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AFMBC for a Class of Nonlinear Discrete-Time Systems with Dead Zone

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Abstract

This paper is fretful about an adaptive fuzzy model-based controller (AFMBC), which is studied and implemented for class of nonlinear discrete-time system with dead zone. Due to immeasurable states and the presence of symmetric/non-symmetric dead zones, design of controller becomes more challenging. AFMBC is design for approximation of such nonlinear system to a relative degree of accuracy, which can be used for adaptation of nonlinear discrete-time systems with or without the presence of symmetric/non-symmetric dead zones. AFMBC employs as a reference model which is useful to closed-loop pure feedback form of fuzzy controller. AFMBC provides approximation of immeasurable states and minimizes effects of unknown bounded disturbances in the system. Based on Lyapunov method, it is proved that proposed scheme for discrete-time nonlinear systems is asymptotically stable. Hence, not only stability of proposed system is assured, but it is also shows that tracking error of model lies in closed neighbourhood of zero after sufficient number of iterations, i.e. tracking error \( (e(t) \to 0\;{\text{as}}\;t \to \infty ) \). The feasibility of the AFMBC is demonstrated by well-known direct current (DC) motor example and other nonlinear discrete-time problem through simulation.

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References

  1. Wang, L.X., Mendel, J.M.: Fuzzy basis functions, universal approximation, and orthogonal least-squares learning. IEEE Trans. Neural Netw. 3(5), 807–814 (1996)

    Article  Google Scholar 

  2. Funahashi, K.: On the approximate realization of continuous mappingby neural networks. Neural Netw. 2, 183–192 (1989)

    Article  Google Scholar 

  3. Hornik, K., Stinchcombe, M., White, H.: Multilayered feedforwardnetwork are universal approximators. Neural Netw. 2, 359–366 (1989)

    Article  MATH  Google Scholar 

  4. Poggio, T., Girosi, F.: Networks for approximation and learning. Proc. IEEE 78, 1481–1497 (1990)

    Article  MATH  Google Scholar 

  5. Lewis, F.L., Campos, J., Selmic, R.: Neuro-fuzzy control of industrial systems with actuator nonlinearities. Soc. Ind. Appl. Math. (2002). ISBN: 0-89871-505-9

  6. Chen, B., Liu, K., Liu, X., Shi, P., Lin, C., Zhang, H.: Approximation-based adaptive neural control design for a class ofnonlinear systems. IEEE Trans. Cybern. 44(5), 610–619 (2014)

    Article  Google Scholar 

  7. Pan, Y.P., Er, M.J., Huang, D., Wang, Q.: Adaptive fuzzy controlwith guaranteed convergence of optimal approximation error. IEEE Trans. Fuzzy Syst. 19(5), 807–818 (2011)

    Article  Google Scholar 

  8. Zhang, H.G., Luo, Y.H., Liu, D.R.: Neural network-basednear-optimal control for a class of discrete-time affine nonlinear systemswith control constraint. IEEE Trans. Neural Netw. 20(9), 1490–1503 (2009)

    Article  Google Scholar 

  9. Li, H.X., Deng, H.: An approximate internal model-based neuralcontrol for unknown nonlinear discrete processes. IEEE Trans. Neural Netw. 17(3), 659–670 (2006)

    Article  Google Scholar 

  10. Ge, S.S., Zhang, J., Lee, T.H.: Adaptive neural network control for aclass of MIMO nonlinear systems with disturbances in discrete-time. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 34(4), 1630–1645 (2004)

    Article  Google Scholar 

  11. Chen, C.L.P., Pao, Y.H.: An integration of neural network andrule-based systems for design and planning of mechanical assemblies. IEEE Trans. Syst. Man Cybern. 23(5), 1359–1371 (1993)

    Article  Google Scholar 

  12. Wang, L.X.: Adaptive Fuzzy Systems and Control: Design and StabilityAnalysis. Prentice-Hall, Englewood Cliffs (1994)

    Google Scholar 

  13. Zhou, Q., Shi, P., Xu, S.Y., Li, H.: Observer-based adaptive neuralnetwork control for nonlinear stochastic systems with time delay. IEEE Trans. Neural Netw. Learn. Syst. 24(1), 71–80 (2013)

    Article  Google Scholar 

  14. Chen, C.L.P., Liu, Y.J., Wen, G.X.: Fuzzy neural network-basedadaptive control for a class of uncertain nonlinear stochastic systems. IEEE Trans Cybern 44(5), 583–593 (2014)

    Article  Google Scholar 

  15. Na, J., Ren, X.M., Zheng, D.D.: Adaptive control for nonlinear purefeedbacksystems with high-order sliding mode observer. IEEE Trans. Neural Netw. Learn. Syst. 24(3), 370–382 (2013)

    Article  Google Scholar 

  16. Sakhre, V., Singh, U.P., Jain, S.: FCPN approach for uncertain nonlinear dynamical system with unknown disturbance. Int. J. Fuzzy Syst, vol. 18 (2016). https://doi.org/10.1007/s40815-016-0145-5

