×

zbMATH — the first resource for mathematics

A multilayer feed forward small-world neural network controller and its application on electrohydraulic actuation system. (English) Zbl 1271.92004
Summary: Being difficult to attain the precise mathematical models, traditional control methods such as proportional integral (PI) and proportional integral differentiation (PID) cannot meet the demands for real time and robustness when applied in some nonlinear systems. The neural network controller is a good replacement to overcome these shortcomings. However, the performance of neural network controller is directly determined by neural network model. In this paper, a new neural network model is constructed with a structure topology between the regular and random connection modes based on complex network, which simulates the brain neural network as far as possible, to design a better neural network controller. Then, a new controller is designed under small-world neural network model and is investigated in both linear and nonlinear systems control. The simulation results show that the new controller basing on small-world network model can improve the control precision by 30% in the case of system with random disturbance. Besides the good performance of the new controller in tracking square wave signals, which is demonstrated by the experiment results of direct drive electro-hydraulic actuation position control system, it works well on anti-interference performance.

MSC:
92B20 Neural networks for/in biological studies, artificial life and related topics
05C82 Small world graphs, complex networks (graph-theoretic aspects)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] D. Batalle, E. Eixarch, F. Figueras et al., “Altered small-world topology of structural brain networks in infants with intrauterine growth restriction and its association with later neurodevelopmental outcome,” NeuroImage, vol. 60, no. 2, pp. 1352-1366, 2012.
[2] M. Bolaños, E. M. Bernat, B. He, and S. Aviyente, “A weighted small world network measure for assessing functional connectivity,” Journal of Neuroscience Methods, vol. 212, no. 1, pp. 133-142, 2013.
[3] O. Sporns and C. J. Honey, “Small worlds inside big brains,” Proceedings of the National Academy of Sciences of the United States of America, vol. 103, no. 51, pp. 19219-19220, 2006.
[4] R. Albert and A. L. Barabási, “Statistical mechanics of complex networks,” Reviews of Modern Physics, vol. 74, no. 1, pp. 47-97, 2002. · Zbl 1205.82086
[5] J. Lu, D. W. C. Ho, and Z. Wang, “Pinning stabilization of linearly coupled stochastic neural networks via minimum number of controllers,” IEEE Transactions on Neural Networks, vol. 20, no. 10, pp. 1617-1629, 2009.
[6] J. Cao, P. Li, and W. Wang, “Global synchronization in arrays of delayed neural networks with constant and delayed coupling,” Physics Letters A, vol. 353, no. 4, pp. 318-325, 2006.
[7] Y. Xia and J. Wang, “A general methodology for designing globally convergent optimization neural networks,” IEEE Transactions on Neural Networks, vol. 9, no. 6, pp. 1331-1343, 1998.
[8] S. Hu, X. Liao, and X. Mao, “Stochastic Hopfield neural networks,” Journal of Physics A, vol. 36, no. 9, pp. 2235-2249, 2003. · Zbl 1042.82036
[9] K. O. Stanley, D. B. D’Ambrosio, and J. Gauci, “A hypercube-based encoding for evolving large-scale neural networks,” Artificial Life, vol. 15, no. 2, pp. 185-212, 2009.
[10] O. R. de Lautour and P. Omenzetter, “Prediction of seismic-induced structural damage using artificial neural networks,” Engineering Structures, vol. 31, no. 2, pp. 600-606, 2009.
[11] E. Gelenbe and J. M. Fourneau, “Random neural networks with multiple classes of signals,” Neural Computation, vol. 11, no. 4, pp. 953-963, 1999.
[12] D. J. Watts and S. H. Strogatz, “Collective dynamics of ’small-world9 networks,” Nature, vol. 393, no. 6684, pp. 440-442, 1998. · Zbl 1368.05139
[13] G. A. Pagani and M. Aiello, “The power grid as a complex network: a survey,” Physica A, vol. 392, no. 11, pp. 2688-2700, 2013. · Zbl 1395.94418
