An LMI approach to design H∞ controllers for discrete-time nonlinear systems based on unified models

International Journal of Neural Systems

Volumn 18, Issue 5, 2008, Pages 443-452

  Liu, Meiqin ^a   Zhang, Senlin ^a  

^a ZHEJIANG UNIVERSITY   (China)

Author keywords

Asymptotic stability; Discrete time nonlinear system; Eigenvalue problem; H control; L2 gain; Linear matrix inequality (LMI); Standard neural network model (SNNM); Takagi and Sugeno (T S) fuzzy model

Indexed keywords

ASYMPTOTIC STABILITY; CONTINUOUS TIME SYSTEMS; CONTROL THEORY; DELAY CONTROL SYSTEMS; EIGENVALUES AND EIGENFUNCTIONS; FEEDBACK; FUZZY CONTROL; FUZZY NEURAL NETWORKS; IMAGE CLASSIFICATION; LINEAR CONTROL SYSTEMS; LINEAR MATRIX INEQUALITIES; NONLINEAR SYSTEMS; RECURRENT NEURAL NETWORKS; ROBUST CONTROL; STATE FEEDBACK; SWITCHING SYSTEMS; SYSTEM STABILITY; UNCERTAIN SYSTEMS; VEGETATION;

DISCRETE-TIME NONLINEAR SYSTEM; EIGENVALUE PROBLEM; L2 GAIN; LINEAR MATRIX INEQUALITY (LMI); STANDARD NEURAL NETWORK MODEL (SNNM); TAKAGI AND SUGENO (T-S) FUZZY MODEL;

NEURAL NETWORKS;

ALGORITHM; ARTICLE; ARTIFICIAL INTELLIGENCE; ARTIFICIAL NEURAL NETWORK; COMPUTER PROGRAM; FUZZY LOGIC; NONLINEAR SYSTEM; TIME;

ALGORITHMS; ARTIFICIAL INTELLIGENCE; FUZZY LOGIC; NEURAL NETWORKS (COMPUTER); NONLINEAR DYNAMICS; SOFTWARE; TIME FACTORS;

EID: 55849110440     PISSN: 01290657     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129065708001701     Document Type: Article

References (21)

1. J. A. K. Suykens, J. P. L. Vandewalle and B. L. R. De Moor, Artificial Neural Networks for Modeling and Control of Non-Linear Systems, Kluwer Academic Publishers, Boston, Dordrecht, London (1996).
2. M. Nørgaard, O. Ravn, N. K. Poulsen and L. K. Hansen, Neural Networks for Modeling and Control of Dynamic Systems, Springer-Verlag, London Berlin Heidelberg (2000).
3. C. Sun and C.-B. Feng. Discrete-time analogues of integro-differential equations modeling neural networks, Physics Letters A 334 (2-3) (Jan. 2005) 180-191.
4. K. Tanaka and H. O. Wang, Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach, John Wiley & Sons, Inc. (2001).
5. ∞ design approach for neural net-based control schemes, IEEE Transactions on Automatic Control 46 (10) (Oct. 2001) 1599-1605.
6. ∞ control design, IEE Proceedings-Control Theory and Applications 149 (4) (Jul. 2002) 331-342.
7. 2 guaranteed cost fuzzy control for uncertain nonlinear systems via linear matrix inequalities, Fuzzy Sets and Systems 148 (3) (Dec. 2004) 411-429.
8. ∞ control of fuzzy dynamic systems, Fuzzy Sets and Systems 137 (3) (Aug. 2003) 367-386.
9. K. Tanaka, Stability and stabilizability of fuzzyneural-linear control systems, IEEE Trans. on Fuzzy Systems 3 (4) (Nov. 1995) 438-447.
10. K. Tanaka, An approach to stability criteria of neural-network control system, IEEE Transactions on Neural Networks 7 (3) (May 1996) 629-642.
11. S. P. Boyd, L. El Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, PA (1994).
12. M. Liu, Delayed standard neural network models for control systems, IEEE Trans. on Neural Networks 18 (5) (Sep. 2007) 1376-1391.
13. M. Liu, Discrete-time delayed standard neural network model and its application, Science in China Ser. F-Information Sciences 49 (2) (Apr. 2006) 137-154.
14. ∞ controllers, Proceedings of the 1997 American Control Conference, 1 (4-6 Jan. 1997) 493-498.
15. D. Banjerdpongchai and H. Kimura, Robust analysis of discrete-time Lur'e systems with slope restrictions using convex optimization, Asian Journal of Control 4 (2) (Jun. 2002) 119-126.
16. T. Nampradit and D. Banjerdpongchai, Performance analysis of Lur'e systems with multiple slope restrictions using convex optimization, Proc. of the 4th Asian Control Conf. (Singapore, 25-27, Sep. 2002) 1097-1102.
17. C. Y. Sun and L. F. Li, Dynamics of general neural networks with distributed delays," 3rd International Symposium on Neural Networks (ISSN), Springer-Verlag Berlin Heidelberg, Vol. LNCS3971 (28-31 May 2006) 135-140.
18. P. Gahinet, A. Nemirovski, A. J. Laub and M. Chilali, LMI Control Toolbox - For Use with Matlab, MA: The MATH Works, Inc., Natick (1995).
19. S. Limanond and J. Si, Neural-network-based control design: an LMI approach, IEEE Trans. on Neural Networks 9 (6) (Jun. 1998) 1422-1429.
20. K. Tanaka and M. Sano, A robust stabilization problem of fuzzy control systems and its application to backing up control of a truck-trailer, IEEE Trans. on Fuzzy Systems 2 (2) (Apr. 1994) 119-134.
21. ∞ control of uncertain dynamical fuzzy discrete-time systems, IEEE Trans. on Systems, Man, and Cybernetics - Part B: Cybernetics 31 (5) (Oct. 2001) 802-812.