Parameter identification based on finite-time synchronization for Cohen–Grossberg neural networks with time-varying delays

Abdujelil Abdurahman, Haijun Jiang, Cheng Hu, Zhidong Teng
2015 Nonlinear Analysis: Modelling and Control  
In this paper, the finite-time synchronization problem for chaotic Cohen-Grossberg neural networks with unknown parameters and time-varying delays is investigated by using finitetime stability theory. Firstly, based on the parameter identification of uncertain delayed neural networks, a simple and effective feedback control scheme is proposed to tackle the unknown parameters of the addressed network. Secondly, by modifying the error dynamical system and using some inequality techniques, some
more » ... el and useful criteria for the finite-time synchronization of such a system are obtained. Finally, an example with numerical simulations is given to show the feasibility and effectiveness of the developed methods. Parameter identification based on finite-time synchronization 349 Being a unique and very relevant nonlinear phenomenon, chaos has been intensively investigated in the context of several specific problems arising in physics, mathematics, engineering science, and secure communication, etc. Synchronization means two or more systems which are either chaotic or periodic share a common dynamical behavior and it has been shown that this common behavior can be induced by coupling or by external force. Due to this property, chaos synchronization has been successfully applied in a variety of fields, including secure communication, chemical and biological systems, human heartbeat regulation, information science, image processing, and harmonic oscillation generation, etc. [9, 10, 20, 29] . Up to now, a wide variety of approaches have been proposed for synchronization of chaotic systems, such as adaptive control [18, 28] , observer-based control [26], impulsive control [17, 25], fuzzy control [16, 37], coupling control [15], periodically intermittent control [4, 12, 13], and so on. However, most of the above mentioned studies have assumed that the parameters of chaotic systems are known in advance. But in many practical situations, the parameters of chaotic systems are inevitably perturbed by external inartificial factors and the values of these parameters cannot be exactly known in advance, and the synchronization will be destroyed and broken by the effects of these uncertainties. Therefore, the investigation of synchronizing two chaotic systems with unknown parameters has become an important research issue [19, 22, 31] . In [14] , by combining the adaptive control and linear feedback with update law, the authors investigated the synchronization of a class of chaotic Hopfield neural networks with known or unknown parameters. Based on the Lyapunov stability theory and by utilizing adaptive linear feedback control technique, the synchronization problem of chaotic CGNNs with unknown parameters and mixed time-varying delays was studied in [11] . Nevertheless, the works in [11] concerning the synchronization of CGNNs mainly focus on the Lipschitzian amplification gains and unknown parameters. There are no results for the synchronization of CGNNs with the general amplification functions, unknown parameters and time-varying delays. Therefore, it is interesting to study this problem both in theory and in applications, so there exists an open room for further improvement. Another thing is worth to note that, all of the methods mentioned above, have been used to guarantee the asymptotic stability or exponential stability of the synchronization error dynamics. This means that the trajectories of the slave system can reach to the trajectories of the master system over the infinite horizon. In the practical engineering process, however, it is more reasonable that synchronization objective is realized in a finite horizon. To achieve faster synchronization in control systems, an effective method is using finite-time control techniques. Finite-time synchronization means the optimality in convergence time. Moreover, the finite-time control techniques have demonstrated better robustness and disturbance rejection properties [3, 5, 30] . In [1], by introducing nonsingular terminal sliding surface and designing adaptive controller, the authors studied the finite-time chaos synchronization problem between two different chaotic systems with unknown parameters. In [27] , based on the finite-time stability theory and by designing feedback controller, the authors investigated the finite-time synchronization problem between two chaotic cellular neural networks with constant delays. Nevertheless, the given updated laws in [27] are highly complex and are not easily applicable. Whether it is
doi:10.15388/na.2015.3.3 fatcat:6pmi5vc77rgknnj7vkphrm4264