Abstract
This paper investigates the problem of projective lag synchronization behavior with delayed coupling in drive-response dynamical networks model with identical and non-identical nodes. An adaptive control method is designed to achieve the projective lag synchronization with constant time delay and with time-varying coupling delay. In addition the model harbors fully unknown parameters and disturbances. By using Lyapunov stability theory and adaptive laws, the unknown parameters are estimated. In addition, the unknown bounded mismatch and disturbance terms are also overcome by the proposed control. Finally, the simulation results reveal that the states of the dynamical network with delayed coupling can be asymptotically synchronized onto a desired scaling factor under the designed controller. Additionally, the results prove the validity of the proposed method.
Highlights
In the past few years, synchronization of dynamical systems has shown interesting behaviors which have received increasing attention in various fields of industry and various sciences [ – ]
The projective lag synchronization with time-varying delayed coupling in the driveresponse dynamical networks can be realized if the control input and adaptive lows are chosen as ui(t) = –qiei(t) – βi sgn ei(t) – gi xri (t) – Gi xri (t) θi(t)
The estimated parameters of the reference node and network nodes are depicted in Figure (a) and Figure (b), respectively, which converge to their real values
Summary
Ghada Al-mahbashi1*, Mohd Salmi Md Noorani[1], Sakhinah Abu Bakar[1,2] and Mohammed Mossa Al-Sawalha[2]
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