Abstract
A class of nonlinear systems with unknown input power is discussed about their tracking control problem in this paper. To guarantee that the output of this system can converge asymptotically to the reference signal, a robust adaptive control method is proposed. Based on Lyapunov stability theory, it is proven that the tracking error asymptotically converges to an adjustable neighborhood of the origin. The method improves some inadequacies of existing results and relaxes several assumptions imposed on the system. Finally, the viability and effectiveness of the control method presented in this paper are verified by performing numerical simulations.
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References
W. Lin, C. Qian, Adaptive control of nonlinear parameterized systems: the nonsmooth feedback framework. IEEE Trans. Autom. Control 47(5), 757–774 (2002)
W. Lin, C. Qian, Adaptive control of nonlinear parameterized systems: the smooth feedback case. IEEE Trans. Autom. Control 47(8), 249–1266 (2002)
J.Z. Liu, S. Yan, D.L. Zeng et al., A dynamic model used for controller design of a coal fired once-through boiler-turbine unit. Energy 93(2), 2069–2078 (2015)
Y.M. Li, Y.J. Liu, S.C. Tong, Observer-based neuro-adaptive optimized control for strict-feedback nonlinear systems with state constraints. IEEE Trans. Neural Netw. Learn. Syst. (2021). https://doi.org/10.1109/TNNLS.2021.3051030
H. Liang, G. Liu, H. Zhang et al., Neural-network-based event-triggered adaptive control of nonaffine nonlinear multiagent systems with dynamic uncertaintie. IEEE Trans. Neural Netw. Learn. Syst. 32(5), 2239–2250 (2020)
Y.C. Man, Y.G. Liu, Global adaptive stabilization and practical tracking for nonlinear systems with unknown powers. Automatica 100, 171–181 (2019)
Y.C. Man, Y.G. Liu, Global adaptive stabilization for planar nonlinear systems with unknown input powers. Sci. China Inf. Sci. (2020). https://doi.org/10.1007/s11432-018-9774-v
Y. Pan, Q. Li, H. Liang et al., A novel mixed control approach for fuzzy systems via membership functions online learning policy. IEEE Trans. Fuzzy Syst. (2021). https://doi.org/10.1109/TFUZZ.2021.3130201
Y. Pan, Y. Wu, H. Lam, Security-based fuzzy control for nonlinear networked control systems with DoS attacks via a resilient event-triggered scheme. IEEE Trans. Fuzzy Syst. (2022). https://doi.org/10.1109/TFUZZ.2022.3148875
C. Qian, W. Lin, A continuous feedback approach to global strong stabilization of nonlinear systems. IEEE Trans. Autom. Control 46(7), 1061–1079 (2001)
C. Qian, W. Lin, Practical output tracking of nonlinearly systems with uncontrollable unstable linearization. IEEE Trans. Autom. Control 47(1), 21–37 (2002)
C.L. Rui, M. Reyhanoglu, I. Kolmanovsky, et al. Nonsmooth stabilization of an underactuated unstable two degrees of freedom mechanical system. In Proceedings of the 36th IEEE Conference on Decision and Control (IEEE, 1997), pp. 3998–4003
Z.Y. Sun, Y.G. Liu, Stabilizing control design for a class of high-order nonlinear systems with unknown but identical control coefficients. Acta Autom. Sin. 33(3), 331–334 (2007)
Z.Y. Sun, Y.G. Liu, Adaptive state-feedback stabilization for a class of high-order nonlinear uncertain systems. Automatica 43(10), 1772–1783 (2007)
Z.G. Su, C.J. Qian, Interval homogeneity-based control for a class of nonlinear systems with unknown power drifts. IEEE Trans. Autom. Control 62(3), 1445–1450 (2017)
X. Tang, G. Tao, S.M. Joshi, Adaptive actuator failure compensation for nonlinear MIMO systems with an aircraft application. Automatica 43(11), 1975–1982 (2007)
S.C. Tong, Y.M. Li, G. Feng, Observer-based adaptive fuzzy backstepping dynamic surface control for a class of MIMO nonlinear systems. IEEE Trans. Syst. Man Cybern. B (Cybern.) 41(4), 1124–1135 (2011)
S.C. Tong, S. Sui, Y.M. Li, Fuzzy adaptive output feedback control of MIMO nonlinear systems with partial tracking errors constrained. IEEE Trans. Fuzzy Syst. 23(4), 729–742 (2015)
W. Wang, C. Wen, Adaptive compensation for infinite number of actuator failures or faults. Automatica 47(12), 2197–2210 (2011)
M.Q. Wang, Y.G. Liu, Y.C. Man, Switching adaptive controller for the nonlinear systems with uncertainties from unknown powers. IEEE Trans. Syst. Man Cybern. Syst. 50(7), 2375–2385 (2020)
X.X. Zheng, Q.K. Shen, Neural network-based adaptive fault-tolerant control for a class of high-order strict-feedback nonlinear systems. IEEE Access 8, 56510–56517 (2020)
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This work is partially supported by the national Natural Science Foundation of China (61873229, 61473250, 62273300).
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Sun, Z., Shen, Q. Adaptive Stability Control for a Class of Nonlinear Systems in the p-Norm Form. Circuits Syst Signal Process 42, 1438–1456 (2023). https://doi.org/10.1007/s00034-022-02171-8
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DOI: https://doi.org/10.1007/s00034-022-02171-8