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Adaptive NN finite-time tracking control of output constrained nonlinear system with input saturation

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Abstract

This paper considers the finite-time tracking control problem for the strict-feedback nonlinear continuous systems involving input saturation and output constraints. A sequence of desired and auxiliary virtual control signals and real control input is designed to derive a representation of the system estimation errors and stabilize the system. The proposed approach is further developed via a finite-time stability theory, barrier Lyapunov function, and neural network approximation scheme to achieve an expected performance of the considered system. According to the proposed scheme, we solve the finite-time tracking control problem of the nonlinear systems with input saturation. Then, a theorem is provided to address that all the signals and system states are bounded, and the system output is driven to track the reference signal in a finite time to a small neighborhood of zero and remains in the predefined compact sets. The effectiveness of the proposed scheme is confirmed via two simulation examples.

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References

  1. Chen, B., Liu, X., Tong, S.: Adaptive fuzzy output tracking control of MIMO nonlinear uncertain systems. IEEE Trans. Fuzzy Syst. 15(2), 287–300 (2007)

    Article  Google Scholar 

  2. Li, H., Wu, C., Shi, P., Gao, Y.: Control of nonlinear networked systems with packet dropouts: interval type-2 fuzzy model-based approach. IEEE Trans. Cybern. 45(11), 2378–2389 (2015)

    Article  Google Scholar 

  3. Li, H., Wang, J., Du, H., Karimi, H.R.: Adaptive sliding mode control for Takagi-Sugeno fuzzy systems and its applications. IEEE Trans. Fuzzy Syst. (2017). https://doi.org/10.1109/TFUZZ.2017.2686357

    Google Scholar 

  4. Wang, N., Sun, J.C., Meng, J.E.: Tracking-error-based universal adaptive fuzzy control for output tracking of nonlinear systems with completely unknown dynamics. IEEE Trans. Fuzzy Syst. PP(99), 1–1 (2017)

    Google Scholar 

  5. Wang, M., Wang, C.: Learning from adaptive neural dynamic surface control of strict-feedback systems. IEEE Trans. Neural Netw. Learn. Syst. 26(6), 1247–1259 (2015)

    Article  MathSciNet  Google Scholar 

  6. Liu, Z., Wang, F., Zhang, Y.: Adaptive visual tracking control for manipulator with actuator fuzzy dead-zone constraint and unmodeled dynamic. IEEE Trans. Syst. Man Cybern. Syst. 45(10), 1301–1312 (2015)

    Article  Google Scholar 

  7. Liu, Y., Tong, S.: Adaptive fuzzy control for a class of nonlinear discrete-time systems with backlash. IEEE Trans. Fuzzy Syst. 22(5), 1359–1365 (2014)

    Article  Google Scholar 

  8. Wang, N., Sun, J.C., 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. PP(99), 1–14 (2017)

    Google Scholar 

  9. Boiko, I., Fridman, L., Iriarte, R.: Analysis of chattering in continuous sliding mode control. In: Proceedings of the American Control Conference, 2005, vol. 4, pp. 2439–2444. IEEE (2005)

  10. Li, H., Wang, J., Lam, H.-K., Zhou, Q., Du, H.: Adaptive sliding mode control for interval type-2 fuzzy systems. IEEE Trans. Syst. Man Cybern. Syst. 46(12), 1654–1663 (2016)

    Article  Google Scholar 

  11. Li, H., Wang, J., Shi, P.: Output-feedback based sliding mode control for fuzzy systems with actuator saturation. IEEE Trans. Fuzzy Syst. 24(6), 1282–1293 (2016)

    Article  Google Scholar 

  12. Utkin, V.I.: Sliding mode control design principles and applications to electric drives. IEEE Trans. Industr. Electron. 40(1), 23–36 (1993)

    Article  Google Scholar 

  13. Liu, Y., Tong, S.: Adaptive fuzzy identification and control for a class of nonlinear pure-feedback MIMO systems with unknown dead zones. IEEE Trans. Fuzzy Syst. 23(5), 1387–1398 (2015)

