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Adaptive neural DSC for stochastic nonlinear constrained systems under arbitrary switchings

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Abstract

This paper proposes an adaptive neural dynamic surface control scheme for a class of strict-feedback stochastic nonlinear systems with guaranteed predefined performance under arbitrary switchings. First, by utilizing the prescribed performance control, the prescribed tracking control performance can be ensured with unknown initial errors, and input constraints are achieved by employing a continuous differentiable asymmetric saturation model. Second, RBF neural networks are used to handle unknown nonlinear functions and stochastic disturbances, and the dynamic surface control technique is used to avoid the problem of ‘explosion of complexity’ in control design. At last, by combining the common Lyapunov function method with the backstepping design principle, a common adaptive neural controller is constructed. The designed controller overcomes the problem of the over-parameterization and further alleviates the computational burden. Under the proposed common adaptive controller, all the signals in the closed-loop system are four-moment (or two-moment) semi-globally uniformly ultimately bounded, and the prescribed transient and steady tracking control performance are guaranteed under arbitrary switchings. The arbitrary switching behaviors among two and three subsystems are performed to demonstrate and verify the effectiveness of the proposed method.

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References

  1. Bechlioulis, C.P., Doulgeri, Z., Rovithakis, G.A.: Neuro-adaptive force/position control with prescribed performance and guaranteed contact maintenance. IEEE Trans. Neural Netw. 21(12), 1857–1868 (2010)

    Article  Google Scholar 

  2. Bechlioulis, C.P., Rovithakis, G.A.: Robust adaptive control of feedback linearizable mimo nonlinear systems with prescribed performance. IEEE Trans. Autom. Control 53(9), 2090–2099 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  3. Dai, S.L., Wang, M., Wang, C.: Neural learning control of marine surface vessels with guaranteed transient tracking performance. IEEE Trans. Ind. Electron. 63(3), 1717–1727 (2016)

    Article  Google Scholar 

  4. Deng, H., Krstić, M.: Stochastic nonlinear stabilization—I: a backstepping design. Syst. Control Lett. 32(3), 143–150 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  5. Deng, H., Krstic, M.: Output-feedback stochastic nonlinear stabilization. IEEE Trans. Autom. Control 44(2), 328–333 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  6. Deng, H., Krstic, M., Williams, R.J.: Stabilization of stochastic nonlinear systems driven by noise of unknown covariance. IEEE Trans. Autom. Control 46(8), 1237–1253 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  7. Gao, H., Zhang, T., Xia, X.: Adaptive neural control of stochastic nonlinear systems with unmodeled dynamics and time-varying state delays. J. Frankl. Inst. 351(6), 3182–3199 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  8. Han, S.I., Lee, J.M.: Partial tracking error constrained fuzzy dynamic surface control for a strict feedback nonlinear dynamic system. IEEE Trans. Fuzzy Syst. 22(5), 1049–1061 (2014)

    Article  Google Scholar 

  9. He, W., Chen, Y., Yin, Z.: Adaptive neural network control of an uncertain robot with full-state constraints. IEEE Trans. Cybern. 46(3), 620–629 (2016)

    Article  Google Scholar 

  10. He, W., Dong, Y.: Adaptive fuzzy neural network control for a constrained robot using impedance learning. IEEE Trans. Neural Netw. Learn. Syst. (2017). doi:10.1109/TNNLS.2017.2665581

    Google Scholar 

  11. He, W., Dong, Y., Sun, C.: Adaptive neural impedance control of a robotic manipulator with input saturation. IEEE Trans. Syst. Man Cybern. Syst. 46(3), 334–344 (2016)

    Article  Google Scholar 

  12. He, W., Ge, S.S.: Cooperative control of a nonuniform gantry crane with constrained tension. Automatica 66, 146–154 (2016)

    Article  MATH  MathSciNet  Google Scholar 

  13. He, W., Ouyang, Y., Hong, J.: Vibration control of a flexible robotic manipulator in the presence of input deadzone. IEEE Trans. Ind. Inf. 13(1), 48–59 (2017)

    Article  Google Scholar 

  14. Kostarigka, A.K., Doulgeri, Z., Rovithakis, G.A.: Prescribed performance tracking for flexible joint robots with unknown dynamics and variable elasticity. Automatica 49(5), 1137–1147 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  15. Li, Y., Tong, S.: Prescribed performance adaptive fuzzy output-feedback dynamic surface control for nonlinear large-scale systems with time delays. Inf. Sci. 292, 125–142 (2015)

    Article  MATH  MathSciNet  Google Scholar 

  16. Li, Y., Tong, S.: Adaptive fuzzy output-feedback stabilization control for a class of switched nonstrict-feedback nonlinear systems. IEEE Trans. Cybern. 47(4), 1007–1016 (2017)

