参数不匹配的时滞忆阻神经网络的指数同步
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摘要
研究了参数不匹配情况下时滞忆阻神经网络的指数同步控制问题。由于忆阻神经网络连接权重的切换特性,相较于传统的连续神经网络,其同步控制更加困难。首先利用微分包含和集值映射理论,将不连续的忆阻神经网络转化为带有区间参数的不确定系统。其次,设计了新的切换控制器,该切换控制器能够消除参数不匹配产生的同步误差。然后,通过选取合适的李雅普诺夫泛函,利用不等式放缩技术得到了两个忆阻神经网络取得指数同步的充分条件。最后,利用一个数值模拟算例验证了理论结果的正确性。
In this paper,the exponential synchronization of delayed memristor-based neural networks(DMNNs) with parameter mismatches was studied.Due to the switching characteristics of the memristive synaptic weights of memristor-based neural networks,the synchronization control of DMNNs is more difficult than traditional continuous neural networks.Firstly,differential inclusion and set-valued map theories were used to transform discontinuous memristor-based neural networks into an uncertain system with interval parameters.Secondly,a new switching controller was designed,which could eliminate the synchronization errors caused by parameter mismatches.Then,a sufficient condition for the exponential synchronization was obtained by choosing appropriate Lyapunov functional and using the inequality technique.Finally,a numerical simulation example was given to verify the correctness of the theoretical results.
In this paper,the exponential synchronization of delayed memristor-based neural networks(DMNNs) with parameter mismatches was studied.Due to the switching characteristics of the memristive synaptic weights of memristor-based neural networks,the synchronization control of DMNNs is more difficult than traditional continuous neural networks.Firstly,differential inclusion and set-valued map theories were used to transform discontinuous memristor-based neural networks into an uncertain system with interval parameters.Secondly,a new switching controller was designed,which could eliminate the synchronization errors caused by parameter mismatches.Then,a sufficient condition for the exponential synchronization was obtained by choosing appropriate Lyapunov functional and using the inequality technique.Finally,a numerical simulation example was given to verify the correctness of the theoretical results.
引文
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[11]DING S,WANG Z,NIU H,et al.Stop and go adaptive strategy for synchronization of delayed memristive recurrent neural networks with unknown synaptic weights[J].Journal of the Franklin Institute,2017,354(12):4989-5010.
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[14]YANG X,CAO J,LIANG J.Exponential synchronization of memristive neural networks with delays:Interval matrix method[J].IEEE Transactions on Neural Networks and Learning Systems,2017,28(8):1878-1888.
[15]FILIPPOV A F.Differential equations with discontinuous righthand sides[M].Boston:Kluwer Academic Publishers,1988.
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[2]STRUKOV D B,SNIDER G S,STEWART D R,et al.The missing memristor found[J].Nature,2008,453(7191):80-83.
[3]BATAS D,FIEDLER H.A memristor SPICE implementation and a new approach for magnetic flux-controlled memristor modeling[J].IEEE Transactions on Nanotechnology,2011,10(2):250-255.
[4]HO Y,HUANG G M,LI P.Nonvolatile memristor memory:Device characteristics and design implications[C]//IEEE/ACM International Conference on Computer-aided Design,2009:485-490.
[5]JO S H,CHANG T,EBONG I,et al.Nanoscale memristor device as synapse in neuromorphic systems[J].Nano Letters,2010,10(4):1297-1301.
[6]ITOH M,CHUA L O.Memristor cellular automata and memristor discrete-time cellular neural networks[J].International Journal of Bifurcation and Chaos,2009,19(11):3605-3656.
[7]XIN Y,LI Y,CHENG Z,et al.Global exponential stability for switched memristive neural networks with time-varying delays[J].Neural Networks,2016,80:34-42.
[8]GUO Z,WANG J,YAN Z.Global exponential dissipativity and stabilization of memristor-based recurrent neural networks with time-varying delays[J].Neural Networks,2013,48(6):158-172.
[9]DING S,WANG Z,RONG N,et al.Exponential stabilization of memristive neural networks via saturating sampled-data control[J].IEEE Transactions on Cybernetics,2017,(47)10:3027-3039.
[10]GUO Z,WANG J,YAN Z.Global exponential synchronization of two memristor-based recurrent neural networks with time delays via static or dynamic coupling[J].IEEE Transactions on Systems,Man,and Cybernetics:Systems,2015,45(2):235-249.
[11]DING S,WANG Z,NIU H,et al.Stop and go adaptive strategy for synchronization of delayed memristive recurrent neural networks with unknown synaptic weights[J].Journal of the Franklin Institute,2017,354(12):4989-5010.
[12]GAO J,ZHU P,ALSAEDI A,et al.A new switching control for finite-time synchronization of memristor-based recurrent neural networks[J].Neural Networks,2017,86:1-9.
[13]YANG X,HO D W.Synchronization of delayed memristive neural networks:robust analysis approach[J].IEEE Transactions on Cybernetics,2016,46(12):3377-3387.
[14]YANG X,CAO J,LIANG J.Exponential synchronization of memristive neural networks with delays:Interval matrix method[J].IEEE Transactions on Neural Networks and Learning Systems,2017,28(8):1878-1888.
[15]FILIPPOV A F.Differential equations with discontinuous righthand sides[M].Boston:Kluwer Academic Publishers,1988.
[16]HENDERSON J,OUAHAB A.Fractional functional differential inclusions with finite delay[J].Nonlinear Analysis:Theory,Methods & Applications,2009,70(5):2091-2105.
[17]AUBIN J P,CELLINA A.Differential inclusions:Set-valued maps and viability theory[M].Berlin:Springer,1984.