# zbMATH — the first resource for mathematics

Robust adaptive control for a class of uncertain strict-feedback nonlinear systems. (English) Zbl 1166.93334
Summary: Robust adaptive control is presented for a class of perturbed strict-feedback nonlinear systems with both completely unknown control coefficients and parametric uncertainties. The proposed design method does not require a priori knowledge of the signs of the unknown control coefficients. For the first time, the key technical Lemma is proven when the Nussbaum function is chosen by $$N(\zeta ) = \zeta ^{2}\cos(\zeta)$$, based on which the proposed robust adaptive scheme can guarantee the global uniform ultimate boundedness of the closed-loop system signals. Simulation results show the validity of the proposed scheme.

##### MSC:
 93C40 Adaptive control/observation systems 93B35 Sensitivity (robustness) 93C10 Nonlinear systems in control theory
Full Text:
##### References:
 [1] Krstić, Nonlinear and Adaptive Control Design (1995) [2] Polycarpou, A robust adaptive nonlinear control design, Automatica 32 (3) pp 423– (1996) · Zbl 0847.93031 [3] Yao, Adaptive robust control of SISO nonlinear systems in a semi-strict feedback form, Automatica 33 (5) pp 893– (1997) · Zbl 0876.93083 [4] Jiang, A robust adaptive backstepping scheme for nonlinear systems with unmodeled dynamics, IEEE Transactions on Automatic Control 44 pp 1705– (1999) · Zbl 0958.93053 [5] Ge, Stable adaptive control for nonlinear multivariable systems with a triangular control structure, IEEE Transactions on Automatic Control 45 (6) pp 1221– (2000) · Zbl 0972.93062 [6] Ge, Stable Adaptive Neural Network Control (2002) · doi:10.1007/978-1-4757-6577-9 [7] Nussbaum, Some remarks on the conjecture in parameter adaptive control, Systems and Control Letters 3 pp 243– (1983) · Zbl 0524.93037 [8] Mårtensson, Remarks on adaptive stabilization of first-order nonlinear systems, Systems and Control Letters 14 pp 1– (1990) · Zbl 0692.93059 [9] Ye, Adaptive nonlinear design without a priori knowledge of control directions, IEEE Transactions on Automatic Control 43 (11) pp 1617– (1998) · Zbl 0957.93048 [10] Ye, Asymptotic regulation of time-varying uncertain nonlinear systems with unknown control direction, Automatica 35 (5) pp 929– (1999) · Zbl 0945.93542 [11] Ding, Adaptive control of nonlinear systems with unknown virtual control coefficients, International Journal of Adaptive Control and Signal Processing 14 pp 505– (2000) · Zbl 0958.93049 [12] Ye, Robust tracking control of uncertain nonlinear systems with unknown control directions, Systems and Control Letters 42 pp 1– (2001) [13] Ye, Adaptive nonlinear output-feedback control with unknown high-frequency gain sign, IEEE Transactions on Automatic Control 46 pp 112– (2001) · Zbl 1062.93517 [14] Ding, A flat-zone modification for robust adaptive control of nonlinear output feedback systems with unknown high-frequency gains, IEEE Transactions on Automatic Control 47 (2) pp 358– (2002) · Zbl 1364.93699 [15] Ding, Universal disturbance rejection for nonlinear systems in output feedback form, IEEE Transactions on Automatic Control 48 (7) pp 1222– (2003) · Zbl 1364.93332 [16] Ge, Robust adaptive tracking for time-varying uncertain nonlinear systems with unknown control coefficients, IEEE Transactions on Automatic Control 48 (8) pp 1463– (2003) · Zbl 1364.93704 [17] Ge, Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients, IEEE Transactions on Systems, Man and Cybernetics, Part B 34 (1) pp 499– (2004) [18] Ilchmann, Non-identifier-based High-Gain Adaptive Control (1993) · Zbl 0786.93059 [19] Ryan, A universal adaptive stabilizer for a class of nonlinear systems, Systems and Control Letters 16 pp 209– (1991) · Zbl 0728.93050 [20] Hredzak B, Hong F, Ge SS, Zhang J, He Z. Modeling and compensation of pivot nonlinearity in hard disk drives. Proceedings of the IEEE Multiple-Conference on Systems and Control, Singapore, 2007; 108-113. [21] Ge, Adaptive Neural Network Control of Robotic Manipulators (1998) · doi:10.1142/3774 [22] Rosenlicht, Introduction to Analysis (1968)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.