Introduction to Control of Oscillations and Chaos

Dynamics, Information and Control in Physical Systems

“…A variety of design methods have been developed both for linear and for nonlinear systems [16,17,18]. Methods of partial control and weak control are also available [11,15].…”

“…In order to make a reasonable choice of the control algorithm parameters the applicability conditions should be developed and checked. A number of applicability conditions can be found in [11,16]. The main conditions are the following ones: convexity of the function ω(x, u, t) in u and existence of "ideal" control u * such that ω(x, u * , t) ≤ 0 for all x (attainability condition).…”

“…Reachability of the control goal by means of arbitrarily small control was observed in a broad class of oscillatory systems [11] It is important that the obtained results were interpreted as discovering new properties of physical systems. Thousands of papers had been published aimed at studying properties of systems by means of control, identification and other cybernetical means.…”

Synchronization of an uncertain unified chaotic system via adaptive control

“…Over the last decade, a large variety of approaches have been proposed for chaos synchronization such as the master-slave method [4], backstepping design method [5,6], impulsive control method [7], and invariant manifold method [3], among many others [1,8].…”

Stabilization of invariant sets for nonlinear non-affine systems

“…(Chernousko, Akulenko & Sokolov, 1980;A s strom & Furuta, 1996;Bloch, Krishnaprasad, Marsden & SaH nchez de Alvarez, 1992;Wiklund, Kristenson & A s stroK m, 1993;Vorotnikov, 1998;Fradkov & Pogromsky, 1998). Control of oscillatory systems requires achieving nonclassical control goals (swinging, synchronization) as well as describing and analyzing complex motions of the closed loop system.…”