Central suboptimal H∞ control design for nonlinear polynomial systems

International Journal of Systems Science

Volumn 42, Issue 5, 2011, Pages 801-808

  Basin, Michael V ^a   Shi, Peng ^b,c,d   Calderon Alvarez, Dario ^a  

^a UNIVERSIDAD AUTÓNOMA DE NUEVO LEÓN   (Mexico)

^b UNIVERSITY OF GLAMORGAN   (United Kingdom)

^c VICTORIA UNIVERSITY   (Australia)

^d UNIVERSITY OF SOUTH AUSTRALIA   (Australia)

Author keywords

H control; nonlinear systems

Indexed keywords

ATTENUATION CONTROL; AUTOMATIC CONTROL; CONTROL DESIGN; CONTROL PROBLEMS; NONLINEAR POLYNOMIAL SYSTEMS; NUMERICAL SIMULATION; OPTIMAL CONTROLLER; POLYNOMIAL SYSTEMS; STANDARD H; STATE-SPACE;

AUTOMATION; CONTROL; NONLINEAR SYSTEMS; OPTIMIZATION;

POLYNOMIALS;

EID: 79952024676     PISSN: 00207721     EISSN: 14645319     Source Type: Journal    
DOI: 10.1080/00207721.2010.543491     Document Type: Article

References (33)

1. Albrekht, E.G. (1962), 'On the Optimal Stabilization of Nonlinear Systems', Journal of Applied Mathematics and Mechanics, 25, 1254-1266.
2. Basin, M.V., and Calderon-Alvarez, D. (2008a), 'Alternative Optimal Filter for Linear Systems with Multiple State and Observation Delays', International Journal of Innovative Computing, Information and Control, 4, 2889-2898.
3. Basin, M.V., and Calderon-Alvarez, D. (2008b), 'Optimal Controller for Uncertain Stochastic Polynomial Systems', Journal of the Franklin Institute, 345, 293-302.
4. Basin, M.V., Perez, J., and Calderon-Alvarez, D. (2008), 'Optimal Filtering for Linear Systems over Polynomial Observations', International Journal of Innovative Computing, Information and Control, 4, 313-320.
5. Basin, M.V., Perez, J., and Skliar, M. (2006), 'Optimal Filtering for Polynomial System States with Polynomial Multiplicative Noise', International Journal of Robust and Nonlinear Control, 16, 287-298.
6. Bellman, R. (1957), Dynamic Programming, Princeton: Princeton University Press.
7. Chen, B.S., and Tseng, C.S. (1994), 'H∞ Control Design in Bilinear Systems: A Tensor Formal Series Approach', Systems and Control Letters, 23, 15-26.
8. 2 and H∞ Control Problems', IEEE Transactions on Automatic Control, 34, 831-847.
9. Fleming, W.H., and Rishel, R.W. (1975), Deterministic and Stochastic Optimal Control, New York: Springer-Verlag.
10. Fridman, E. (2001), 'State-feedback H∞ Control of Nonlinear Singularly Perturbed Systems', International Journal of Robust and Nonlinear Control, 11, 1115-1125. (Pubitemid 33018103)
11. Gao, H.J., Lam, J., and Wang, Z.D. (2002), 'Discrete Bilinear Stochastic Systems with Time-varying Delay: Stability Analysis and Control Synthesis', International Journal of Systems Science, 33, 885-900.
12. Guo, L., and Lam, J. (2002), ' Robust H∞ Performance Problem for Linear Systems with Nonlinear Uncertainties in all System Matrices', International Journal of Systems Science, 33, 885-900.
13. Haime, A., and Hamalainen, R. (1975), On the Nonlinear Regulator Problem', Journal of Optimization Theory and Applications, 16, 255-275.
14. Hsiao, F.H. (2007),' Robust H∞ Fuzzy Control of Nonlinear Systems with Multiple Time Delays', International Journal of Systems Science, 38, 351-360.
15. Isidori, A. (2001), Nonlinear Systems, Berlin: Springer.
16. Katebi, M.R., and Zhang, Y. (1995), ' H∞ Control, Analysis, and Design for Nonlinear Systems', International Journal of Control, 61, 459-474.
17. Kwarkernaak, H., and Sivan, R. (1972), Linear Optimal Control Systems, New York: Wiley-Interscience.
18. Liao, C.W., Lu, C.Y., Zheng, K.Y., and Ting, C.C. (2009), A Delay-dependent Approach to Design State Estimator for Discrete Stochastic Recurrent Neural Network with Interval Time-varying Delays', ICIC Express Letters,3, 465-470.
19. Lukes, D.L. (1969), 'Optimal Regulation of Nonlinear Dynamic Systems', SIAM Journal of Control Optimization, 7, 75-100.
20. Nguang, S.K. (1997), 'Global Robust H∞ Control for a Class of Nonlinear Systems', International Journal of Robust and Nonlinear Control, 7, 75-84. (Pubitemid 127664953)
21. Sain, M.K. (ed.) (1985), 'Applications of Tensors to Modeling and Control', Control Systems Technical Report (Vol. 38), Notre Dame University, Department of Electrical Engineering.
22. Shi, P., Shue, S.P., Shi, Y., and Agarwal, R.K. (1999), 'Controller Design for Bilinear Systems with Parametric Uncertainties', Mathematical Problems in Engineering,4, 505-528.
23. Van der Schaft, A.J. (1991), 'On a State-Space Approach to Nonlinear H∞ Control', Systems and control Letters, 16, 1-8.
24. 2-gain Analysis of Nonlinear Systems and Nonlinear State Feedback H∞ Control', IEEE Transactions on Automatic Control, 37, 770-784.
25. Wang, Y.Y., Xie, L.H., and De Souza, C.E. (1992), 'Robust Control of a Class of Uncertain Nonlinear Systems', Systems and Control Letters, 19, 139-149.
26. Willemstein, A.P. (1977), 'Optimal Regulation of Nonlinear Dynamical Systems in a Finite Interval', SIAM Journal of Control Optimization, 15, 1050-1069.
27. Xia, Y., Qiu, J., Zhang, J., Gao, Z., and Wang, J. (2008), 'Delay-dependent Robust H∞ Control for Uncertain Stochastic Time-delay System', International Journal of Systems Science, 39, 1139-1152.
28. Xie, L.H., Shi, P., and De Souza, C.E. (1993), 'On Designing Controllers for a Class of Uncertain Sampled-data Nonlinear-systems', IEE Proceedings, Series D. Control Theory and Applications, 140, 119-126. (Pubitemid 23701769)
29. Xu, S., and Chen, T. (2002), 'Robust H∞ Control for Uncertain Stochastic Systems with State Delay', IEEE Transactions on Automatic Control, 47, 2089-2094.
30. Xu, S., Lu, J.W., Zhou, S.S., and Yang, C.W. (2004), 'Design of Observers for a Class of Discrete-time Uncertain Nonlinear Systems with Time Delay', Journal of the Franklin Institute, 341, 295-308.
31. Yoshida, T., and Loparo, K. (1989), 'Quadratic Regulatory Theory for Analytic Nonlinear Systems with Additive Controls', Automatica, 25, 531-544. (Pubitemid 20612646)
32. 2 and H∞ Static Output Feedback Control for Uncertain Discrete-time Fuzzy Systems', IET Control Theory & Applications, 3, 865-876.
33. Zhang, J., Xia, Y., Shi, P., and Qiu, J. (2009), 'H∞ Output Feedback Control Design for Discrete-time Fuzzy Systems', Optimal Control, Applications and Methods, 30, 415-437.