Abstract
This paper is concerned with the global regulation via output feedback for the time-delay nonlinear systems with unknown continuous output function and unknown growth rate. Different from the existing literature, the output is perturbed by an unknown continuous function, and nonlinearities are upper bounded by unmeasured states multiplying an unknown constant and a polynomial of the output. A unified methodology is proposed to construct a new type of full-order observer with a dynamic gain by filtering unknown nonlinearities and time-varying delay. In light of a delicate scaling transformation, a combined system is derived to perform the one-step assignment of the controller instead of traditional backstepping recursive design. The stability analysis is completed by reductio and another scaling transformation with the upper bound of the dynamic gain. The efficiency of the proposed control scheme is demonstrated by two simulation examples including a practical one.
Similar content being viewed by others
References
Krstić, M., Kanellakopoulos, I., Kokotović, P.: Nonlinear and Adaptive Design. Wiley, New York (1995)
Khalil, H.: Nonlinear systems. Prentice Hall, Upper Saddle River, NJ (2002)
Qian, C., Lin, W.: A continuous feedback approach to global strong stabilization of nonlinear systems. IEEE Trans. Autom. Control 46(7), 1061–1079 (2001)
Isidori, A.: Nonlinear Control Systems. Springer, Berlin (1995)
Lei, H., Lin, W.: Adaptive regulation of uncertain nonlinear systems by output feedback: a universal control approach. Syst. Control Lett. 56(7–8), 529–537 (2007)
Defoort, M., Floquet, T., Kokosy, A., Perruquetti, W.: A novel higher order sliding mode control scheme. Syst. Control Lett. 58(2), 102–108 (2009)
Wu, Y., Gao, F., Zhang, Z.: Saturated finite-time stabilization of uncertain nonholonomic systems in feedforward-like form and its application. Nonlinear Dyn. 84(3), 1609–1622 (2016)
Liu, L., Li, X., Wang, H., Niu, B.: Global asymptotic stabilization of stochastic feedforward nonlinear systems with input time-delay. Nonlinear Dyn. 83(3), 1503–1510 (2016)
Sun, Z., Wang, M.: Disturbance attenuation via double-domination approach for feedforward nonlinear system with unknown output function. Nonlinear Dyn. 96(4), 2523–2533 (2019)
Man, Y., Liu, Y.: Global output-feedback stabilization for a class of uncertain time-varying nonlinear systems. Syst. Control Lett. 90(4), 20–30 (2016)
Ding, S., Liu, L., Zheng, W.: Sliding mode direct yaw-moment control design for in-wheel electric vehicles. IEEE Trans. Autom. Control 64(8), 6752–6762 (2017)
Ding, S., Mei, K., Li, S.: A new second-order sliding mode and its application to nonlinear constrained systems. IEEE Trans. Autom. Control 64(6), 2545–2552 (2019)
Sun, Z., Zhang, C., Wang, Z.: Adaptive disturbance attenuation for generalized high-order uncertain nonlinear systems. Automatica 80, 102–109 (2017)
Sun, Z., Yun, M., Li, T.: A new approach to fast global finite-time stabilization of high-order nonlinear system. Automatica 91, 455–463 (2017)
Sun, Z., Shao, Y., Chen, C.: Fast finite-time stability and its application in adaptive control of high-order nonlinear system. Automatica 106, 339–348 (2019)
Meng, Q., Qian, C., Liu, R.: Dual-rate sampled-data stabilization for active suspension system of electric vehicle. Int. J. Robust Nonlinear Control 28(5), 1610–1623 (2018)
Sun, Z., Song, Z., Li, T., Yang, S.: Output feedback stabilization for high-order uncertain feedforward time-delay nonlinear systems. J. Frankl. Inst. 352(11), 5308–5326 (2015)
Zhang, X., Liu, L., Feng, G., Zhang, C.: Output feedback control of large-scale nonlinear time-delay systems in lower triangular form. Automatica 49(11), 3476–3483 (2013)
Zhai, J., Zha, W.: Global adaptive output feedback control for a class of nonlinear time-delay systems. ISA Trans. 53(1), 2–9 (2014)
Zhang, X., Lin, Y.: Adaptive output feedback control for a class of large-scale nonlinear time-delay systems. Automatica 52, 87–94 (2015)
Zhang, C., He, Y., Jiang, L., Wu, M.: An improved summation inequality to discrete-time systems with time-varying delay. Automatica 74(12), 10–15 (2016)
Zhang, X., Lin, W., Lin, Y.: Nonsmooth feedback control of time-delay nonlinear systems: a dynamic gain based approach. IEEE Trans. Autom. Control 62(1), 438–444 (2017)
Sun, Z., Zhang, D., Meng, Q., Chen, C.: Feedback stabilization of time-delay nonlinear systems with continuous time-varying output function. Int. J. Syst. Sci. 50(2), 244–255 (2019)
