The improved results with Mathematica and effects of external uncertainty and disturbances on synchronization using a robust adaptive sliding mode controller: a comparative study

Abstract

In this computational article, the improved results when different chaotic systems are synchronized using robust adaptive sliding mode controller (RASMC) has been presented in which the simulation is based on Mathematica as well as the effects of external uncertainties (EU) and external disturbances (ED) have been studied in the synchronization of two different chaotic systems. For the same pairs (master and slave systems) of considered chaotic systems (Lorenz, Chen and Liu) and implemented technique (RASMC), a comparative study has been done between the results obtained using Mathematica and MATLAB, as well as the effects of EU and ED on the convergence of synchronization have been studied.

Internal synchronization using adaptive sliding mode

“…There are innumerable robust techniques have been developed based on the advantages over predecessor one in terms of stability, time response, low chattering, effects of modeling uncertainty and noise. 18,19 There can also be seen innumerable researches based on the systems like synchronization of identical/non-identical systems, different orders (called as Reduced/Increased order), and integer/fractional. [20][21][22][23][24] Numerous worthy researches have also been investigated based on applications of synchronization including security through multi-switching, compound, combination-combination synchronization.…”

“…for identical, non‐identical, integer, fractional systems with and without the effects of modeled uncertainty and noise. There are innumerable robust techniques have been developed based on the advantages over predecessor one in terms of stability, time response, low chattering, effects of modeling uncertainty and noise 18,19 . There can also be seen innumerable researches based on the systems like synchronization of identical/non‐identical systems, different orders (called as Reduced/Increased order), and integer/fractional 20–24 .…”

“…For the case study, the author has chosen LCS and LHCS. Owing to the intrinsic desirable characteristics of SMC, such as robustness against parameter variations and external noise, easy realization, quick response to the external input, and suitable transient action, the methodology has been chosen in the current study 10,13,14,18,19 . As it has been mentioned above that in the IS, the part dynamics of a certain system represented by a single or more state variables is synchronized with other part dynamics represented by other different set of same number of state variables within the same system.…”

Internal Synchronization Using Adaptive Control

“…For demonstration purposes, circular restricted threebody problem and the Lorenz system were used as a master and slave system, respectively. Shahzad [24] has investigated the improved results with Mathematica and further studied the effects of external uncertainty and disturbances on stability using adaptive sliding mode control. It has been seen that the synchronization of chaotic systems with unknown parameters is an issue.…”

Improved Time Response of Stabilization in Synchronization of Chaotic Oscillators Using Mathematica

“…A recent study of Shahzad [23] focused the attention of researchers on how to choose a model based synchronization technique and the appropriate mathematical tools for simulation. Pourmahmood et al [24] have developed a Robust Adaptive Sliding Mode Control (RASMC) and implemented it successfully on three well known chaotic systems (Lorenz, Chen and Liu) using MATLAB for all of the simulations, but when the same study was done using Mathematica by Shahzad [23], remarkable changes were observed in terms of time response to stabilize the synchronization.…”