Abstract
We propose a novel approach of parameter identification using the adaptive synchronized observer by introducing an auxiliary subsystem, and some sufficient conditions are given to guarantee the convergence of synchronization and parameter identification. We also demonstrate the mean convergence of synchronization and parameters identification under the influence of noise. Furthermore, in order to suppress the influence of noise, we complement a filter in the output. Numerical simulations on Lorenz and Chen systems are presented to demonstrate the effectiveness of the proposed approach.
Highlights
Since the pioneering work of Pecora and Carroll 1, chaos synchronization has become an active research subject due to its potential applications in physics, chemical reactions, biological networks, secure communication, control theory, and so forth 2–12
We propose a novel approach of parameter identification using the adaptive synchronized observer by introducing an auxiliary subsystem, and some sufficient conditions are given to guarantee the convergence of synchronization and parameter identification
We demonstrate the mean convergence of synchronization and parameters identification under the influence of noise
Summary
Since the pioneering work of Pecora and Carroll 1 , chaos synchronization has become an active research subject due to its potential applications in physics, chemical reactions, biological networks, secure communication, control theory, and so forth 2–12. To achieve system synchronization and parameter convergence, there are two general approaches based on the typical Lyapunov’s direct method 2–9 or LaSalle’s principle 10. When adaptive synchronization methods are applied to identify the uncertain parameters, some restricted conditions on dynamical systems, such as persistent excitation. We explore a novel method for parameter estimation by introducing an auxiliary subsystem in adaptive synchronized observer instead of Lyapunov’s direct method and LaSalle’s principle. It will be shown that through harnessing the auxiliary subsystem, parameters can be well estimated from a time series of dynamical systems based on adaptive synchronized observer. Noise plays an important role in parameter identification. We demonstrate the mean convergence of synchronization and parameters identification under the influence of noise. We implement a filter to recover the performance of parameter identification suppressing the influence of the noise
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