    Article  Google Scholar 

  14. Li, Y., Tong, S.: Adaptive fuzzy output-feedback control of pure-feedback uncertain nonlinear systems with unknown dead zone. IEEE Trans. Fuzzy Syst. 22(5), 1341–1347 (2014)

    Article  Google Scholar 

  15. Li, Y., Tong, S., Li, T.: Adaptive fuzzy output feedback dynamic surface control of interconnected nonlinear pure-feedback systems. IEEE Trans. Cybern. 45(1), 138–149 (2015)

    Article  Google Scholar 

  16. Su, C.Y., Stepanenko, Y.: Adaptive control of a class of nonlinear systems with fuzzy logic. IEEE Trans. Fuzzy Syst. 2(4), 285–294 (1994)

    Article  Google Scholar 

  17. Tsay, D.L., Chung, H.Y., Lee, C.J.: The adaptive control of nonlinear systems using the Sugeno-type of fuzzy logic. IEEE Trans. Fuzzy Syst. 7(2), 225–229 (1999)

    Article  Google Scholar 

  18. Wang, L.X.: Stable adaptive fuzzy control of nonlinear systems. In: Proceedings of the IEEE Conference on Decision and Control, 1992, vol. 3, pp. 2511–2516. IEEE (2002)

  19. Tong, S., Zhang, L., Li, Y.: Observed-based adaptive fuzzy decentralized tracking control for switched uncertain nonlinear large-scale systems with dead zones. IEEE Trans. Syst. Man Cybern. Syst. 46(1), 37–47 (2015)

    Article  Google Scholar 

  20. Wang, L., Basin, M., Li, H., Lu, R.: Observer-based composite adaptive fuzzy control for nonstrict-feedback systems with actuator failures. IEEE Trans. Fuzzy Syst. (2017). https://doi.org/10.1109/TFUZZ.2017.2774185

    Google Scholar 

  21. Liang, H., Li, H., Yu, Z., Li, P., Wang, W.: Cooperative robust containment control for general discrete-time multi-agent systems with external disturbance. IET Control Theory Appl. 11(12), 1928–1937 (2017)

    Article  MathSciNet  Google Scholar 

  22. 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. 28(9), 2156–2167 (2016)

    Google Scholar 

  23. Gong, J.Q., Yao, B.: Neural network adaptive robust control of nonlinear systems in semi-strict feedback form. Automatica 37(8), 1149–1160 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  24. Johnson, E.N., Calise, A.J.: Neural network adaptive control of systems with input saturation. In: Proceedings of the American Control Conference, 2001, vol. 5, pp. 3527–3532. IEEE (2001)

  25. Wang, D., Huang, J.: Adaptive neural network control for a class of uncertain nonlinear systems in pure-feedback form. Automatica 38(8), 1365–1372 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  26. Hayakawa, T., Haddad, W.M., Hovakimyan, N.: Neural network adaptive control for a class of nonlinear uncertain dynamical systems with asymptotic stability guarantees. IEEE Trans. Neural Netw. 19(1), 80 (2008)

    Article  Google Scholar 

  27. Deng, F., Guo, S., Zhou, R., Chen, J.: Sensor multifault diagnosis with improved support vector machines. IEEE Trans. Autom. Sci. Eng. PP(99), 1–11 (2015)

    Google Scholar 

  28. Deng, F., Guan, S., Yue, X., Gu, X., Chen, J., Lv, J., Li, J.: Energy-based sound source localization with low power consumption in wireless sensor networks. IEEE Trans. Ind. Electron. PP(99), 1–1 (2017)

    Google Scholar 

  29. Chen, C.P., Wen, G., Liu, Y., Wang, F.: Adaptive consensus control for a class of nonlinear multiagent time-delay systems using neural networks. IEEE Trans. Neural Netw. Learn. Syst. 25(6), 1217–1226 (2014)

