Abstract
The paper mainly deals with the optimization of synchronization for fractional-order memristive neural networks (FOMNNs) with a time delay. Based on synchronization conditions, an optimization model for control parameters is designed and computed. It’s significative to design an appropriate controller which can synchronize the drive FOMNNs and response FOMNNs. Based on the proposed controller, some synchronization conditions of FOMNNS can be obtained with the help of the linear matrix inequality, along with fractional-order Lyapunov methods and matrix analysis. The optimal model of control parameters includes a target function and some constraints. The target function is the minimal sum of control energy and integral square error index. The constraint conditions choose the sufficient conditions for synchronization of FOMNNs. The optimization model is difficult to compute but can be solved by means of the stochastic inertia weight particle swarm optimization algorithm. A simulation is provided to verify the validity of the proposed theoretical results.
Similar content being viewed by others
References
Namias V (1980) The fractional order Fourier transform and its application to quantum mechanics. IMA J Appl Math 25(3):241–265
Craiem D, Rojo FJ, Atienza JM, Armentano RL, Guinea GV (2008) Fractional-order viscoelasticity applied to describe uniaxial stress relaxation of human arteries. Phys Med Biol 53(17):4543
Azar AT, Vaidyanathan S, Ouannas A (2017) Fractional order control and synchronization of chaotic systems, vol 688. Springer, Berlin
Liu D, Zhang Y, Lou J, Lu J, Cao J (2018) Stability analysis of quaternion-valued neural networks: Decomposition and direct approaches. IEEE Trans Neural Netw Learn Syst 29(9):4201–4211
Zhang D, Kou KI, Liu Y, Cao J (2017) Decomposition approach to the stability of recurrent neural networks with asynchronous time delays in quaternion field. Neural Netw 94:55–66
Liu Y, Xu P, Lu J, Liang J (2016) Global stability of Clifford-valued recurrent neural networks with time delays. Nonlinear Dyn 2(84):767–777
Zhang J, Wu J, Bao H, Cao J (2018) Synchronization analysis of fractional-order three-neuron BAM neural networks with multiple time delays. Appl Math Comput 339:441–450
Bao H, Cao J, Kurths J, Alsaedi A, Ahmad B (2018) H\(\infty \) state estimation of stochastic memristor-based neural networks with time-varying delays. Neural Netw 99:79–91
Bao H, Park JH, Cao J (2015) Exponential synchronization of coupled stochastic memristor-based neural networks with time-varying probabilistic delay coupling and impulsive delay. IEEE Trans Neural Netw Learn Syst 27(1):190–201
Zhang G, Shen Y, Wang L (2013) Global anti-synchronization of a class of chaotic memristive neural networks with time-varying delays. Neural Netw 46:1–8
Yang X, Cao J, Yu W (2014) Exponential synchronization of memristive Cohen–Grossberg neural networks with mixed delays. Cogn Neurodyn 8(3):239–249
Yang S, Guo Z, Wang J (2015) Robust synchronization of multiple memristive neural networks with uncertain parameters via nonlinear coupling. IEEE Trans Syst Man Cybern Syst 45(7):1077–1086
Bao H, Park JH, Cao J (2015) Adaptive synchronization of fractional-order memristor-based neural networks with time delay. Nonlinear Dyn 82(3):1343–1354
Wang F, Yang Y (2018) Intermittent synchronization of fractional order coupled nonlinear systems based on a new differential inequality. Phys A 512:142–152
Liu Y, Tong L, Lou J, Lu J, Cao J (2018) Sampled-data control for the synchronization of Boolean control networks. IEEE Trans Cybern 99:1–7
Wang F, Yang Y (2019) On leaderless consensus of fractional-order nonlinear multi-agent systems via event-triggered control. Nonlinear Anal Model 24(3):353–367
He W, Qian F, Lam J, Chen G, Han QL, Kurths J (2015) Quasi-synchronization of heterogeneous dynamic networks via distributed impulsive control: error estimation, optimization and design. Automatica 62:249–262
Yu W, Li C, Yu X, Wen G, Lv J (2018) Economic power dispatch in smart grids: a framework for distributed optimization and consensus dynamics. China Inf Sci 61(1):012204
