Lag quasi-synchronization of incommensurate fractional-order memristor-based neural networks with nonidentical characteristics via quantized control: A vector fractional Halanay inequality approach |
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| Institution: | 1. School of Artificial Intelligence and Automation, the Key Laboratory of Image Processing and Intelligent Control, Huazhong University of Science and Technology, Wuhan 430074, China;2. School of Control Science and Engineering, Shandong University, Jinan 250061, China;3. School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, China;1. School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong 273165, People’s Republic of China;2. School of Science, Jiangnan University, Wuxi, Jiangsu 214122, People’s Republic of China;1. Department of Mathematics, Qingdao University of Technology, Qingdao 266520, PR China;2. Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai 264209, PR China;1. Faculty of Sciences, Beijing University of Technology, Beijing 100124, China;2. Faculty of Information Technology, Beijing University of Technology, Beijing 100124, China;3. School of Computer Science, Beijing Information Science and Technology University, Beijing 100101, China |
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| Abstract: | This work realizes lag quasi-synchronization of incommensurate fractional-order memristor-based neural networks (FMNNs) with nonidentical characteristics via quantized control. The motivations behind this research work are threefold: (1) quantized controllers, which generate discrete control signals, can be more easily realized in computers than non-quantized controllers, and can consume smaller communication capacity; (2) incommensurate orders in a single FMNN and nonidentical characteristics in drive-response FMNNs are inescapable due to the differences among the circuit elements used to implement FMNNs; (3) convergence analysis of delayed incommensurate fractional-order nonlinear systems, which is the basis for the derivation of synchronization criterion, has not been handled perfectly. As an effective tool for convergence analysis of delayed incommensurate fractional-order nonlinear systems, especially for estimation of ultimate state bound, a vector fractional Halanay inequality is established at first. Then, a quantized synchronization controller, in which the dead-zone is introduced into some logarithmic quantizers to avoid chattering phenomenon, is designed. By means of vector Lyapunov function together with the newly derived vector fractional Halanay inequality, the synchronization criterion is proved theoretically. Lastly, numerical simulations supplementarily illustrate the correctness of the synchronization criterion. In contrast with the hypotheses in the relevant literature, the hypotheses in this paper are weaker. |
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