Abstract
Based on neural networks, a robust control design method is proposed for strict-feedback block nonlinear systems with mismatched uncertainties. Firstly, Radial-Basis-Function (RBF) neural networks are used to identify the nonlinear parametric uncertainties of the system, and the adaptive tuning rules for updating all the parameters of the RBF neural networks are derived using the Lyapunov stability theorem to improve the approximation ability of RBF neural networks on-line. Considering the known information, neural network and robust control are used to deal with the design problem when control coefficient matrices are unknown and avoid the possible singularities of the controller. For every subsystem, a nonlinear tracking differentiator is introduced to solve the “computer explosion” problem in backstepping design. It is proved that all the signals of the closed-loop system are uniform ultimate bounded.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Sastry, S.S., Isidori, A.: Adaptive Control of Linearizable System. IEEE Translations on Automatic Control 11, 1123–1131 (1989)
Seto, D., Annaswamy, A.M., Baillieul, J.: Adaptive Control of Nonlinear Systems with a Triangular Structure. IEEE Translations on Automatic Control 7, 1411–1428 (1994)
Polycarpou, M.M.: Stable Adaptive Neural Control Scheme for Nonlinear Systems. IEEE Translations on Automatic Control 3, 447–451 (1996)
Krstic, M., Kanellakopoulos, I., Kokotovic, P.: Nonlinear and Adptive Control Design. Wiley–Interscience Publication, Chichester (1995)
Vadim, I.U., De-Shiou, C., Hao-Chi, C.: Block Control Principle for Mechanical Systems. Journal of Dynamic Systems, Measurement, and Control 1, 1–10 (2000)
Loukianov, A., Toledo, B.C., Dodds, S.J.: Nonlinear Sliding Surface Design in the Presence of Uncertainty. In: Proceedings of the 14th IFAC, Beijing, P.R.China, pp. 55–60 (1999)
Jagannathan, S., Lewis, F.L.: Robust Backstepping Control of a Class of Nonlinear Systems Using Fuzzy Logic. Information Sciences 2, 223–240 (2000)
Yan, L., Sundararajan, N., Saratchandran, P.: Neuro-controller Design for Nonlinear Fighter Aircraft Maneuver Using Fully Tuned RBF Networks. Automatica 8, 1293–1301 (2001)
Park, J., Sandberg, I.W.: Universal Approximation Using Radial Basis Function Networks. Neural Computation 2, 246–257 (1991)
Zhang, T., Ge, S.S., Hang, C.C.: Adaptive Neural Network Control for Strict-Feedback Nonlinear Systems Using Backstepping Design. Automatica 12, 1835–1846 (2000)
Ge, S.S., Wang, C.: Adaptive NN Control of Uncertain Nonlinear Pure-Feedback Systems. Automatica 4, 671–682 (2002)
Jin, Y.Q.: Nonlinear Adaptive Control System Design for Missile, Yantai, P.R.China (2003)
Han, J., Wang, W.: Nonlinear Tracking Differentiator. System Science and Mathematics 2, 177–183 (1994)
Ordonez, R., Spooner, J.T.: Stable Multi-input Multi-output Adaptive Fuzzy Control. In: Proceedings of the 35th CDC, Japan, pp. 610–615 (1996)
Khalil, H.K.: Adaptive Output Feedback Control of Nonlinear Systems Represented by Input-Output Models. IEEE Transactions on Automatic Control 2, 177–188 (1996)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hu, Y., Jin, Y., Cui, P. (2004). RBF NN-Based Backstepping Control for Strict Feedback Block Nonlinear System and Its Application. In: Yin, FL., Wang, J., Guo, C. (eds) Advances in Neural Networks - ISNN 2004. ISNN 2004. Lecture Notes in Computer Science, vol 3174. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28648-6_20
Download citation
DOI: https://doi.org/10.1007/978-3-540-28648-6_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22843-1
Online ISBN: 978-3-540-28648-6
eBook Packages: Springer Book Archive