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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 715026, 8 pages
Optimal Control for a Family of Systems in Novel State Derivative Space Form with Experiment in a Double Inverted Pendulum System
Department of Electrical Engineering, I-Shou University, Kaohsiung 84001, Taiwan
Received 13 June 2013; Accepted 29 July 2013
Academic Editor: Chang-Hua Lien
Copyright © 2013 Yuan-Wei Tseng and Jer-Guang Hsieh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes, Wiley, New York, NY, USA, 1962.
- K. Zhou and J. C. Doyle, Essentials of Robust Control, Prentice-Hall, New Jersey, NJ, USA, 1997.
- Y. Shoham and K. Leyton-Brown, Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations, Cambridge University Press, New York, NY, USA, 2009.
- D. Simon, Optimal State Estimation: Kalman, H∞, and Nonlinear Approaches, Wiley, New York, NY, USA, 2006.
- G. C. Verghese, B. C. Lévy, and T. Kailath, “A generalized state-space for singular systems,” IEEE Transactions on Automatic Control, vol. 26, no. 4, pp. 811–831, 1981.
- D. G. Luenberger, “Dynamic equations in descriptor form,” IEEE Transactions on Automatic Control, vol. 22, no. 3, pp. 312–321, 1977.
- S. L. Campbell, Singular Systems of Differential Equations, Pitman, San Francisco, Calif, USA, 1980.
- R. W. Newcomb, “The semistate description of nonlinear time-variable circuits,” IEEE Transactions on Circuits and Systems, vol. 28, no. 1, pp. 62–71, 1981.
- K. E. Brenan, “Numerical simulation of trajectory prescribed path control problems by the backward differentiation formulas,” IEEE Transactions on Automatic Control, vol. 31, no. 3, pp. 266–269, 1986.
- Y. W. Tseng, “Vibration control of piezoelectric smart plate using estimated state derivatives feedback in reciprocal state space form,” International Journal of Control Theory and Applications, vol. 2, no. 1, pp. 61–71, 2009.
- C. C. Pantelides, “The consistent initialization of differential-algebraic systems,” SIAM Journal on Scientific and Statistical Computing, vol. 9, no. 2, pp. 213–231, 1988.
- D. G. Luenberger and A. Arbel, “Singular dynamic Leontief systems,” Econometrica, vol. 45, no. 4, pp. 991–995, 1977.
- P. Liu, Q. Zhang, X. Yang, and L. Yang, “Passivity and optimal control of descriptor biological complex systems,” IEEE Transactions on Circuits and Systems, vol. 53, special issue on systems biology, pp. 122–125, 2008.
- F. B. Yeh and H. N. Huang, “state feedback control of smart beam-plates via the descriptor system approach,” Tunghai Science, vol. 2, pp. 21–42, 2000.
- D. Cobb, “State feedback impulse elimination for singular systems over a Hermite domain,” SIAM Journal on Control and Optimization, vol. 44, no. 6, pp. 2189–2209, 2006.
- E. Jonckheere, “Variational calculus for descriptor problems,” IEEE Transactions on Automatic Control, vol. 33, no. 5, pp. 491–495, 1988.
- D. Liu, G. Zhang, and Y. Xie, “Guaranteed cost control for a class of descriptor systems with uncertainties,” International Journal of Information & Systems Sciences, vol. 5, no. 3-4, pp. 430–435, 2009.
- S. M. Saadni, M. Chaabane, and D. Mehdi, “Robust stability and stabilization of a class of singular systems with multiple time-varying delays,” Asian Journal of Control, vol. 8, no. 1, pp. 1–11, 2006.
- A. Varga, “Robust pole assignment for descriptor systems,” in Proceeding of Mathematical Theory of Networks and Systems, Perpignan, France, 2000.
- D. Cobb, “Eigenvalue conditions for convergence of singularly perturbed matrix exponential functions,” SIAM Journal on Control and Optimization, vol. 48, no. 7, pp. 4327–4351, 2010.
- Y. W. Tseng and R. K. Yedavalli, “Vibration control of a wing box via reciprocal state space framework,” in Proceedings of the IEEE International Conference on Control Applications, pp. 854–859, Hartford, Conn, USA, October 1997.
- Y. W. Tseng, “Control designs of singular systems expressed in reciprocal state space form with state derivative feedback,” International Journal of Control Theory and Applications, vol. 1, no. 1, pp. 55–67, 2008.
- T. F. Elbert, Estimation and Control of Systems, Van Nostrand Reinhold, New York, NY, USA, 1984.
- EMECS (electro-mechanical engineering control system) developed by TeraSoft Inc, http://www.terasoft.com.tw/product/product_dsp_control.asp.
- C. H. Huang, An application of FPGA board in the inverted pendulum system with time delay [M.S. thesis], Department of Electrical Engineering, I-Shou University, Kaohsiung, Taiwan, 2012.
- X. H. Yang, H. S. Liu, G. P. Liu, and G. F. Xiao, “Control experiment of the inverted pendulum using adaptive neural-fuzzy controller,” in Proceedings of the International Conference on Electrical and Control Engineering (ICECE '10), pp. 629–632, Wuhan, China, June 2010.