    Article  Google Scholar 

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

    Article  Google Scholar 

  31. Park, J.H., Park, C., Kwon, O., Lee, S.-M.: A new stability criterion for bidirectional associative memory neural networks of neutral-type. Appl. Math. Comput. 199(2), 716–722 (2008)

    MathSciNet  MATH  Google Scholar 

  32. Zhang, T., Ge, S.S., Hang, C.C.: Adaptive neural network control for strict-feedback nonlinear systems using backstepping design. Automatica 36(12), 1835–1846 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  33. Kwon, O., Park, J.H., Lee, S., Cha, E.: New augmented Lyapunov–Krasovskii functional approach to stability analysis of neural networks with time-varying delays. Nonlinear Dyn. 76(1), 221–236 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  34. Shen, H., Park, J.H., Wu, Z.-G.: Finite-time synchronization control for uncertain Markov jump neural networks with input constraints. Nonlinear Dyn. 77(4), 1709–1720 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  35. Li, T., Li, Z., Wang, D., Chen, C.L.P.: Output-feedback adaptive neural control for stochastic nonlinear time-varying delay systems with unknown control directions. IEEE Trans. Neural Netw. Learn. Syst. 26(6), 1188–1201 (2015)

    Article  MathSciNet  Google Scholar 

  36. Li, Z., Li, T., Feng, G.: Adaptive neural control for a class of stochastic nonlinear time-delay systems with unknown dead zone using dynamic surface technique. Int. J. Robust Nonlinear Control 26(4), 759–781 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  37. Zhou, Q., Li, H., Wang, L., Lu, R.: Prescribed performance observer-based adaptive fuzzy control for nonstrict-feedback stochastic nonlinear systems, IEEE Trans. Fuzzy Syst Man Cybern Syst. (2017). https://doi.org/10.1109/TSMC.2017.2738155

    Google Scholar 

  38. Wang, B., Cheng, J., Al-Barakati, A., Abdullah, H.M.: A mismatched membership function approach to sampled-data stabilization for T-S fuzzy systems with time-varying delayed signals. Sig. Process. 140, 161–170 (2017)

    Article  Google Scholar 

  39. Cheng, J., Park, J.H., Zhang, L., Zhu, Y.: An asynchronous operation approach to event-triggered control for fuzzy Markovian jump systems with general switching policies. IEEE Trans. Fuzzy Syst. 99, 1–1 (2016)

    Google Scholar 

  40. Cheng, J., Park, J.H., Karimi, H.R., Shen, H.: A flexible terminal approach to sampled-data exponentially synchronization of Markovian neural networks with time-varying delayed signals. IEEE Trans. Cybern. 99, 1–13 (2017)

    Article  Google Scholar 

  41. Lee, T.H., Ju, H.P.: Improved criteria for sampled-data synchronization of chaotic Lure systems using two new approaches. Nonlinear Anal. Hybrid Syst. 24, 132–145 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  42. Lee, T.H., Wu, Z., Ju, H.P.: Synchronization of a complex dynamical network with coupling time-varying delays via sampled-data control. Appl. Math. Comput. 219(3), 1354–1366 (2012)

    MathSciNet  MATH  Google Scholar 

  43. Li, T.H., Ju, H.P., Xu, S.: Relaxed conditions for stability of time-varying delay systems. Automatica 75, 11–15 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  44. Tee, K.P., Ge, S.S., Tay, E.H.: Barrier Lyapunov functions for the control of output-constrained nonlinear systems. Automatica 45(4), 918–927 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  45. Tee, K.P., Ge, S.S., Li, H., Ren, B.: Control of nonlinear systems with time-varying output constraints. In: IEEE International Conference on Control and Automation, pp. 2511–2516. IEEE (2010)

  46. Li, T., Li, R., Li, J.: Decentralized adaptive neural control of nonlinear interconnected large-scale systems with unknown time delays and input saturation. Neurocomputing 74(14C15), 2277–2283 (2011)