    Article  Google Scholar 

  17. Li, Y., Tong, S.: Command-filtered-based fuzzy adaptive control design for mimo-switched nonstrict-feedback nonlinear systems. IEEE Trans. Fuzzy Syst. 25(3), 668–681 (2017)

    Article  Google Scholar 

  18. Li, Y., Tong, S., Li, T.: Observer-based adaptive fuzzy tracking control of mimo stochastic nonlinear systems with unknown control directions and unknown dead zones. IEEE Trans. Fuzzy Syst. 23(4), 1228–1241 (2015)

    Article  Google Scholar 

  19. Li, Y., Tong, S., Li, T.: Hybrid fuzzy adaptive output feedback control design for uncertain mimo nonlinear systems with time-varying delays and input saturation. IEEE Trans. Fuzzy Syst. 24(4), 841–853 (2016)

    Article  Google Scholar 

  20. Li, Y., Tong, S., Li, T., Jing, X.: Adaptive fuzzy control of uncertain stochastic nonlinear systems with unknown dead zone using small-gain approach. Fuzzy Sets Syst. 235, 1–24 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  21. Li, Y., Tong, S., Liu, L., Feng, G.: Adaptive output-feedback control design with prescribed performance for switched nonlinear systems. Automatica 80, 225–231 (2017)

    Article  MATH  MathSciNet  Google Scholar 

  22. Li, Z., Li, T., Miao, B., Chen, C.P.: Adaptive nn control for a class of stochastic nonlinear systems with unmodeled dynamics using dsc technique. Neurocomputing 149, 142–150 (2015)

    Article  Google Scholar 

  23. Liu, L., Wang, Z., Zhang, H.: Adaptive dynamic surface error constrained control for mimo systems with backlash-like hysteresis via prediction error technique. Nonlinear Dyn. 84(4), 1989–2002 (2016)

  24. Liu, Z., Chen, B., Lin, C.: Adaptive neural backstepping for a class of switched nonlinear system without strict-feedback form. IEEE Trans. Syst. Man Cybern. Syst. 47(7), 1315–1320 (2017)

  25. Ma, J., Ge, S.S., Zheng, Z., Hu, D.: Adaptive nn control of a class of nonlinear systems with asymmetric saturation actuators. IEEE Trans. Neural Netw. Learn. Syst. 26(7), 1532–1538 (2015)

    Article  MathSciNet  Google Scholar 

  26. Sanner, R.M., Slotine, J.J.: Gaussian networks for direct adaptive control. IEEE Trans. Neural Netw. 3(6), 837–863 (1992)

    Article  Google Scholar 

  27. Sui, S., Li, Y., Tong, S.: Observer-based adaptive fuzzy control for switched stochastic nonlinear systems with partial tracking errors constrained. IEEE Trans. Syst. Man Cybern. Syst. 46(12), 1605–1617 (2016)

  28. Swaroop, D., Hedrick, J.K., Yip, P.P., Gerdes, J.C.: Dynamic surface control for a class of nonlinear systems. IEEE Trans. Autom. Control 45(10), 1893–1899 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  29. Theodorakopoulos, A., Rovithakis, G.A.: A simplified adaptive neural network prescribed performance controller for uncertain mimo feedback linearizable systems. IEEE Trans. Neural Netw. Learn. Syst. 26(3), 589–600 (2015)

    Article  MathSciNet  Google Scholar 

  30. Tong, S., Li, Y.: Adaptive fuzzy output feedback control of mimo nonlinear systems with unknown dead-zone inputs. IEEE Trans. Fuzzy Syst. 21(1), 134–146 (2013)

    Article  Google Scholar 

  31. Tong, S., Li, Y., Feng, G., Li, T.: Observer-based adaptive fuzzy backstepping dynamic surface control for a class of non-linear systems with unknown time delays. IET Control Theory Appl. 5(12), 1426–1438 (2011)

    Article  MathSciNet  Google Scholar 

  32. Tong, S., Sui, S., Li, Y.: Observed-based adaptive fuzzy tracking control for switched nonlinear systems with dead-zone. IEEE Trans. Cybern. 45(12), 2816–2826 (2015)

    Article  Google Scholar 

  33. Wang, F., Chen, B., Zhang, Z., Lin, C.: Adaptive tracking control of uncertain switched stochastic nonlinear systems. Nonlinear Dyn. 84(4), 2099–2109 (2016)

  34. Wang, H., Chen, B., Lin, C.: Adaptive neural control for strict-feedback stochastic nonlinear systems with time-delay. Neurocomputing 77(1), 267–274 (2012)

