Adaptive synchronization of GLHS with unknown parameters

Abstract

SUMMARYIn this paper, an adaptive controller for the synchronization of two generalized Lorenz hyperchaos systems (GLHSs) is designed by using the Lyapunov method. In the synchronization schema, the parameters of the drive system are unknown and different from those of the response system. By introducing update laws for both the control coefficients and the parameters of the response system, the adaptive controller proposed in this paper is brand new compared with the former relative works. The proposed adaptive controller is feasible for any possible parameters of GLHS. Numerical simulation is carried out to verify and illustrate the analytical result.

Analytical equations for oscillation amplitude of MOS Colpitts oscillator

“…Equation (23) is frequently used assumption in Colpitts oscillator (Huang 1997;Mayaram 2000;Hegazi et al 2005;Filanovsky et al 2007;Khatibi and Shanechi 2009;Palumbo et al 2009). Note that, validity of (6), (22) and (23) is restricted to having high quality factor (Q) for the LC tank.…”

“…In this article, it is assumed that because of the narrow band passing nature of LC tank and high quality factor (Q) assumption for it (Huang 1997;Mayaram 2000;Hegazi et al 2005;Filanovsky et al 2007;Khatibi and Shanechi 2009;Palumbo et al 2009), the fundamental component of V O which is of interest will have the frequency of (6) that is sufficient for the considered case. However, the amplitude behaviour of this oscillator is poorly understood mainly because of the nonlinear dynamic of the oscillator and complicated mathematical calculations.…”

“…Although the proposed analytical equations are somewhat complicated but in comparison with simulation results, it will be shown that they are very accurate. In fact, the output voltage is not completely sinusoidal, but because of the filtering selectivity of the LC tank and assuming high quality factor Q for it, this assumption is reasonable (Huang 1997;Mayaram 2000;Hegazi et al 2005;Filanovsky et al 2007; Khatibi and Shanechi 2009;Palumbo et al 2009). The rest of this article is as follows: In Section 2, some existing methods for amplitude analysis of MOS Colpitts oscillator are introduced.…”

“…Obtaining the transfer function or any knowledge about the amplitude and frequency of the oscillator and phase noise poses some challenges in the design of Colpitts oscillator as any other types of oscillators and voltage controlled oscillators. Varieties of methods are presented for finding the transient or steady state behaviour of this oscillator (Huang 1997;Mayaram 2000;Hegazi et al 2005;Filanovsky, Verhoeven and Reja 2007;Khatibi and Shanechi 2009;Palumbo, Pennisi, and Pennisi 2009). The aim of this article is to determine the steady state oscillation amplitude in MOS Colpitts oscillator.…”

Control and synchronization of the generalized Lorenz system with mismatched uncertainties using backstepping technique and time‐delay estimation

“…These applications are shown in various fields, including physical, chemical and ecological systems, and secure communications [1][2][3]. Correspondingly, a variety of control theories have been applied to managing chaotic signals [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Recently, for a faster response and enhanced robustness, hybrid methods have appeared in regulating and synchronizing chaotic systems.…”