  17. Chen, M., Ge, S.S., Ren, B.B.: Adaptive tracking control of uncertain MIMO nonlinear systems with input constraints. Automatica 47(3), 452–465 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  18. Liu, M.: Decentralized control of robot manipulators: nonlinearand adaptive approaches. IEEE Trans. Autom. Control 44, 357–366 (1999)

    Article  MATH  Google Scholar 

  19. Singh, U.P., Jain, S.: Optimization of neural network for nonlinear discrete time system using modified quaternion firefly algorithm: case study of indian currency exchange rate prediction. Soft Comput. 22(8), 2667–2681 (2017). https://doi.org/10.1007/s00500-017-2522-x

    Article  Google Scholar 

  20. Rivals, I., Personnaz, L.: Nonlinear internal model control usingneural networks application to processes with delay and designissues. IEEE Trans. Neural Netw. 11, 80–90 (2000)

    Article  Google Scholar 

  21. KenallaKopulas, I., Kokotovic, P.V., Morse, A.S.: Systematicdesign of adaptive controller for feedback linearizable system. IEEE Trans. Autom. Control 36, 1241–1253 (1991)

    Article  Google Scholar 

  22. Wang, N., Su, S., Han, M., Chen, W.: Backpropagating constraints-based trajectory tracking control of a quadrotor with constrained actuator dynamics and complex unknowns. IEEE Trans. Syst. Man Cybern. Syst. (2018). https://doi.org/10.1109/tsmc.2018.2834515

    Google Scholar 

  23. Wang, N., Sun, J., Han, M., Zheng, Z., Er, M.J.: Adaptive approximation-based regulation control for a class of uncertain nonlinear systems without feedback linearizability. IEEE Trans. Neural Netw. Learn. Syst. 29(8), 3747–3760 (2018). https://doi.org/10.1109/TNNLS.2017.2738918

    Article  MathSciNet  Google Scholar 

  24. Kokotovic, P.V.: The joy feedback: nonlinear and adaptive. IEEE Control Syst. Mag. 12, 7–17 (1992)

    Article  Google Scholar 

  25. Elmali, H., Olgac, N.: Robust output tracking control of nonlinearMIMO system via sliding mode technique. Automatica 28, 145–151 (1992)

    Article  MathSciNet  Google Scholar 

  26. Sadati, N., Ghadami, R.: Adaptive multi-model sliding modecontrol of robotic manipulators using soft computing. Neurocomputing 17, 2702–2710 (2008)

    Article  Google Scholar 

  27. Singh, U.P., Jain, S., Tiwari, A.K., Singh, R.K.: Gradient evolution based counter propagation network for approximation of noncanonical system. Soft Comput. (2018) https://doi.org/10.1007/s00500-018-3160-7

  28. Li, Z.J., Ding, L., Gao, H., Duan, G.R., Su, C.Y.: Trilateral teleoperationof adaptive fuzzy force/motion control for nonlinear teleoperatorswith communication random delays. IEEE Trans. Fuzzy Syst. 21(4), 610–624 (2013)

    Article  Google Scholar 

  29. Chen, W.S., Wen, C.Y., Hua, S.Y., Sun, C.Y.: Distributedcooperative adaptive identification and control for a group of continuoustimesystems with a cooperative PE condition via consensus. IEEE Trans. Autom. Control 59(1), 91–106 (2014)

    Article  MATH  Google Scholar 

  30. Li, Z.J., Su, C.Y.: Neural-adaptive control of single-master–multiple-slaves teleoperation for coordinated multiple mobile manipulatorswith time-varying communication delays and input uncertainties. IEEE Trans. Neural Netw. Learn. Syst. 24(9), 1400–1413 (2013)

    Article  Google Scholar 

  31. Li, H.Y., Yu, J.Y., Liu, H.H., Hilton, C.: Adaptive sliding modecontrol for nonlinear active suspension vehicle systems using T–S fuzzyapproach. IEEE Trans. Indus. Electron. 60(8), 3328–3338 (2013)

    Article  Google Scholar 

  32. Škrjanc, I., Matko, D.: Predictive functional control based on fuzzymodel for heat-exchanger pilot plant. IEEE Trans. Fuzzy Syst. 8(6), 705–712 (2000)

    Article  Google Scholar 

  33. Zhang, H.G., Cai, L.L.: Decentralized nonlinear adaptive control ofan HVAC system. IEEE Trans. Syst. Man Cybern. Part C: Appl. Rev. 32(4), 493–498 (2002)

    Article  Google Scholar 

  34. He, W., Zhang, S., Ge, S.S.: Adaptive control of a flexible cranesystem with the boundary output constraint. IEEE Trans. Ind. Electron. 61(8), 4126–4133 (2014)

