Adaptive Neural Network Dynamic Surface Control for Nonlinear Stochastic Systems in The Strict-Feedback Form with Prandtl-Ishlinskii Hysteresis in The Actuator

Subject Areas : Renewable energy

Mohammad Mahdi Aghajary ¹ , Mahnaz Hashemi ²

1 - Department of Electrical Engineering- Najafabad Branch, Islamic Azad University, Najafabad, Iran
2 - Smart Microgrid Research Center- Najafabad Branch, Islamic Azad University, Najafabad, Iran

Received: 2020-01-14 Accepted : 2020-05-20 Published : 2020-08-05

Keywords: Actuator nonlinearity, adaptive RBF neural networks, Dynamic Surface Control (DSC), Nonlinear Stochastic Systems, Prandtl-Ishlinskii Hysteresis,

Abstract :

Using the adaptive radial basis function (RBF) neural network dynamic surface control design method, a controller design approach is presented in order to the stabilization of strict-feedback nonlinear stochastic systems subjected to Prandtl-Ishlinskii nonlinearity in the actuator. This method is capable to be applied to nonlinear stochastic systems with any unknown dynamics. According to the universal approximation capability the RBF neural networks make it possible to approximate the unknown dynamics of the nonlinear stochastic systems. Using the minimal-learning-parameters algorithm the approximation procedure is done with a minimum complexity and required calculations. The stability of the proposed control system is proven analytically and its results are demonstrated using a simulation example. It is shown that the proposed design approach guarantees the boundedness in probability for adaptive control system, and in turn the uniformly ultimately boundedness of all closed-loop signals. It is also shown, that using this method the tracking error can be made arbitrarily small.

References:

[1]     M. Krstic, I. Kanellakopoulos, P. V. Kokotovic, Nonlinear and adaptive control design. Wiley New York, 1995.

[2]     H. Wang, B. Chen, C. Lin, "Direct adaptive neural control for strict-feedback stochastic nonlinear systems”, Nonlinear Dynamics, vol. 67, no. 4, pp. 2703-2718, Mar. 2012 (doi: 10.1007/s11071-011-0182-4).

[3]     D. Swaroop, J. K. Hedrick, P. P. Yip, J. C. Gerdes, "Dynamic surface control for a class of nonlinear systems”, IEEE Trans. on Automatic Control, vol. 45, no. 10, pp. 1893-1899, Oct. 2000 (doi:10.1109/tac.20­0­0­.880994).

[4]     D. Wang J. Huang, "Neural network-based adaptive dynamic surface control for a class of uncertain nonlinear systems in strict-feedback form”, IEEE Trans. on Neural Networks, vol. 16, no. 1, pp. 195-202, Jan. 2005 (doi:10.1109/TNN.2004.839354).

[5]     H. Ma, H. Liang, Q. Zhou, C. K. Ahn, "Adaptive dynamic surface control design for uncertain nonlinear strict-feedback systems with unknown control direction and disturbances”, IEEE Trans. on Systems, Man, Cybernetics: Systems, no. 99, pp. 506 - 515, July 2018 (doi:10.1109/TSMC.2018.2855170).

[6]     D. Lei, T. Wang, D. Cao, J. Fei, "Adaptive dynamic surface control of mems gyroscope sensor using fuzzy compensator”, IEEE Access, vol. 4, pp. 4148-4154, August 2016 (doi:10.1109/ACCESS.201­6.25­965­3­8).

[7]     G.Q. Wu, S.M. Song, J.G. Sun, "Adaptive dynamic surface control for spacecraft terminal safe approach with input saturation based on tracking differentiator”, International Journal of Control, Automation and Systems, vol. 16, no. 3, pp. 1129-1141, May 2018 (doi:10.1007/s12555-017-0531-2).

[8]     G. Liu, G. Li, Z. Peng, H. Pan, "Adaptive neural network dynamic surface control algorithm for pneumatic servo system”, Proceedings of the ICMIC, pp. 821-829, Singapore, 2020 (doi: 10.1007/978-981-15-0474-7_77)

[9]     T.-P. Zhang S. S. Ge, "Adaptive dynamic surface control of nonlinear systems with unknown dead zone in pure feedback form”, Automatica, vol. 44, no. 7, pp. 1895-1903, July 2008 (doi: 10.1016/j.automati­ca.2­007­.11­.025).

[10]  M. Bataghva, M. Hashemi, "Adaptive sliding mode synchronisation for fractional-order non-linear systems in the presence of time-varying actuator faults”, IET Control Theory and Applications, vol. 12, no. 3, pp. 377-383, Jan. 2018 (doi:10.1049/iet-cta.2017.0458).

