Controlling chaotic and hyperchaotic systems via energy regulation

Chaos control using small-amplitude damping signals of the extended Duffing equation

“…In 1990, Ott et al [7] showed that a chaotic attractor could be converted to any one of a large number of possible attracting time-periodic motions by making only small time-dependent parameter perturbation. So far, many different techniques and methods have been proposed to achieve chaos control, such as OGY method [7,9], time-delay feedback method [10,11], Lyapunov method [12,13], impulsive control method [14,15], sliding method control [16,17], differential geometric method [18,19], H 1 control [20,21], methods that coming from classical control theory (adaptive control [22][23][24]), chaos suppression method [24][25][26][27][28][29][30][31][32][33]. Controlling chaos consists in perturbing a chaotic system in order to stabilize a given unstable periodic orbit embedded in the chaotic attractor.…”

Synchronization problems for unidirectional feedback coupled nonlinear systems

“…An approach to synchronization based on the classical notion of observers, when the state is not fully available, can be found in [8] and [15]. In many cases, when one deals with nonlinear chaotic dynamical systems, the interest is that of steering any trajectory of the chaotic system to an equilibrium point or to a limit cycle of the same system or of another coupled system, see [5], [10], [13] and [28]. For an adaptive control approach using a linear reference model we refer to [26].…”