Abstract
Least squares support vector machine (LS-SVM) classifiers are a class of kernel methods whose solution follows a set of linear equations. In this work we present a least squares support vector machine sliding mode control (LS-SVM-SMC) strategy for uncertain discrete system with input saturation. The output of LS-SVM is used for replacing sign function of the reaching law in traditional sliding mode control (SMC). An equivalent matrix is constructed for input saturation condition in the scheme. Combined LS-SVM-SMC with linear Matrix Inequalities (LMIs), a chattering free control algorithm is applied in the uncertain discrete systems with input saturation. The feasibility and effectiveness of the LS-SVM-SMC scheme are demonstrated via numerical examples. As a result, compared with conventional SMC, the LS-SVM-SMC is able to achieve the desire transient response with input saturation. And there is no chattering in steady state while unmatched parameter uncertainty exists.
This is a preview of subscription content, log in via an institution to check access.
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
Utkin, V.I.: Varialbe Structure Systems with Sliding Mode. IEEE Transactions on Automatic Control 22(2), 212–222 (1977)
Gao, W., Wang, Y., Homaifa, A.: Discrete-Time Variable Structure Control Systems. IEEE Transactions on Industrial Electronics 42(2), 117–122 (1995)
Bartoszewicz, A.: Discrete-Time Quasi-Sliding-Mode Control Strategies. IEEE Transactions on Industrial Electronics 45(4), 633–637 (1998)
Yau, H.: Chaos Synchronization of Two Uncertain Chaotic Nonlinear Gyros Using Fuzzy Sliding Mode Control. Mechanical Systems and Signal Processing 22, 408–418 (2008)
Cherati, Z., Motlagh, M.: Control of Spatiotemporal Chaos in Coupled Map Lattice by Discrete-Time Variable Structure Control. Physics Letters A 370, 302–305 (2007)
Wang, Z., Zhang, Y.: Design and Verification of a Robust Formation Keeping Controller. Acta Astronautica 61, 565–574 (2007)
Yau, H., Chen, C.: Chattering-Free Fuzzy Sliding Mode Control for Uncertain Chaotic Systems. Chaos, Solitons and Fractals 30, 709–718 (2006)
Xiao, L., Su, H., Zhang, X., Chu, J.: A New Discrete Variable Structure Control Algorithm Based on Sliding Mode Prediction. In: Jayasuriya, S., Balakrishnan, S.N. (eds.) 2005 American Control Conference, pp. 4643–4648. IEEE, Los Alamitos (2005)
Choi, J.: On the Stabilization of Linear Discrete Time Systems Subject to Input Saturation. System & Control Letters 36, 241–244 (1999)
Zhang, J., Wang, B., Run, P.: Model Predictive Control for Nonlinear Systems with Constraint Inputs. Electric Machines and Control 9(4), 357–361 (2005)
Zhang, J., Run, P., Chen, T.: Model Predictive Control for Time-Delay Systems with Input Constraints. Journal of System Simulation 15(7), 1051–1053 (2003)
Vapnik, V.: The Nature of Statistical Learning Theory. Springer, New York (1995)
Chen, X., Li, Y., Harrison, R., Zhang, Y.: Type-2 Fuzzy Logic-Based Classifier Fusion for Support Vector Machines. Applied Soft Computing 8, 1222–1231 (2008)
Yang, Q., Li, X., Shi, X.: Cellular Automata for Simulating Land Use Changes Based on Support Vector Machines. Computers & Geosciences 34, 592–602 (2008)
Fatemi, M., Gharaghani, S., Mohammadkhani, S., Rezaie, Z.: Prediction of Selectivity Coefficients of Univalent Anions for Anion-Selective Electrode Using Support Vector Machine. Electrochimica Acta 53, 4276–4282 (2008)
Suykens, J., Gestel, T., Brabanter, J., Moor, B., Van de walle, J.: Least Squares Support Vector Machines. World Scientific Publishing, Singapore (2002)
Suykens, J., Vandewalle, J.: Least Squares Support Vector Machine Classifiers. Neural Processing Letters 9(3), 293–300 (1999)
Yu, L.: Robust control. Tsinghua Press, Beijing (2002)
Cao, T., Sun, Y., Cheng, C.: Delay-Dependent Robust Stabilization of Uncertain Systems with Multiple State Delays. IEEE Transactions on Automatic Control 43, 1608–1612 (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Li, J., Zhang, Y., Pan, H. (2008). Chattering-Free LS-SVM Sliding Mode Control. In: Sun, F., Zhang, J., Tan, Y., Cao, J., Yu, W. (eds) Advances in Neural Networks - ISNN 2008. ISNN 2008. Lecture Notes in Computer Science, vol 5263. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87732-5_78
Download citation
DOI: https://doi.org/10.1007/978-3-540-87732-5_78
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87731-8
Online ISBN: 978-3-540-87732-5
eBook Packages: Computer ScienceComputer Science (R0)