Nonlinear Dynamics

, Volume 84, Issue 4, pp 1989–2002 | Cite as

Adaptive dynamic surface error constrained control for MIMO systems with backlash-like hysteresis via prediction error technique

Original Paper


In this paper, we are concerned with the problem of adaptive dynamic surface error constrained control for a class of nonlinear multiple-input-multiple-output systems with unknown backlash-like hysteresis nonlinearities. By transforming the tracking errors into new virtual error variables which are incorporated into the proposed prescribed performance control strategy, the prescribed steady-state and transient performance can be ensured. Compared with the existing methods, we introduce the prediction error which is generated between the system state and the serial–parallel estimation model to construct the adaptive laws for neural network weights. The proposed prediction error technique can be used to compensate the tracking error, which implies that a higher accuracy of the identified neural network model is achieved. It is shown that the proposed control approach can guarantee that all the signals of the resulting closed-loop systems are bounded and the output tracks the desired trajectory, while the tracking error are confined all times within the prescribed bounds. Finally, a simulation example is provided to confirm the effectiveness of the proposed approach.


Adaptive dynamic surface control Unknown backlash-like hysteresis Prediction error technique Serial–parallel estimation model Prescribed performance control 



This work was supported by the National Natural Science Foundation of China of Grants 61473070 and 61433004, the Fundamental Research Funds for the Central Universities (Grant Nos. N130504002, N140406001 and N130104001), and SAPI Fundamental Research Funds (Grant No. 2013ZCX01).


