Partial Synchronization of Nonidentical Chaotic Systems via Adaptive Control, With Applications to Modeling Coupled Nonlinear Systems

Abstract

We consider the coupling of two nonidentical dynamical systems using an adaptive feedback linearization controller to achieve partial synchronization between the two systems. In addition we consider the case where an additional feedback signal exists between the two systems, which leads to bidirectional coupling. We demonstrate the stability of the adaptive controller, and use the example of coupling a Chua system with a Lorenz system, both exhibiting chaotic motion, as an example of the coupling technique. A feedback linearization controller is used to show the difference between unidirectional and bidirectional coupling. We observe that the adaptive controller converges to the feedback linearization controller in the steady state for the ChuaLorenz example. Finally we comment on how this type of partial synchronization technique can be applied to modeling systems of coupled nonlinear subsystems. We show how such modeling can be achieved where the dynamics of one system is known only via experimental time series measurements.

A review of non-linear structural control techniques

“…Even in this case the resulting dynamics of the system are highly non-linear -see, for example references [142] and [143]. However, techniques for non-linear control, such as feedback linearization, can be modified to be adaptive [88,[144][145][146]. Information on the robustness of adaptive control is discussed, for example, in references [147] to [150].…”

Adaptive Integral‐Based Robust Q‐S Synchronization and Parameter Identification of Nonlinear Hyperchaotic Complex Systems

“…In 1990, Pecora and Carroll [6] introduced the synchronization of two identical chaotic systems with different initial conditions. e field of chaotic synchronization flourished extensively in the last two decades, and many new strategies are also proposed in this regard, including complete synchronization [7,8], lag synchronization [9,10], inverse lag synchronization [11], inverse π-lag synchronization [12], generalized synchronization [13][14][15], multiple chaotic systems' synchronization [16,17], phase synchronization [18], antisynchronization [19,20], partial synchronization [21,22], Q-S synchronization [23,24], projective synchronization [25,26], and fractional chaos synchronization [27,28]. In recent years, generalized synchronization (GS) of chaotic systems was widely investigated.…”

Adaptive Switched Generalized Function Projective Synchronization between Two Hyperchaotic Systems with Unknown Parameters

“…Many synchronization schemes have been proposed, which include complete synchronization [10,11], lag synchronization [12], generalized synchronization [13], phase synchronization [14], anti-synchronization [15,16], partial synchronization [17,18], Q-S synchronization [19,20], projective synchronization [21][22][23][24][25][26][27][28][29][30][31][32], anticipating synchronization [33], inverse lag synchronization [34] and inverse π-lag synchronization [35,36].…”