[14] F. Gerhard, G. Pipa, B. Lima, S. Neuenschwander, and W. Gerstner, “Extraction of network topology from multi-electrode recordings: is there a small-world effect?” Frontiers in Computational Neuroscience, vol. 5, no. 4, pp. 1-13, 2011.
[15] H. D. Rozenfeld, C. Song, and H. A. Makse, “Small-world to fractal transition in complex networks: a renormalization group approach,” Physical Review Letters, vol. 104, no. 2, Article ID 025701, 2010.
[16] A. R. Backes, D. Casanova, and O. M. Bruno, “A complex network-based approach for boundary shape analysis,” Pattern Recognition, vol. 42, no. 1, pp. 54-67, 2009. · Zbl 1162.68594
[17] M. Karsai, M. Kivelä, R. K. Pan et al., “Small but slow world: how network topology and burstiness slow down spreading,” Physical Review E, vol. 83, no. 2, Article ID 025102, 2011.
[18] C. Wu and B. Zhou, “Complex network analysis of tag as a social network,” Journal of Zhejiang University, vol. 44, no. 11, pp. 2194-2197, 2010 (Chinese).
[19] V. M. Eguíluz, D. R. Chialvo, G. A. Cecchi, M. Baliki, and A. V. Apkarian, “Scale-free brain functional networks,” Physical Review Letters, vol. 94, no. 1, Article ID 018102, 2005.
[20] D. S. Bassett and E. Bullmore, “Small-world brain networks,” Neuroscientist, vol. 12, no. 6, pp. 512-523, 2006.
[21] J. Piersa, F. Piekniewski, and T. Schreiber, “Theoretical model for mesoscopic-level scale-free self-organization of functional brain networks,” IEEE Transactions on Neural Networks, vol. 21, no. 11, pp. 1747-1758, 2010.
[22] C. Li, “Memorizing morph patterns in small-world neuronal network,” Physica A, vol. 388, no. 2-3, pp. 240-246, 2009.
[23] S. Lu, J. Fang, A. Guo, and Y. Peng, “Impact of network topology on decision-making,” Neural Networks, vol. 22, no. 1, pp. 30-40, 2009. · Zbl 06578184
[24] O. Erkaymaz, M. Özer, and N. Yumu\csakc, “Performance analysis of a feed forward artifical neural network with small-world topology,” Procedia Technology, vol. 1, pp. 291-296, 2012.
[25] D. Simard, L. Nadeau, and H. Kröger, “Fastest learning in small-world neural networks,” Physics Letters A, vol. 336, no. 1, pp. 8-15, 2005. · Zbl 1136.68504
[26] G. Trtnik, F. Kav\vci\vc, and G. Turk, “Prediction of concrete strength using ultrasonic pulse velocity and artificial neural networks,” Ultrasonics, vol. 49, no. 1, pp. 53-60, 2009.
[27] V. Kůrková, P. C. Kainen, and V. Kreinovich, “Estimates of the number of hidden units and variation with respect to half-spaces,” Neural Networks, vol. 10, no. 6, pp. 1061-1068, 1997.
[28] Z. Z. Yuan, Z. Q. Chen, and X. Li, “Connectionism intelligent control: a survey,” Acta Automatica Sinica, vol. 28, no. 1, pp. 38-59, 2002 (Chinese).
[29] H. M. R. Ugalde, J. C. Carmona, V. M. Alvarado, and J. Reyes-Reyes, “Neural network design and model reduction approach for black box nonlinear system identification with reduced number of parameters,” Neurocomputing, vol. 101, pp. 170-180, 2013.
[30] S. Habibi, R. Burton, and E. Sampson, “High precision hydrostatic actuation systems for micro- and nanomanipulation of heavy loads,” Transactions of the ASME, vol. 128, no. 4, pp. 778-787, 2006.
[31] S. R. Habibi and R. Burton, “Parameter identification for a high-performance hydrostatic actuation system using the variable structure filter concept,” Transactions of the ASME, vol. 129, no. 2, pp. 229-235, 2007.
[32] J. L. Liu, J. H. Jiang, T. R. Lu, Q. H. Liu, C. W. Zhang, and H. G. Xu, “Direct drive volume control electro-hydraulic servo active mass driver system,” Journal of Harbin Institute of Technology, vol. 43, no. 9, pp. 51-55, 2011 (Chinese).
[33] K. M. Elbayomy, Z. Jiao, and H. Zhang, “PID controller optimization by GA and its performances on the electro-hydraulic servo control system,” Chinese Journal of Aeronautics, vol. 21, no. 4, pp. 378-384, 2008.
[34] J. Yao, Z. Jiao, Y. Shang, and C. Huang, “Adaptive nonlinear optimal compensation control for electro-hydraulic load simulator,” Chinese Journal of Aeronautics, vol. 23, no. 6, pp. 720-733, 2010.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.