[11]  Z. Li, T. Li, G. Feng, "Adaptive neural control for a class of stochastic nonlinear time‐delay systems with unknown dead zone using dynamic surface technique”, International Journal of Robust Nonlinear Control, vol. 26, no. 4, pp. 759-781, Mar. 2016 (doi:10.1002/rnc.3336).

[12]  W.J. Si, X.D. Dong, F.F. Yang, "Adaptive neural dynamic surface control for a general class of stochastic nonlinear systems with time delays and input dead-Zone”, International Journal of Control, Automation Systems, vol. 15, no. 5, pp. 2416-2424, Sep. 2017 (doi:10.1007/s12555-016-0564-y).

[13]  X. Zhang, C.Y. Su, Y. Lin, L. Ma, J. Wang, "Adaptive neural network dynamic surface control for a class of time-delay nonlinear systems with hysteresis inputs and dynamic uncertainties”, IEEE Trans. On Neural Networks Learning Systems, vol. 26, no. 11, pp. 2844-2860, Feb. 2015 (doi:10.1109/TNNLS.2015.2397935).

[14]  X. Zhang, Y. Lin, J. Mao, "A robust adaptive dynamic surface control for a class of nonlinear systems with unknown Prandtl–Ishilinskii hysteresis”, International Journal of Robust Nonlinear Control, vol. 21, no. 13, pp. 1541-1561, Sep. 2010 (doi:10.1002/rnc.1652).

[15]  B. Xu, "Disturbance observer-based dynamic surface control of transport aircraft with continuous heavy cargo airdrop”, IEEE Trans. on Systems, Man, Cybernetics: Systems, vol. 47, no. 1, pp. 161-170, Jan. 2017 (doi: 10.­11­09/­TSM­C.2016.2558098).

[16]  M. Hashemi, G. Shahgholian, "Distributed robust adaptive control of high order nonlinear multi agent systems”, ISA transactions, vol. 74, pp. 14-27, Feb. 2018 (doi: 10.1016/j.isatra.2018.01.023).

[17]  N. Wang, Z. Liu, Z. Zheng, M. J. Er, "Global exponential trajectory tracking control of underactuated surface vehicles using dynamic surface control approach”, Proceeding of the IEEE/ICoIAS, pp. 221-226, Singapore, March 2018 (doi: 10.1109/ICoIAS.2018.8494037).

[18]  H. Liu, Y. Pan, J. Cao, "Composite learning adaptive dynamic surface control of fractional-order nonlinear systems”, IEEE Trans on Cybernetics, Sep. 2019 (doi:10.1109/TCYB.2019.2938754).

[19]  G. Li, W. Xu, J. Zhao, S. Wang, B. Li, "Precise robust adaptive dynamic surface control of permanent magnet synchronous motor based on extended state observer”, IET Science, Measurement and Technology, vol. 11, no. 5, pp. 590-599, July 2017 (doi:10.1049/iet-smt.2016.0252).

[20]  B. Ren, S. S. Ge, C.Y. Su, T. H. Lee, "Adaptive neural control for a class of uncertain nonlinear systems in pure-feedback form with hysteresis input”, IEEE Trans. on Systems, Man, Cybernetics, Part B, vol. 39, no. 2, pp. 431-443, April 2009 (doi:10.1109/tsmcb.2008.2006368).

[21]  Q. Wang, C.Y. Su, "Robust adaptive control of a class of nonlinear systems including actuator hysteresis with Prandtl–Ishlinskii presentations”, Automatica, vol. 42, no. 5, pp. 859-867, Mar. 2006 (doi: 10.1016/j.autom­a­tic­a.200­6.01­.018).

[22]  H. Wang, B. Chen, K. Liu, X. Liu, C. Lin, "Adaptive neural tracking control for a class of nonstrict-feedback stochastic nonlinear systems with unknown backlash-like hysteresis”, IEEE Trans. on Neural Networks Learning Systems, vol. 25, no. 5, pp. 947-958, May 2014 (doi:10.1109/tnnls.2013.2283879).

[23]  C.Y. Su, Q. Wang, X. Chen, and S. Rakheja, "Adaptive variable structure control of a class of nonlinear systems with unknown Prandtl-Ishlinskii hysteresis”, IEEE Trans. on Automatic Control, vol. 50, no. 12, pp. 2069-2074, Dec. 2005 (doi:10.1109/TAC.2005.860260).