Qin Q, Cheng S, Zhang Q, Li L, Shi Y (2016) Particle swarm optimization with interswarm interactive learning strategy. IEEE Trans Cybern 46(10):2238–2251
Perng JW, Chen GY, Hsu YW (2017) FOPID controller optimization based on SIWPSO-RBFNN algorithm for fractional-order time delay systems. Soft Comput 21(14):4005–4018
Chauhan P, Deep K, Pant M (2013) Novel inertia weight strategies for particle swarm optimization. Memet Comput 5(3):229–251
Huang Z, Cao J, Raffoul YN (2018) Hilger-type impulsive differential inequality and its application to impulsive synchronization of delayed complex networks on time scales. China Inf Sci 61:1–3
Chang W, Zhu S, Li J, Sun K (2018) Global Mittag–Leffler stabilization of fractional-order complex-valued memristive neural networks. Appl Math Comput 338:346–362
Chen J, Chen B, Zeng Z (2018) Global asymptotic stability and adaptive ultimate Mittag–Leffler synchronization for a fractional-order complex-valued memristive neural networks with delays. IEEE Trans Syst Man Cybern Syst 99:1–17
Perng JW, Chen GY, Hsieh SC (2014) Optimal PID controller design based on PSO-RBFNN for wind turbine systems. Energies 7(1):191–209
Fang H, Chen L, Shen Z (2011) Application of an improved PSO algorithm to optimal tuning of PID gains for water turbine governor. Energy Convers Manag 52(4):1763–1770
Chang Q, Yang Y, Sui X, Shi Z (2019) The optimal control synchronization of complex dynamical networks with time-varying delay using PSO. Neurocomputing 333:1–10
Kilbas AAA, Srivastava HM, Trujillo JJ (2006) Theory and applications of fractional differential equations, vol 204. Elsevier, Elsevier
Petrá I (2011) Fractional-order nonlinear systems: modeling, analysis and simulation. Springer, Berlin
Wang F, Yang Y (2018) Quasi-synchronization for fractional-order delayed dynamical networks with heterogeneous nodes. Appl Math Comput 339:1–14
Sanchez EN, Perez JP (1999) Input-to-state stability (ISS) analysis for dynamic neural networks. IEEE Trans Circuits Syst I Fundam Theory Appl 46(11):1395–1398
Boyd S, El Ghaoui L, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory, vol 15. SIAM, Philadelphia
Chen B, Chen J (2015) Razumikhin-type stability theorems for functional fractional-order differential systems and applications. Appl Math Comput 254:63–69
Chua L (2011) Resistance switching memories are memristors. Appl Phys A 102(4):765–783
Chen J, Zeng Z, Jiang P (2014) Global Mittag–Leffler stability and synchronization of memristor-based fractional-order neural networks. Neural Netw 51:1–8
Yang X, Ho DW (2016) Synchronization of delayed memristive neural networks: robust analysis approach. IEEE Trans Cybern 46(12):3377–3387
Bao H, Cao J, Kurths J (2018) State estimation of fractional-order delayed memristive neural networks. Nonlinear Dyn 94(2):1215–1225
Henderson J, Ouahab A (2009) Fractional functional differential inclusions with finite delay. Nonlinear Anal Theory Methods Appl 70(5):2091–2105
Gan Q (2013) Synchronization of competitive neural networks with different time scales and time-varying delay based on delay partitioning approach. Int J Mach Learn Cybern 4(4):327–337
Li K, Yu W, Ding Y (2015) Successive lag synchronization on nonlinear dynamical networks via linear feedback control. Nonlinear Dyn 80(1–2):421–430
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that there is no conflict of interest in preparing this article.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This work was jointly supported by the Natural Science Foundation of Jiangsu Province of China under Grant Nos. BK20161126, BK20170171, BK20181342, and the Postgraduate Research and Practice Innovation Program of Jiangnan University under Grant No. JNKY19\(_{-}\)042.
Rights and permissions
About this article
Cite this article
Chang, Q., Hu, A., Yang, Y. et al. The Optimization of Synchronization Control Parameters for Fractional-Order Delayed Memristive Neural Networks Using SIWPSO. Neural Process Lett 51, 1541–1556 (2020). https://doi.org/10.1007/s11063-019-10157-y
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11063-019-10157-y