Adaptive synchronization design for uncertain chaotic systems in the presence of unknown system parameters: a revisit

Generalized predictive control based on fuzzy sliding-mode control strategy and fuzzy PI controller for synchronization of uncertain chaotic systems

“…U sing the Laplace transform we obtain the analog PI controller in the frequency domain (10) By applying the bilinear transform.5 = (2/T)((z+1)/(z -1)), where T > 0 is the sampling period, we obtain the discrete version By taking and then using the inverse z-transform, we obtain UPI(k) = uPI(k -1) + T6.. uPI(k) (12) Where (13) In Equation (12), T6.. uPI(k) represents the incremental output of a conventional PI controller.…”

“…This feature makes advanced control approaches operate in a new atmosphere without any trouble. On the other hand, classical control approaches such as sliding mode control strategy [10], [11], backstepping [12] and active control method [13], have shown inflexible behavior when they are applied in new environments. This kind of controllers needs improvements, and for each problem, a specific algorithm must be designed.…”

Structure‐triggered asymptotical synchronization for nonidentical generalized stochastic systems with Markovian jumping parameter based on sliding mode control

“…In recent years, due to the wide range of applications in various fields including information science, secure communication systems, and so on (see References 9‐23), the synchronization problems of systems have been intensively investigated. There are several types of synchronization in these researches.…”

Adaptive Multi‐Switching Synchronization of High‐Order Memristor‐Based Hyperchaotic System with Unknown Parameters and Its Application in Secure Communication

“…However, the linear independence condition for some chaotic systems with unknown parameters is neglected to guarantee the true convergence of the estimated parameters. Reference [17] described the principle of the linear independence, the functions ( )( = 1, 2, ⋅ ⋅ ⋅ , ) are said to be linear independent if there do not exist nonzero constants ( = 1, 2, ⋅ ⋅ ⋅ , ), such that 1 ( ) 1 + 2 ( ) 2 + ⋅ ⋅ ⋅ + ( ) = 0. e adaptive multi-switching synchronization was proven to be e ective to solve the identi cation of the unknown parameters in [18].…”