A novel active pinning control for synchronization and anti-synchronization of new uncertain unified chaotic systems

Abstract

This paper discusses the synchronization and anti-synchronization of new uncertain unified chaotic systems (UUCS). Based on the idea of active control, a novel active Pinning control strategy is presented, which only needs a state of new UUCS. The proposed controller can achieve synchronization between a response system and a drive system, and ensure the synchronized robust stability of new UUCS. Numerical simulations of new UUCS show that the controller can make chaotic systems achieve synchronization or anti-synchronization in a quite short period and both are of good robust stability. L. Pan ( ) ·

Sinusoidal disturbance rejection in chaotic planar oscillators

“…Note that, in the expression of the 'oversized' high-gain practical observer (14), the function '.y e;N 1 / does not appear. As a matter of fact, such a high-gain observer can also be used to estimate the time derivatives of a signal, which is not the output of a dynamical system, under the assumption that the higher-order time derivatives, which have to be estimated, are bounded.…”

“…As a matter of fact, such a high-gain observer can also be used to estimate the time derivatives of a signal, which is not the output of a dynamical system, under the assumption that the higher-order time derivatives, which have to be estimated, are bounded. Hence, a high-gain observer similar to (14) is used here to estimate the time derivatives of the control input u of system (1). Therefore, let the polynomial KCmC1 C 1 KCm C C KCm C KCmC1 be Hurwitz, and let 0 < % 1 be a sufficiently small parameter.…”

“…Therefore, let the polynomial KCmC1 C 1 KCm C C KCm C KCmC1 be Hurwitz, and let 0 < % 1 be a sufficiently small parameter. An 'over-sized' high-gain 'practical' observer for the time derivatives of the control input u can be obtained by using (14), with y replaced by u, " replaced by %, N replaced by K, l replaced by m, Á i replaced by i , for i D 0; : : : ; K CmC1, and O y e;N replaced by O u e;K , respectively, obtaining, in this way, an estimate O u e;K of u e;K .…”

“…Some recent results in the analysis and control of chaotic systems are given in [12][13][14][15]. The main objective of this paper is to find a control law for this class of systems, which restores their nominal dynamical behavior (i.e., the non-chaotic one, in absence of the disturbance).…”

Synchronization of dynamical systems of different orders and different dimensions

“…But it is found that information signal masked with chaotic signal is not much secure, therefore to enhance the grade of security of information signal several types of synchronizations were suggested among which projective synchronization was found much effective for secure communication because of its unpredictable multiple factor. Several methods like active control [22], adaptive control [23], feedback control [24], pinning control [25], sliding mode control [26], fuzzy control [27] etc have been studied and found effective to obtain the desired synchronization. Some work have also been done on synchronization of fractional order and integer order system [28,29], but still a very few work have been done on different order and different dimensional systems.…”