Abstract
The robust adaptive exponential synchronization problem of stochastic chaotic systems with structural perturbations is investigated in mean square. The stochastic disturbances are assumed to be Brownian motions that act on the slave system and the norm-bounded uncertainties exist in all parameters after decoupling. The stochastic disturbances could reflect more realistic dynamical behaviors of the coupled chaotic system presented within a noisy environment. By using a combination of the Lyapunov functional method, the robust analysis tool, the stochastic analysis techniques, and adaptive control laws, we derive several sufficient conditions that ensure the coupled chaotic systems to be robustly exponentially synchronized in the mean square for all admissible parameter uncertainties. This approach cannot only make the outputs of both master and slave systems reach H∞ synchronization with the passage of time between both systems but also attenuate the effects of the perturbation on the overall error system to a prescribed level. The main results are shown to be general enough to cover many existing ones reported in the literature.
Highlights
Synchronization is a fundamental phenomenon that enables coherent behavior in coupled dynamical systems
In [15], the stability of adaptive synchronization of chaotic systems was proposed by Sorrentino et al A robust adaptive synchronization for a class of uncertain chaotic systems with application to Chua’s circuit was presented by Koofigar et al [16]
(R-2) It may be shown that the system under control is forward complete; that is, if there exists a set of initial conditions and gains such that, together, they generate solutions that tend to infinity, these solutions may unboundedly grow only in infinite time
Summary
Synchronization is a fundamental phenomenon that enables coherent behavior in coupled dynamical systems. Fang et al developed a robust adaptive exponential synchronization of stochastic perturbed chaotic delayed neural networks with parametric uncertainties [25] It appears clearly from the above works that most did not consider structural perturbations. With the help from the Lyapunov functional method and adaption method, we employ the robust analysis tool and the stochastic analysis techniques to derive some relevant conditions under which the coupled systems is globally robustly synchronized in the mean square for all admissible parameter uncertainties. These conditions guarantee the robustness of the controller against the effect of exoteric perturbations.
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