    Article  Google Scholar 

  35. Wang, H., Chen, B., Liu, X., Liu, K., Lin, C.: Adaptive neural tracking control for stochastic nonlinear strict-feedback systems with unknown input saturation. Inf. Sci. 269, 300–315 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  36. 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(6), 1681–1692 (2011)

    Article  Google Scholar 

  37. Wang, M., Wang, C., Shi, P., Liu, X.: Dynamic learning from neural control for strict-feedback systems with guaranteed predefined performance. IEEE Trans. Neural Netw. Learn. Syst. 27(12), 2564–2576 (2016)

    Article  MathSciNet  Google Scholar 

  38. Wang, M., Yang, A.: Dynamic learning from adaptive neural control of robot manipulators with prescribed performance. IEEE Trans. Syst. Man Cybern. Syst. (2017). doi:10.1109/TSMC.2016.2645942

    Google Scholar 

  39. Wang, Z., Burnham, K.J.: Robust filtering for a class of stochastic uncertain nonlinear time-delay systems via exponential state estimation. IEEE Trans. Signal Process. 49(4), 794–804 (2001)

  40. Yin, S., Yu, H., Shahnazi, R., Haghani, A.: Fuzzy adaptive tracking control of constrained nonlinear switched stochastic pure-feedback systems. IEEE Trans. Cybern. 47(3), 579–588 (2017)

  41. Yoo, S.J., Park, J.B.: Neural-network-based decentralized adaptive control for a class of large-scale nonlinear systems with unknown time-varying delays. IEEE Trans. Syst. Man Cybern. Part B (Cybern.) 39(5), 1316–1323 (2009)

    Article  Google Scholar 

  42. Yu, Z., Du, H.: Adaptive neural control for uncertain stochastic nonlinear strict-feedback systems with time-varying delays: a Razumikhin functional method. Neurocomputing 74(12), 2072–2082 (2011)

    Article  Google Scholar 

  43. Yu, Z., Li, S., Li, F.: Observer-based adaptive neural dynamic surface control for a class of non-strict-feedback stochastic nonlinear systems. Int. J. Syst. Sci. 47(1), 194–208 (2016)

    Article  MATH  MathSciNet  Google Scholar 

  44. Zhai, D., Xi, C., An, L., Dong, J., Zhang, Q.: Prescribed performance switched adaptive dynamic surface control of switched nonlinear systems with average dwell time. IEEE Trans. Syst. Man Cybern. Syst. 47(7), 1257–1269 (2017)

  45. Zhang, L., Sui, S., Li, Y., Tong, S.: Adaptive fuzzy output feedback tracking control with prescribed performance for chemical reactor of mimo nonlinear systems. Nonlinear Dyn. 80(1–2), 945–957 (2015)

    Article  MATH  Google Scholar 

  46. Zhang, L., Yang, G.H.: Dynamic surface error constrained adaptive fuzzy output feedback control for switched nonlinear systems with unknown dead zone. Neurocomputing 199, 128–136 (2016)

    Article  Google Scholar 

  47. Zhao, X., Shi, P., Zheng, X., Zhang, L.: Adaptive tracking control for switched stochastic nonlinear systems with unknown actuator dead-zone. Automatica 60, 193–200 (2015)

    Article  MATH  MathSciNet  Google Scholar 

  48. Zhao, X., Zheng, X., Niu, B., Liu, L.: Adaptive tracking control for a class of uncertain switched nonlinear systems. Automatica 52, 185–191 (2015)

    Article  MATH  MathSciNet  Google Scholar 

  49. Zhou, Q., Shi, P., Tian, Y., Wang, M.: Approximation-based adaptive tracking control for mimo nonlinear systems with input saturation. IEEE Trans. Cybern. 45(10), 2119–2128 (2015)

    Article  Google Scholar 

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

    Article  Google Scholar 

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Acknowledgements

This work was supported in part by National Science Fund for Distinguished Young Scholars of China (Grant No. 61225014), National R&D Program for Major Research Instruments (Grant No. 61527811), National Natural Science Foundation of China (Grant Nos. 61374119, 61473121).

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  1. School of Automation Science and Engineering, South China University of Technology, Guangzhou, 510640, Guangdong, China

    Wenjie Si & Xunde Dong

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  1. Wenjie Si
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  2. Xunde Dong
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Correspondence to Wenjie Si.

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Si, W., Dong, X. Adaptive neural DSC for stochastic nonlinear constrained systems under arbitrary switchings. Nonlinear Dyn 90, 2531–2544 (2017). https://doi.org/10.1007/s11071-017-3821-6

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