  1. 1.
    How, B.V.E., Ge, S.S., Choo, Y.S.: Control of coupled vessel, crane, cable, and payload dynamics for subsea installation operation. IEEE Trans. Control Syst. Technol. 19, 208–220 (2011)CrossRefGoogle Scholar
  2. 2.
    Tee, K.P., Ge, S.S., Tay, E.H.: Adaptive control of electrostatic microactuator with bidirectional drive. IEEE Trans. Control Syst. Technol. 17, 340–352 (2009)CrossRefGoogle Scholar
  3. 3.
    Kothare, M.V., Balakrishnan, V., Morari, M.: Robust constrained model predictive control using linear matrix inequalities. Automatica 32, 1361–1379 (1996)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Hu, T., Lin, Z.: Control Systems with Actuator Saturation: Analysis and Design. Birkhuser, Boston (2001)CrossRefMATHGoogle Scholar
  5. 5.
    Tee, K.P., Ge, S.S., Tay, E.H.: Barrier Lyapunov functions for the control of output-constrained nonlinear systems. Automatica 45, 918–927 (2009)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Niu, B., Zhao, J.: Barrier Lyapunov functions for the output tracking control of constrained nonlinear switched systems. Syst. Control Lett. 62, 963–971 (2013)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Liu, L., Liu, Y.J., Chen, C.L.P.: Adaptive neural network control for a DC motor system with dead-zone. Nonlinear Dyn. 72(1–2), 141–147 (2013)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Liu, Y.J., Li, D.J., Tong, S.C.: Adaptive output feedback control for a class of nonlinear systems with full-state constraints. Int. J. Control 87, 281–290 (2014)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Ren, B.B., Ge, S.S., Tee, K.P., Lee, T.H.: Adaptive neural control for output feedback nonlinear systems using a barrier Lyapunov function. IEEE Trans. Neural Netw. 21, 1339–1344 (2010)CrossRefGoogle Scholar
  10. 10.
    Tong, S.C., Sui, S., Li, Y.M.: Fuzzy adaptive output feedback control of MIMO nonlinear systems with partial tracking errors constrained. IEEE Trans. Fuzzy Syst. doi: 10.1109/TFUZZ.2014.2327987
  11. 11.
    Benchlioulis, C.P., Rovithakis, G.A.: Robust partial-state feedback prescribed performance control of cascade systems with unknown nonlinearities. IEEE Trans. Autom. Control 56, 2224–2239 (2011)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Marantos, P., Eqtami, A., Bechlioulis, C.P., Kyriakopoulos, K.J.: A prescribed performance robust nonlinear model predictive control framework. In: European IEEE Control Conference (ECC), pp. 2182–2187 (2014)Google Scholar
  13. 13.
    Su, X., Shi, P., Wu, L., Karimi, H.R.: Design on fuzzy control for a class of stochastic nonlinear systems. In: IEEE American Control Conference (ACC), pp. 544–547 (2014)Google Scholar
  14. 14.
    Song, H.T., Zhang, T., Zhang, G.L., Lu, C.J.: Robust dynamic surface control of nonlinear systems with prescribed performance. Nonlinear Dyn. 76, 599–608 (2014)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Wang, W., Wen, C.: Adaptive actuator failure compensation control of uncertain nonlinear systems with guaranteed transient performance. Automatica 46, 2082–2091 (2009)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Benchlioulis, C.P., Rovithakis, G.A.: Neuro-adaptive force/position control with prescribed performance and guaranteed contact maintenance. IEEE Trans. Neural Netw. 21, 1857–1868 (2010)CrossRefGoogle Scholar
  17. 17.
    Benchlioulis, C.P., Rovithakis, G.A.: Adaptive control with guaranteed transient and steady state tracking error bounds for strict feedback systems. Automatica 45, 532–538 (2009)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Bechlioulis, C.P., Doulgeri, Z., Rovithakis, G.A.: Guaranteeing prescribed performance and contact maintenance via an approximation free robot force/position controller. Automatica 48, 360–365 (2012)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Liu, Y.J., Tong, S.C.: Barrier Lyapunov functions-based adaptive control for a class of nonlinear pure-feedback systems with full state constraints. Automatica (in press). doi: 10.1016/j.automatica.2015.10.034
  20. 20.
    Zhang, X.Y., Lin, Y.: Adaptive tracking control for a class of pure-feedback nonlinear systems including actuator hysteresis and dynamic uncertainties. IET Control Theory Appl. 5, 1868–1880 (2011)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Su, C.Y., Stepanenko, Y., Svoboda, J., Leung, T.P.: Robust adaptive control of a class of nonlinear systems with unknown backlash-like hysteresi. IEEE Trans. Autom. Control 45, 2427–2432 (2000)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Tao, G., Petar, V.K.: Adaptive control of plants with unknown hystereses. IEEE Trans. Autom. Control 40, 200–212 (1995)MathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    Su, C.Y., Wang, Q.Q., Chen, X.K., Rakheja, S.: Adaptive variable structure control of a class of nonlinear systems with unknown Prandtl–Ishlinskii hysteresis. IEEE Trans. Autom. Control 50, 2069–2073 (2005)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Dong, R.L, Tan, Y.H., Janschek, K.: Non-smooth predictive control for wiener systems with backlash-like hysteresis. IEEE/ASME Trans. Mechatron. doi: 10.1109/TMECH.2015.2453794
  25. 25.
    Hassani, V., Tjahjowidodo, T., Do, T.N.: A survey on hysteresis modeling, identification and control. Mech. Syst. Signal Process. 49, 209–233 (2014)CrossRefGoogle Scholar
  26. 26.
    Wang, H., Chen, B., Liu, K., Liu, X., Lin, C.: Adaptive neural tracking control for a class of nonstrict-feedback stochastic nonlinear systems with unknown backlash-like hysteresis. IEEE Trans. Neural Netw. Learn. Syst. 25, 947–958 (2014)CrossRefGoogle Scholar
