Automation and Remote Control, Vol. 65, No. 4, 2004, pp. 505–533. Translated from Avtomatika i Telemekhanika, No. 4, 2004, pp. 3–34. Original Russian Text Copyright c  2004 by Andrievskii, Fradkov. REVIEWS Control of Chaos: Methods and Applications. II. Applications 1 B. R. Andrievskii and A. L. Fradkov Institute of Problems of Science of Machines, Russian Academy of Sciences, St. Petersburg, Russia Received November 4, 2003 Abstract—Reviewed were the problems and methods for control of chaos, which in the last decade was the subject of intensive studies. Consideration was given to their application in var- ious scientific fields such as mechanics (control of pendulums, beams, plates, friction), physics (control of turbulence, lasers, chaos in plasma, and propagation of the dipole domains), chem- istry, biology, ecology, economics, and medicine, as well as in various branches of engineering such as mechanical systems (control of vibroformers, microcantilevers, cranes, and vessels), spacecraft, electrical and electronic systems, communication systems, information systems, and chemical and processing industries (stirring of fluid flows and processing of free-flowing mate- rials)). 1. INTRODUCTION In the first years after the penetration of the concept of deterministic chaos into the scientific literature, chaotic behavior was regarded as an exotic phenomenon which might be of interest only as a mathematical speculation and would never be encountered in practice. Later on, however, the possibility of chaotic dynamics was discovered in numerous systems in mechanics, communication, laser and radio physics [10, 12, 16, 18, 19], chemistry and biochemistry [46], biology [55], economics [47, 124, 144], and medicine. Yet further development highlighted a number of applications where chaotic modes may appear— sometimes as harmful, sometimes as useful. Moreover, entire classes of problems that are of practi- cal importance arose where one has to control a nonlinear system by reducing or, on the contrary, increasing the degree of its chaoticity. Methods for solving these problems also were actively de- veloped. The main of them were described in the first part [6] of the present review whose second part is devoted to their applications. More than 300 papers devoted to various applications of the methods for control of chaotic processes were published in the peer-reviewed journals between 1997 and 2002. The questions of chaos control are actively discussed in scientific and technical fields such as physics of turbulent processes, laser physics and optics, physics of plasma, molecular and quantum physics, mechanics, chemistry and electrochemistry, biology and ecology, economics and finances, medicine, mechanical engineering, electrical engineering and chemical industry, traffic control, or communication and information systems. It is appropriate to decompose the applied works on chaos into scientific and technical (engineering) applications. The works on engineering applications demonstrate the use of chaos and the methods for control of chaotic systems in particular practical problems or at least show their feasibility. The scientific 1 This work was supported by the Russian Foundation for Basic Research, project no. 02-01-00765, the Scientific Program 19 of the Presidium of the Russian Academy of Sciences, project no. 1.4, and the Federal Program “Integration.” The authors are also grateful to Prof. R.J. Evans of University of Melbourne for support. 0005-1179/04/6504-0505 c  2004 MAIK “Nauka/Interperiodica”