Abstract
Observer design for nonlinear systems is very important in state-based stabilization, fault detection, chaos synchronization and secret communication. This paper deals with synchronization problem of a class of fractional-order neural networks (FONNs) based on system observer. Two sufficient conditions are given for the FONNs with known constant parameters and unknown time-varying parameters, respectively. Based on the fractional Lyapunov stability criterion, the proposed sliding mode observer can guarantee that the synchronization error between two identical FONNs converges to zero asymptotically, and all involved signals keep bounded. Finally, some simulation examples are provided to indicate the effectiveness of the proposed method.
Highlights
1 Introduction Being a very old topic in mathematics, fractional calculus was born on 17th century
It was treated as an area of pure theoretical mathematics
Lots of efforts have been made on synchronization of fractionalorder neural networks (FONNs) [8, 14, 15, 24,25,26]
Summary
Being a very old topic in mathematics, fractional calculus was born on 17th century. Since it was treated as an area of pure theoretical mathematics. Observer design for nonlinear dynamic systems is a significant and interesting research area, and it has a lot of potential applications in control engineering, fault reconstruction, state estimation, and signal tracking [27,28,29,30,31,32,33,34,35,36,37,38,39]. There was only little work that considered the observer design for fractional-order nonlinear systems. In this paper, we will give some stability analysis criteria in observer design for FONNs. The other is that in the aforementioned literature the system model should be known in advance. It is worth mentioning that in this paper: (1) To handle the problem of state estimation for the FONNs, a robust sliding mode observer is proposed.
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