Chaos Under Control

Presents an introduction to the dynamics of order and chaos, fractals, and complexity.

This long-awaited revised second edition of the standard reference on the subject has been considerably expanded to include such recent developments as novel control schemes, control of chaotic space-time patterns, control of noisy nonlinear systems, and communication with chaos, as well as promising new directions in research. The contributions from leading international scientists active in the field provide a comprehensive overview of our current level of knowledge on chaos control and its applications in physics, chemistry, biology, medicine, and engineering. In addition, they show the overlap with the traditional field of control theory in the engineering community. An interdisciplinary approach of interest to scientists and engineers working in a number of areas.

The explosive, behind-the-scenes story of Donald Trump’s high-stakes confrontation with Beijing, from an award-winning Washington Post columnist and peerless observer of the U.S.–China relationship There was no calm before the storm. Donald Trump’s surprise electoral victory shattered the fragile understanding between Washington and Beijing, putting the most important relationship of the twenty-first century in the hands of a novice who had bitterly attacked China from the campaign trail. Almost as soon as he entered office, Trump brought to a boil the long-simmering rivalry between the two countries, while also striking up a “friendship” with Chinese president Xi Jinping — whose manipulations of his American counterpart would undermine the White House’s already disjointed response to the historic challenge of a rising China. All the while, Trump’s own officials fought to steer U.S. policy from within. By the time the COVID-19 pandemic erupted in Wuhan, Trump’s love-hate relationship with Xi had sparked a trade war, while Xi’s aggression had pushed the world to the brink of a new Cold War. But their quarrel had also forced a long-overdue reckoning within the United States over China’s audacious foreign-influence operations, horrific human rights abuses, and creeping digital despotism. Ironically, this awakening was one of the biggest foreign-policy victories of Trump’s fractious term in office. ​Filled with shocking revelations drawn from Josh Rogin’s unparalleled access to top U.S. officials from the White House and deep within the country’s foreign policy machine, Chaos Under Heaven reveals an administration at war with itself during perhaps our most urgent hour.

In this book, leading researchers present their current work in the challenging area of chaos control in nonlinear circuits and systems, with emphasis on practical methodologies, system design techniques and applications. A combination of overview, tutorial and technical articles, the book describes state-of-the-art research on significant problems in this area. The scope and aim of this book are to bridge the gap between chaos control methods and circuits and systems. It is an ideal starting point for anyone who needs a fundamental understanding of controlling chaos in nonlinear circuits and systems.

This book gives an exposition of the exciting field of control of oscillatory and chaotic systems, which has numerous potential applications in mechanics, laser and chemical technologies, communications, biology and medicine, economics, ecology, etc.A novelty of the book is its systematic application of modern nonlinear and adaptive control theory to the new class of problems. The proposed control design methods are based on the concepts of Lyapunov functions, Poincare maps, speed-gradient and gradient algorithms. The conditions which ensure such control goals as an excitation or suppression of oscillations, synchronization and transformation from chaotic mode to the periodic one or vice versa, are established. The performance and robustness of control systems under disturbances and uncertainties are evaluated.The described methods and algorithms are illustrated by a number of examples, including classical models of oscillatory and chaotic systems: coupled pendula, brusselator, Lorenz, Van der Pol, Duffing, Henon and Chua systems. Practical examples from different fields of science and technology such as communications, growth of thin films, synchronization of chaotic generators based on tunnel diods, stabilization of swings in power systems, increasing predictability of business-cycles are also presented.The book includes many results on nonlinear and adaptive control published previously in Russian and therefore were not known to the West.Researchers, teachers and graduate students in the fields of electrical and mechanical engineering, physics, chemistry, biology, economics will find this book most useful. Applied mathematicians and control engineers from various fields of technology dealing with complex oscillatory systems will also benefit from it.

Chaotic behavior arises in a variety of control settings. In some cases, it is beneficial to remove this behavior; in others, introducing or taking advantage of the existing chaotic components can be useful for example in cryptography. Chaos in Automatic Control surveys the latest methods for inserting, taking advantage of, or removing chaos in a variety of applications. This book supplies the theoretical and pedagogical basis of chaos in control systems along with new concepts and recent developments in the field. Presented in three parts, the book examines open-loop analysis, closed-loop control, and applications of chaos in control systems. The first section builds a background in the mathematics of ordinary differential and difference equations on which the remainder of the book is based. It includes an introductory chapter by Christian Mira, a pioneer in chaos research. The next section explores solutions to problems arising in observation and control of closed-loop chaotic control systems. These include model-independent control methods, strategies such as H-infinity and sliding modes, polytopic observers, normal forms using homogeneous transformations, and observability normal forms. The final section explores applications in wireless transmission, optics, power electronics, and cryptography. Chaos in Automatic Control distills the latest thinking in chaos while relating it to the most recent developments and applications in control. It serves as a platform for developing more robust, autonomous, intelligent, and adaptive systems.