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A Gap Emergent in Parameters Identification Based on Adaptive Synchronization Techniques

In this paper, several concrete examples as well as their numerical simulations are provided to show that parameters identification based on the so-called adaptive synchronization techniques might be failed in case that those terms with pending identified parameters in coupled systems are not properly designed. This gap might be emergent not only when the orbit in the synchronization manifold approaches some sort of equilibrium or of periodic oscillation produced by driving system but even when the orbit in synchronization manifold is some kind of chaotic attractor generated by driving system, which implies that chaotic property of driving signal is not necessary to a successful parameters identification. More importantly, the mechanism inducing this gap and boundedness of all trajectories are expatiated in light of the well-known LaSalle invariance principle. In addition, new synchronization techniques are utilized to rigorously realize the complete synchronization and parameters identification in a class of systems dissatisfying global Lipschitz condition. Also, parameters identification are discussed for systems with time delay.