    Article  Google Scholar 

  35. Wang, N., Su, S., Yin, J., Zheng, Z., Er, M.J.: Global asymptotic model-free trajectory-independent tracking control of an uncertain marine vehicle: an adaptive universe-based fuzzy control approach. IEEE Trans. Fuzzy Syst. 26(3), 1613–1625 (2018). https://doi.org/10.1109/TFUZZ.2017.2737405

    Article  Google Scholar 

  36. Wang, N., Sun, J.C., Meng, E.J., Liu, Y.C.: A novel extreme learning control framework of unmanned surface vehicles. IEEE Trans. Cybern. 46(5), 1106–1117 (2016)

    Article  Google Scholar 

  37. Wang, N., Lv, S., Zhang, W., Liu, Z., Er, M.J.: Finite-time observer based accurate tracking control of a marine vehicle with complex unknowns. Ocean Eng. 145, 406–415 (2017). https://doi.org/10.1016/j.oceaneng.2017.09.062

    Article  Google Scholar 

  38. Li, Z.J., Xiao, H.Z., Yang, C.G., Zhao, Y.W.: Model predictive control of nonholonomic chained systems using general projection neuralnetworks optimization. IEEE Trans. Syst. Man Cybern. Syst. 45(10), 1313–1321 (2015)

    Article  Google Scholar 

  39. Ibrir, S., Xie, W.F., Su, C.Y.: Adaptive tracking of nonlinearsystems with non-symmetric dead-zone input. Automatica 43(3), 522–530 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  40. Wang, N., Qian, C., Sun, J.C., Liu, Y.C.: Adaptive robust finite-time trajectory tracking control of fully actuated marine surface vehicles. IEEE Trans. Control Syst. Technol. 24(4), 1454–1462 (2016)

    Article  Google Scholar 

  41. Wang, N., Meng, E.J., Sun, J.C., Liu, Y.C.: Adaptive robust online constructive fuzzy control of a complex surface vehicle system. IEEE Trans. Cybern. 46(7), 1511–1523 (2016)

    Article  Google Scholar 

  42. Wang, X.S., Su, C.Y., Hong, H.: Robust adaptive control of a classof nonlinear systems with unknown dead-zone. Automatica 40(3), 407–413 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  43. Na, J., Ren, X.M., Herrmann, G., Qiao, Z.: Adaptive neural dynamicsurface control for servo systems with unknown dead-zone. Control Eng. Pract. 19(11), 1328–1343 (2011)

    Article  Google Scholar 

  44. Selmic, R.R., Lewis, F.L.: Dead-zone compensation in motioncontrol systems using neural networks. IEEE Trans. Autom. Control 45(4), 602–613 (2000)

    Article  MATH  Google Scholar 

  45. Xu, B., Yang, C., Shi, Z.: Reinforcement learning output feedback NN controlusing deterministic learning technique. IEEE Trans. Neural Netw. Learn. Syst. 25(3), 635–641 (2014)

    Article  Google Scholar 

  46. Li, D.J.: Neural network control for a class of continuous stirredtank reactor process with dead-zone input. Neurocomputing 131, 453–459 (2014)

    Article  Google Scholar 

  47. Wang, N., Meng, E.J.: Direct adaptive fuzzy tracking control of marine vehicles with fully unknown parametric dynamics and uncertainties. IEEE Trans. Control Syst. Technol. 24(5), 1845–1852 (2016)

    Article  Google Scholar 

  48. Tong, S.C., Li, Y.M.: Adaptive fuzzy output feedback trackingbackstepping control of strict-feedback nonlinear systems with unknowndead zones. IEEE Trans. Fuzzy Syst. 20(1), 168–180 (2012)

    Article  Google Scholar 

  49. Tong, S.C., Li, Y.M.: Adaptive fuzzy output feedback control ofMIMO nonlinear systems with unknown dead-zone inputs. IEEE Trans. Fuzzy Syst. 21(3), 134–146 (2013)

    Article  Google Scholar 

  50. Liu, Y.J., Tong, S.: Adaptive fuzzy control for a class of unknown nonlinear dynamical systems. Fuzzy Sets Syst. 263, 49–70 (2015). https://doi.org/10.1016/j.fss.2014.08.008

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Shri Mata Vaishno Devi University, Kakryal, Kattra, J&K, 182320, India

    Uday Pratap Singh & Sanjeev Jain

  2. Madhav Institute of Technology and Science, Gwalior, M.P., 474005, India

    Rajendra Kumar Gupta & Akhilesh Tiwari

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  1. Uday Pratap Singh
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  2. Sanjeev Jain
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  4. Akhilesh Tiwari
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Correspondence to Uday Pratap Singh.

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Singh, U.P., Jain, S., Gupta, R.K. et al. AFMBC for a Class of Nonlinear Discrete-Time Systems with Dead Zone. Int. J. Fuzzy Syst. 21, 1073–1084 (2019). https://doi.org/10.1007/s40815-019-00621-1

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  • DOI: https://doi.org/10.1007/s40815-019-00621-1

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