Sun, Z., Zhou, C., Chen, C., Meng, Q.: Fast finite-time adaptive stabilization of high-order uncertain nonlinear systems with output constraint and zero dynamics. Inf. Sci. 514(4), 571–586 (2020)
Liu, B., Xu, S., Park, J., Zhuang, G.: Reliable exponential \(H_{\infty }\) filtering for singular Markovian jump systems with time-varying delays and sensor failures. Int. J. Robust Nonlinear Control 28(14), 4230–4245 (2018)
Qian, C., Lin, W.: Output feedback control of a class of nonlinear systems: a nonseparation principle paradigm. IEEE Trans. Autom. Control 47(10), 1710–1715 (2002)
Zhang, X., Cheng, Z.: Global stabilization of a class of time-delay nonlinear systems. Int. J. Syst. Sci. 8(20), 461–468 (2005)
Li, F., Liu, Y.: Global stabilization via time-varying output-feedback for stochastic nonlinear systems with unknown growth rate. Syst. Control Lett. 77, 69–79 (2015)
Qian, C.: A homogeneous domination approach for global output feedback stabilization of a class of nonlinear systems. In: American Control Conference, Portland, pp. 4708–4715 (2005)
Polendo, J., Qian, C.: A generalized homogeneous domination approach for global stabilization of inherently nonlinear systems via output feedback. Int. J. Robust Nonlinear Control 17(7), 605–629 (2007)
Man, Y., Liu, Y.: Global output-feedback stabilization for high-order nonlinear systems with unknown growth rate. Int. J. Robust Nonlinear Control 27(5), 804–829 (2016)
Yang, S., Sun, Z., Wang, Z., Li, T.: A new approach to global stabilization of high-order time-delay uncertain nonlinear systems via time-varying feedback and homogeneous domination. J. Frankl. Inst. 355(14), 6469–6492 (2018)
Zhai, J., Qian, C.: Global control of nonlinear systems with uncertain output function using homogeneous domination approach. Int. J. Robust Nonlinear Control 22(14), 1543–1561 (2012)
Ai, W., Zhai, J., Fei, S.: Universal adaptive regulation for a class of nonlinear systems with unknown time delays and output function via output feedback. J. Frankl. Inst. 350(10), 3168–3187 (2013)
Li, Z., Zhao, J.: Output feedback stabilization for a general class of nonlinear systems via sampled-data control. Int. J. Robust Nonlinear Control 28(7), 2853–2867 (2018)
Jia, X., Xu, S., Cui, G., Zhang, B., Ma, Q.: Global adaptive regulation of feedforward nonlinear time-delay systems by output feedback. Int. J. Robust Nonlinear Control 27(14), 2451–2472 (2017)
Chen, C., Qian, C., Sun, Z., Liang, Y.: Global output feedback stabilization of a class of nonlinear systems with unknown measurement sensitivity. IEEE Trans. Autom. Control 63(7), 2212–2217 (2018)
Sun, Z., Liu, C., Su, S., Sun, W.: Robust stabilization of high-order nonlinear systems with unknown sensitivities and applications in humanoid robot manipulation. IEEE Trans. Syst. Man Cybern. Syst. (2019). https://doi.org/10.1109/TSMC.2019.2931768
Li, H., Zhang, X., Hou, T.: Output feedback control of large-scale nonlinear time-delay systems with unknown measurement sensitivities. IET Control Theory Appl. 13(13), 2122–2127 (2019)
Li, H., Zhang, X., Li, M.: Design of output feedback controller for stochastic feedforward systems with unknown measurement sensitivity. ISA Trans. (2019). https://doi.org/10.1016/j.isatra.2019.08.027
Sun, Z., Shao, Y., Chen, C., Meng, Q.: Global output-feedback stabilization for stochastic nonlinear systems: a double-domination approach. Int. J. Robust Nonlinear Control 28(15), 4635–4646 (2018)
Praly, L., Jiang, Z.: Linear output feedback with dynamic high gain for nonlinear systems. Syst. Control Lett. 53(2), 107–116 (2004)
Lv, L., Sun, Z., Xie, X.: Adaptive control for high-order time-delay uncertain nonlinear system and application to chemical reactor system. Int. J. Adapt. Control Signal Process. 29(2), 224–241 (2015)
Funding
This study was supported by National Natural Science Foundation of China (Grant No. 61773237), Shandong Qingchuang Science and Technology Program of Universities (Grant No. 2019KJN036) and Shandong Province Quality Core Curriculum of Postgraduate Education (Grant No. SDYKC17079).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Sun, ZY., Xing, JW. & Meng, Q. Output feedback regulation of time-delay nonlinear systems with unknown continuous output function and unknown growth rate. Nonlinear Dyn 100, 1309–1325 (2020). https://doi.org/10.1007/s11071-020-05552-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-020-05552-3