    Article  Google Scholar 

  47. Li, Y., Tong, S., Li, T.: Composite adaptive fuzzy output feedback control design for uncertain nonlinear strict-feedback systems with input saturation. IEEE Trans. Cybern. 45(10), 2299 (2015)

    Article  Google Scholar 

  48. 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 

  49. Mou, C., Gang, T., Jiang, B.: Dynamic surface control using neural networks for a class of uncertain nonlinear systems with input saturation. IEEE Trans. Neural Netw. Learn. Syst. 26(9), 2086 (2015)

    Article  MathSciNet  Google Scholar 

  50. Wen, C., Zhou, J., Liu, Z., Su, H.: Robust adaptive control of uncertain nonlinear systems in the presence of input saturation and external disturbance. IEEE Trans. Autom. Control 56(7), 1672–1678 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  51. Hu, Q., Jiang, B., Zhang, Y.: Observer-based output feedback attitude stabilization for spacecraft with finite-time convergence. IEEE Trans. Control Syst. Technol. PP(99), 1–9 (2017)

    Google Scholar 

  52. Hu, Q., Tan, X., Akella, M.R.: Finite-time fault-tolerant spacecraft attitude control with torque saturation. J. Guid. Control Dyn. 40(10), 1–14 (2017)

    Article  Google Scholar 

  53. Fu, J., Chai, T., Chai, T.: Global Finite-Time Stabilization of a Class of Switched Nonlinear Systems with the Powers of Positive Odd Rational Numbers. Pergamon Press Inc., New York (2015)

    MATH  Google Scholar 

  54. Wang, F., Chen, B., Lin, C., Zhang, J.: Adaptive neural network finite-time output feedback control of quantized nonlinear systems. IEEE Trans. Cybern. PP(99), 1–10 (2017)

    Google Scholar 

  55. Yu, S., Yu, X., Stonier, R.: Continuous finite-time control for robotic manipulators with terminal sliding modes. Automatica 41(11), 1957–1964 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  56. Wang, H., Chen, B., Liu, X., Liu, K., Lin, C.: Robust adaptive fuzzy tracking control for pure-feedback stochastic nonlinear systems with input constraints. IEEE Trans. Cybern. 43(6), 2093–2104 (2013)

    Article  Google Scholar 

  57. Zhu, Z., Xia, Y., Fu, M.: Attitude stabilization of rigid spacecraft with finite-time convergence. Int. J. Robust Nonlinear Control 21(6), 686–702 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  58. Qian, C., Lin, W.: Non-Lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization. Syst. Control Lett. 42(3), 185–200 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  59. 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 (2013)

    Article  Google Scholar 

  60. Chen, B., Liu, X., Liu, K., Lin, C.: Direct adaptive fuzzy control of nonlinear strict-feedback systems. Automatica 45(6), 1530–1535 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  61. Liu, Y.J., Tong, S.: Barrier Lyapunov functions for Nussbaum gain adaptive control of full state constrained nonlinear systems. Automatica 76, 143–152 (2017)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

This work is partially supported by the National Natural Science Foundation of China (61703051) and the Department of Education of Liaoning Province (LZ2017001).

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Authors and Affiliations

  1. School of Mathematics and Physics, Bohai University, Jinzhou, 121013, Liaoning, China

    Shiyi Zhao & Peihao Du

  2. College of Engineering, Bohai University, Jinzhou, 121013, Liaoning, China

    Hongjing Liang

  3. School of Biomedical Engineering, Health Science Center, Shenzhen University, Shenzhen, 518060, Guangdong, China

    Suwen Qi

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  1. Shiyi Zhao
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  2. Hongjing Liang
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  3. Peihao Du
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  4. Suwen Qi
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Correspondence to Hongjing Liang or Suwen Qi.

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Zhao, S., Liang, H., Du, P. et al. Adaptive NN finite-time tracking control of output constrained nonlinear system with input saturation. Nonlinear Dyn 92, 1845–1856 (2018). https://doi.org/10.1007/s11071-018-4167-4

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