Controlling chaos: the OGY method, its use in mechanics, and an alternative unified framework for control of non-regular dynamics

In this chapter we review the development of the control of chaos theory subsequent to the seminal paper by Ott, Grebogi and Yorke in 1990. After summarizing the main characteristics of the OGY method, we analyze and discuss various applications in several fields of mechanics.We then illustrate the main aspects of an alternative control method which aims at controlling the overall system dynamics instead of stabilizing a single periodic orbit, as the OGY method does. The two methods are both based on the modern idea of exploiting the chaotic properties of systems, instead of simply eliminating chaos. This paper is one of a collection written in honour of Celso Grebogi, on the occasion of his 60th birthday. So we have thought it appropriate to start with short personal reminiscences by two of the present authors