criteria which can be computationally implemented. The second edition is major update to reflect the state of art in this field greatly expanding on the original material in addition to two new chapters on Systems of Neutral Type and an Introduction to Frequency Domain Method. Requiring only basic knowledge of linear systems and Lyapunov stability theory, Stability of Time-Delay Systems, 2nd ed is accessible to a broad audience of researchers, professional engineers, and graduate students. It may be used for self-study or as a reference; portions of the text may be used in advanced graduate courses and seminars.

This book evolved from a one-year sequence of courses offered by the authors at Iowa State University. The audience for this book typically included theoreti­ cally oriented first- or second-year graduate students in various engineering or science disciplines. Subsequently, while serving as Chair of the Department of Electrical Engineering, and later, as Dean of the College of Engineering at the University of Notre Dame, the first author continued using this book in courses aimed primarily at graduate students in control systems. Since administrative demands precluded the possibility of regularly scheduled classes, the Socratic method was used in guiding students in self study. This method of course deliv­ ery turned out to be very effective and satisfying to student and teacher alike. Feedback from colleagues and students suggests that this book has been used in a similar manner elsewhere. The original objectives in writing this book were to provide the reader with ap­ propriate mathematical background for graduate study in engineering or science; to provide the reader with appropriate prerequisites for more advanced subjects in mathematics; to allow the student in engineering or science to become famil­ iar with a great deal of pertinent mathematics in a rapid and efficient manner without sacrificing rigor; to give the reader a unified overview of applicable mathematics, thus enabling him or her to choose additional courses in math­ ematics more intelligently; and to make it possible for the student to understand

Although there is an emerging literature on the topic, this is the first book that attempts to present a systematic theory of estimation and control over communication networks. Using several selected problems of estimation and control over communication networks, the authors present and prove a number of results concerning optimality, stability, and robustness having practical significance for networked control system design. In particular, various problems of Kalman filtering, stabilization, and optimal control over communication channels are considered and solved. The results establish fundamental links among mathematical control theory, Shannon information theory, and entropy theory of dynamical systems. This essentially self-contained monograph offers accessible mathematical models and results for advanced postgraduate students, researchers, and practitioners working in the areas of control engineering, communications, information theory, signal processing, and applied mathematics.

The theory of dynamic games continues to evolve, and one purpose of this volume is to report a number of recent theoretical advances in the?eld, which are covered in Parts I, II and IV. Another aim of this work is to present some new applications of dynamic games in various areas, including pursuit-evasion games (Part III), ecology (Part IV), and economics (Part V). The volume concludes with a number of contributions in the?eld of numerical methods and algorithms in dynamic games (Part VI). With a single exception, the contributions of this volume are outgrowths of talks that were presented at the Eleventh International Symposium on Dynamic Games and Applications, held in Tucson, Arizona, USA, in December 2004, and organized by the International Society of Dynamic Games. The symposium was co-sponsored by the University of Arizona, College of Engineering and Aerospace and Mechanical Engineering, as well as GERAD, Montréal, Canada, and the ISDG Organizing Society. The volume contains thirty-?ve chapters that have been peer-reviewed according to the standards of international journals in game theory and applications. Part I deals with the theory of dynamic games and contains six chapters. Cardaliaguet, Quincampoix, and Saint-Pierre provide a survey of the state-- the-art of the use of viability theory in the formulation and analysis of differential games, in particular zero-sum games. An important result of viability theory is that many zero-sum differential games can be formulated as viability problems.

This monograph presents our recent results on the proportional-integr- derivative (PID) controller and its design, analysis, and synthesis. The fo­ cus is on linear time-invariant plants that may contain a time delay in the feedback loop. This setting captures many real-world practical and in­ dustrial situations. The results given here include and complement those published in Structure and Synthesis of PID Controllers by Datta, Ho, and Bhattacharyya [10]. In [10] we mainly dealt with the delay-free case. The main contribution described here is the efficient computation of the entire set of PID controllers achieving stability and various performance specifications. The performance specifications that can be handled within our machinery are classical ones such as gain and phase margin as well as modern ones such as Hoo norms of closed-loop transfer functions. Finding the entire set is the key enabling step to realistic design with several design criteria. The computation is efficient because it reduces most often to lin­ ear programming with a sweeping parameter, which is typically the propor­ tional gain. This is achieved by developing some preliminary results on root counting, which generalize the classical Hermite-Biehler Theorem, and also by exploiting some fundamental results of Pontryagin on quasi-polynomials to extract useful information for controller synthesis. The efficiency is im­ portant for developing software design packages, which we are sure will be forthcoming in the near future, as well as the development of further capabilities such as adaptive PID design and online implementation.