Internal synchronization using adaptive sliding mode

Abstract

Synchronization of chaotic systems by means of the combination of drive‐response/master–slave systems have been widely utilized. In the current study, the author introduces the concept of internal synchronization (IS) that is based on the synchronization within the system among the subsystems. Furthermore, the two types of Internal Multi‐Switching Synchronization (IMSS): the first one based on single error while the other one is based on two errors, have been discussed. In order to demonstrate, the author chooses the Lorenz Chaotic System (LCS) and Lorenz Hyper Chaotic System (LHCS) together with the adaptive sliding mode control (SMC) technique in multi‐switching manner. In addition, the efficiency of the IMSS is illustrated using Mathematica. The computational part is the witness of the achievement of stability of the IS.

Adaptive internal synchronization control of chaotic systems based on DNA strand displacement

“…The following describes the derivative for v 1 along the trajectory of Formula ( 19). The master (17) and slave (18) systems are synchronized since v 1 is positive definite and ̇v1 is semi-negative definite. ▪…”

“…Therefore, exploring new synchronization mechanisms for chaotic systems have important practical value. Shahzad 16,17 gives the concept of internal synchronization, which realizes the synchronization of specific subsystems or the whole system and eliminates dependence on external systems.…”

Fixed time function combination synchronization of perturbed chaotic systems via adaptive control

“…In 1990s, the drive‐response synchronization between two chaotic subsystems 6 was firstly developed, which triggers off researchers' enthusiasm on the investigation of chaos synchronization. In addition, various noticeable control techniques on systems have been presented, for instance, feedback control, 7 adaptive technique, 8 impulsive control, 9 sliding mode technique, 10 observer‐based method 11 . In the meantime, there are some deferent synchronization concepts in the chaotic systems, for instance, the complete synchronization (PC), 12,13 projective synchronization (PS), 14 function projective synchronization (FPS) 15 .…”

Adaptive Anti-disturbance Switching Control for Switched T-S Fuzzy Systems

“…Limited by the production level and cost, it is very difficult to change the equipment structure of the system to reduce the impact of disturbances. Fortunately, some disturbance attenuation technologies have been developed, such as the 𝐻 ∞ control strategy 26 , model-based AD control scheme 27 and sliding mode technique 28,29 . The disturbance model-based AD control method is an attractive control strategy which has been widely utilized in control systems including the switched systems 30 , LPV systems 31 , the T-SFSs 32 , etc.…”