臺灣博碩士論文加值系統

本論文延續了Glover以及Mustafa在1989年的成果[5],我們把狀態空間的結果推廣到描述子系統,首先,我們定義了描述子系統的熵以及證明了熵的計算公式,接著我們找出所有的描述子系統H∞控制器來最小化對應的閉迴路系統的熵。

This thesis continues the line of the work of Glover and Mustafa[5], we extend the results from state-space systems case to descriptor systems case. Moreprecisely, we first give the explicit definition and formulae for calculating the entropy for descriptor systems. Next, we find the parameterization of all H∞ controllers for descriptor systems, and one special choice can result in the minimum entropy among all closed-loop systems.

1 Introduction.........................................1
2 Preliminaries........................................3
2.1 Elements of Descriptor Systems Theory..............3
2.2 Problem Statement..................................6
3 H∞ Control Problem For Descriptor Systems............10
3.1 H∞ Full Information Control Problem For Descriptor Systems................................................10
3.2 H∞ Disturbance Feedforward Control Problem For Descriptor Systems.....................................16
3.3 H∞ Output Estimation Control Problem For Descriptor Systems................................................20
4 The Minimum Entropy H∞ Control Problem For Descriptor Systems................................................21
4.1 Entropy Minimization For Descriptor Systems........21
4.2 Formulae of the Minimum Entropy For Descriptor Systems................................................25
5 Conclusion...........................................29
References.............................................30

[1]D. Cobb, ”Controllability, observability, and duality in singular systems,” IEEE Transactions on AutomaticControl, vol.26,no.12,pp.1076-1082,1984.
[2]L. Dai, Singular control systems, Springer-Verlag,1989.
[3]J. C. Doyle, K. Glover, P. P. Khargonekar, and B. A. Francis, ”State-space solutions to standard H2 & H∞ control problems,” IEEE Transactions on Automatic Control, vol. 34, no. 8, pp. 831-846, 1989.
[4]G. R. Duan, Analysis and design of descriptor linear systems, Vol. 23. Springer Science and Business Media,2010.
[5]K. Glover, and D. Mustafa, ”Derivation of the maximum entropy H∞ controller and a state-space formula for its entropy,” International Journal of Control, vol. 50, no. 3, pp. 899-916, 1989.
[6]A. Kawamoto, K. Takaba, and T. Katayama, ”On the generalized algebraic Riccati equation for continuous-time descriptor systems,” Linear Algebra and its Applications, vol. 296,no. 1, pp. 1-14, 1999.
[7]P. Losse, V. Mehrmann, L. Poppe, and T. Reis, ”The modified optimal H∞ control problem for descriptor systems,” SIAM Journal Control and Optimization, vol. 47,
no. 6, pp. 2795-2811, 2008.
[8]I. Masubuchi, Y. Kamitane, A. Ohara, and N. Suda, ”H∞ control for descriptor systems: A matrix inequalities approach,” Automatica, vol. 33, no. 4, pp. 669-673, 1997.
[9]I. Masubuchi, ”Output feedback controller synthesis for descriptor systems satisfying closed-loop dissipativity,” Automatica, vol. 43,no. 2,pp. 229-245, 2008.
[10]I. R. Petersen, B. D. O. Anderson, and E. A. Jonckheere, ”A first principles solution to the nonsingular H∞ control problem,” International Journal of Robust and Nonlinear Control, vol. 1, no. 2, pp. 153-170, 1991.
[11]W. Rudin, Real and complex Analysis, McGraw-Hill, third edition, 1986.
[12]T. Stykel, ”Analysis and numerical solution of generalized Lyapunov equations,” Institut fur Mathematik, Technische Universitat, Berlin, 2002.
[13]H. S. Wang, C. F. Yung, and F. R. Chang, ”Bounded real lemma and H∞ control for descriptor systems, ” IEE Proceedings-Control Theory and Applications, vol. 145, no. 3, pp. 316-322, 1998.
[14]H. S. Wang, C. F. Yung, and F. R. Chang, H∞ control for nonlinear descriptor systems, Lecture Notes in Control and Information Sciences, 326, London: Springer-Verlag, 2006.
[15]P. F. Wu, and C. F. Yung, ”On the geometric and dynamic structures of the H∞ optimal and H2 central controllers,” Automatica, vol. 46, no. 11, pp. 1824-1828,
2010.
[16]C. F. Yung, ”Reduced-order H∞ controller design-An algebraic Riccati equation approach,” Automatica, vol. 36, no. 6, pp. 923-926, 2000.
[17]K. Zhou, J. C. Doyle, and K. Glover, Robust and optimal control, Vol. 40. New Jersey: Prentice hall, 1996.
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