  27. 27.
    Wang, M., Liu, X., Shi, P.: Adaptive neural control of pure-feedback nonlinear time-delay systems via dynamic surface technique. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 41, 1681–1692 (2011)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Liu, L., Wang, Z.S., Zhang, H.G.: Adaptive NN fault-tolerant control for discrete-time systems in triangular forms with actuator fault. Neurocomputing 152, 209–221 (2015)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Liu, Z., Lai, G.Y., Zhang, Y., Chen, X., Chen, C.L.P.: Adaptive neural control for a class of nonlinear time-varying delay systems with unknown hysteresis. IEEE Trans. Neural Netw. Learn. Syst. 25, 2129–2140 (2014)CrossRefGoogle Scholar
  30. 30.
    Huang, J., Dou, L.H., Fang, H., Chen, J., Yang, Q.K.: Distributed backstepping-based adaptive fuzzy control of multiple high-order nonlinear dynamics. Nonlinear Dyn. 81, 63–75 (2015)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Seto, D., Annaswamy, A., Baillieul, J.: Adaptive control of nonlinear systems with a triangular structure. IEEE Trans. Autom. Control 39, 1411–1428 (1994)MathSciNetCrossRefMATHGoogle Scholar
  32. 32.
    Wang, D., Huang, J.: Neural network-based adaptive dynamic surface control for a class of uncertain nonlinear systems in strict-feedback form. IEEE Trans. Neural Netw. 16, 195–202 (2005)CrossRefGoogle Scholar
  33. 33.
    Xie, X.J., Zhao, C.R.: State feedback stabilization of stochastic feedforward nonlinear systems with input time-delay. Acta Autom. Sin. 40(12), 2972–2976 (2014)MathSciNetCrossRefGoogle Scholar
  34. 34.
    Chen, W., Jiao, L., Li, J., Li, R.: Adaptive NN backstepping output-feedback control for stochastic nonlinear strict-feedback systems with time-varying delays. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 40, 939–950 (2010)CrossRefGoogle Scholar
  35. 35.
    Xu, B., Huang, X., Wang, D., Sun, F.: Dynamic surface control of constrained hypersonic flight models with parameter estimation and actuator compensation. Asian J. Control 16, 162–174 (2014)MathSciNetCrossRefMATHGoogle Scholar
  36. 36.
    Mehraeen, S., Jagannathan, S., Crow, M.: Power system stabilization using adaptive neural network-based dynamic surface control. IEEE Trans. Power Syst. 26, 669–680 (2011)CrossRefGoogle Scholar
  37. 37.
    Xu, B., Shi, Z.K., Yang, C.G., Sun, F.C.: Composite neural dynamic surface control of a class of uncertain nonlinear systems in strict-feedback form. IEEE Trans. Neural Netw. 44, 2626–2634 (2014)Google Scholar
  38. 38.
    Bellomo, D., Naso, D., Turchiano, B., Babu ska, R.: Composite adaptive fuzzy control. In: Proceedings of the 16th IFAC World Congress Prague, Czech Republic, pp. 97–102 (2005)Google Scholar
  39. 39.
    Pan, Y., Er, M.J., Sun, T.: Composite adaptive fuzzy control for synchronizing generalized Lorenz systems. Chaos: an interdisciplinary. J. Nonlinear Sci. 22, 023144 (2012)MathSciNetMATHGoogle Scholar
  40. 40.
    Chen, C., Liu, Z., Zhang, Y., Chen, C.L.P., Xie, S.: Adaptive control of MIMO mechanical systems with unknown actuator nonlinearities based on the Nussbaum gain approach. IEEE/CAA J. Autom. Sin. 3(1), 26–34 (2016)MathSciNetCrossRefGoogle Scholar
  41. 41.
    Chen, L., Wang, Q.: Adaptive robust control for a class of uncertain MIMO non-affine nonlinear systems. IEEE/CAA J. Autom. Sin. 3(1), 105–112 (2016)MathSciNetCrossRefGoogle Scholar
  42. 42.
    Han, S.I., Lee, J.: Partial tracking error constrained fuzzy dynamic surface control for a strict feedback nonlinear dynamic system. IEEE Trans. Fuzzy Syst. 22, 1049–1061 (2014)CrossRefGoogle Scholar
  43. 43.
    Tong, S.C., Li, Y.M., Feng, G., Li, T.S.: Observer-based adaptive fuzzy backstepping dynamic surface control for a class of MIMO nonlinear systems. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 41, 1124–1135 (2011)CrossRefGoogle Scholar
  44. 44.
    Wang, Z.S., Liu, L., Zhang, H.G., Xiao, G.Y.: Fault-tolerant controller design for a class of nonlinear MIMO discrete-time systems via online reinforcement learning algorithm. IEEE Trans. Syst. Man Cybern.: Syst. (in press). doi: 10.1109/TSMC.2015.2478885
  45. 45.
    Liu, L., Wang, Z.S., Zhang, H.G.: Adaptive fault-tolerant tracking control for MIMO discrete-time systems via reinforcement learning algorithm with less learning parameters. IEEE Trans. Autom. Sci. Eng. (in press). doi: 10.1109/TASE.2016.2517155
  46. 46.
    Macki, J.W., Nistri, P., Zecca, P.: Mathematical models for hysteresis. SIAM Rev. 35, 94–123 (1993)MathSciNetCrossRefMATHGoogle Scholar
  47. 47.
    Antonelli, R., Astolfi, A.: Continuous stirred tank reactors: easy to stabilise. Automatica 39, 1817–1827 (2003)MathSciNetCrossRefMATHGoogle Scholar
  48. 48.
    Kaddissi, C., Kenne, J.P.: Maarouf Saad: indirect adaptive control of an electrohydraulic servo system based on nonlinear backstepping. IEEE/ASME Trans. Mechatron. 16, 1171–1177 (2011)CrossRefGoogle Scholar
  49. 49.
    Wang, H.Q., Liu, X.P., Chen, B., Zhou, Q.: Adaptive fuzzy decentralized control for a class of pure-feedback large-scale nonlinear systems. Nonlinear Dyn. 75(3), 449–460 (2014)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.School of Information Science and EngineeringNortheastern UniversityShenyangChina
  2. 2.The State Key Laboratory of Synthetical Automation for Process IndustriesShenyangChina

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