ABSTRACT
This chapter introduces the interest in dealing with the control of chaotic and hyperchaotic systems. It presents several control methodologies, coming from either the control theory framework or other seminal approaches. The chapter utilizes that the readers in understanding the basics of the field of chaos control, and in appreciating some of the existing methods. It focuses on physicists and mathematicians, consists of model-independent control methods that aims at directly exploiting the intrinsic properties of chaotic systems to stabilize either fixed points or periodic orbits. The chapter provides some of these methods, some particularities and fundamental problems occurring when dealing with the control of hyperchaotic systems. It highlights a modified Ott–Grebogy–York method sometimes referred to as the YLM method, and an enhanced version of this latest one, based on the use of the so-called Adaptive Adjustment Mechanism. Such motivations have lead to a huge amount of proposals of chaos control methodologies, and reports on successful applications to experimental processes.
