Abstract
Based on backstepping design, a novel adaptive tracking control scheme is proposed for a class of strict feedback nonlinear systems with unmodeled dynamics and completely unknown function control gain in this paper. An available dynamic signal is used to dominate the unmodeled dynamics. The unknown virtual control gain signs are dealt with using the property of Nussbaum function. The controller singularity problem is avoided using integral Lyapunov function. By theoretical analysis, the closed-loop systems is proved to be semi-global uniformly ultimately bounded.
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References
Nussbaum RD (1983) Some remarks on the conjecture in parameter adaptive control. Syst Control Lett 3(3):243–246
Zhang T, Ge SS, Hang CC (2000) Stable adaptive control for a class of nonlinear systems using a modified Lyapunov function. IEEE Trans Autom Control 45(1):129–132
Zhang TP, Ge SS (2007) Adaptive neural control of MIMO nonlinear state time-varying delay systems with unknown nonlinear dead-zones and gain signs. Automatica 43(6):1021–1033
Zhang TP, Zhu Q, Yang YQ (2012) Adaptive neural control of non-affine pure-feedback nonlinear systems with input nonlinearity and perturbed uncertainties. Int J Syst Sci 43(4):691–706
Jiang ZP, Hill DJ (1999) A Robust Adaptive backstepping scheme for nonlinear systems with unmodeled dynamics. IEEE Trans Autom Control 44(9):1705–1711
Jiang ZP, Praly L (1998) Design of robust adaptive controllers for nonlinear systems with dynamic uncertainties. Automatica 34(7):825–840
Zhang TP, Lu Y (2012) Adaptive dynamic surface control of nonlinear systems with unmodeled dynamics. Control Decision 27(3):335–342
Jiang ZP (1999) A combined backstepping and small-gain approach to adaptive output feedback control. Automaotica 35(6):1131–1139
Tong SC, Li YM (2009) Fuzzy adaptive robust control for a class of nonlinear systems with unmodeled dynamics. Control Decision 24(3):417–422
Zhang XY, Lin Y (2011) Adaptive tracking control for a class of pure-feedback nonlinear systems including actuator hysteresis and dynamic uncertainties. IET Control Theory Appl 5(16):1868–1880
Tong SC, Li YM (2010) Fuzzy adaptive robust backstepping stabilization for SISO nonlinear systems with unknown virtual control direction. Inf Sci 180(23):4619–4640
Lin W, Qian CJ (2002) Adaptive control of nonlinearly parameterized systems: a non-smooth feedback framework. IEEE Trans Autom Control 47(5):757–774
Ge SS, Hong F, Lee TH (2004) Adaptive neural control of nonlinear time-delay system with unknown virtual control coefficients. IEEE Trans Syst Man Cybernetics Part B Cybernetics 34(1):499–516
Ryan EP (1991) A universal adaptive stabilizer for a class of nonlinear systems. Syst Control Lett 16(3):209–218
Acknowledgments
This work was partially supported by the National Natural Science Foundation of China (61174046 & 61175111).
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© 2013 Springer-Verlag Berlin Heidelberg
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Gao, Z., Zhang, T., Yang, Y. (2013). Adaptive Tracking Control of Nonlinear Systems with Unmodeled Dynamics and Unknown Gain Sign. In: Sun, Z., Deng, Z. (eds) Proceedings of 2013 Chinese Intelligent Automation Conference. Lecture Notes in Electrical Engineering, vol 254. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38524-7_11
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DOI: https://doi.org/10.1007/978-3-642-38524-7_11
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