跳到主要內容

臺灣博碩士論文加值系統

(54.224.133.198) 您好!臺灣時間:2022/01/29 22:05
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果 :::

詳目顯示

: 
twitterline
研究生:李錦雄
論文名稱:以羅莎模型表示之二維線性系統的最佳化控制:動態規劃法
論文名稱(外文):Optimal control of two-dimensional linear systems in Roesser's model:dynamic programming approach
指導教授:蔡聖鴻
學位類別:博士
校院名稱:國立成功大學
系所名稱:電機工程學系
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2001
畢業學年度:90
語文別:中文
論文頁數:102
中文關鍵詞:二維系統最佳化控制羅莎模型動態規劃法數位再設計
相關次數:
  • 被引用被引用:0
  • 點閱點閱:723
  • 評分評分:
  • 下載下載:164
  • 收藏至我的研究室書目清單書目收藏:0
本文主要研究探討以下幾個問題:連續二維系統之狀態空間實現、離散二維線性系統的最佳控制、離散二維線性系統的最佳追蹤器、連續時間二維系統之離散化二次最佳化控制,及利用連續時間最佳追蹤器之二維線性系統之數位再設計。
本文的貢獻在於(一)藉由已知的轉移函數,提出連續二維系統狀態空間實現的準則,(二)根據羅莎(Roesser)模型,吾人推導出二維系統的一維等效模型,並提出具有可變係數及自由邊界條件之離散二維系統之最佳控制方法,(三)建構一個控制律,並藉由閉迴路控制在完整時間內使離散二維系統追蹤想要的軌跡,(四)提出連續二維系統之離散化二次最佳控制,利用新的狀態向量直接轉換原始連續二維二次成本函數為耦合之離散型態,以建構具有新虛擬控制輸入的新虛擬離散二維模型,間接的求出連續二維系統的離散化二次最佳控制及(五)提出新的二維系統的最佳數位再設計方法,得到動態數位控制法則。

In this dissertation, several researches are presented: state-space realization from a given transfer function of continuous-time two-dimensional systems, optimal regulator for discrete-time two-dimensional linear systems, discrete linear quadratic tracker for two-dimensional linear systems, discretized quadratic optimal regulator for continuous- time two-dimensional systems and digital redesign of continuous-time suboptimal tracker for two-dimensional systems.
This includes the following novel features: (i) An algorithm is presented for the state-space realization of continuous-time two-dimensional systems via a given transfer function, (ii) Based on the Roesser’s model, an equivalent general one-dimensional model of the two-dimensional system has been presented. Then, an optimal control method for discrete-time two-dimensional linear systems with variable coefficients and free boundary conditions is developed, (iii) Construct a control scheme to make the discrete-time two-dimensional linear systems follow the desired trajectories over the entire time intervals by using a closed-loop control law, (iv) A discretized quadratic optimal control for continuous-time two-dimensional system is proposed. A new state vector to directly convert the original continuous-time two-dimensional quadratic cost function into a decoupled discretized form is newly induced. Then, a new virtual discrete-time two-dimensional model with the new virtual control input is constructed for indirectly finding the desired discretized quadratic optimal regulator for the continuous-time two-dimensional system, and (v) Present a new optimal digital redesign technique of two-dimensional system for finding a dynamic digital control law from the given continuous-time two-dimensional systems by minimizing a quadratic cost function.

Chapter 1 Introduction
1.1 Two-dimensional systems and applications
1.2 State-space models of two-dimensional linear systems
1.3 Relations between the models
1.4 Optimal control problem of two-dimensional systems
1.5 Organization of the dissertation
Chapter 2 Mathematical Preliminaries
2.1 Transition matrix and general response formula for Roesser’s model
2.2 Controllability and observability of two-dimensional systems
2.3 Stability of two-dimensional systems
Chapter 3 State-Space Realization of Continuous-Time Two-dimensional Systems
3.1 Introduction
3.2 Background
3.3 Realization of continuous-time two-dimensional systems
3.4 An illustrative example
3.5 Summary
Chapter 4 Optimal Control for Discrete-Time Two-Dimensional Linear Systems with Variable Coefficients
4.1 Introduction
4.2 An equivalent one-dimensional state-space model for discrete-time two-dimensional linear systems
4.3 Optimal control law for discrete-time two-dimensional linear systems
4.4 An illustrative example
4.5 Summary
Chapter 5 Discrete Linear Quadratic Tracker for Discrete-Time
Two-Dimensional Linear Systems
5.1 Introduction
5.2 An equivalent one-dimensional state-space model for discrete-time two-dimensional linear systems
5.3 Discrete linear quadratic tracker for discrete-time two-dimensional systems
5.4 An illustrative example
5.5 Summary
Chapter 6 Discretized Quadratic Optimal Control for Continuous-Time Two-Dimensional Systems
6.1 Introduction
6.2 The discretized cost function
6.3 Optimal control of discretized continuous-time two-dimensional systems
6.4 An illustrative example
6.5 Summary
Chapter 7 Alternative Digital Redesign of Continuous-Time Suboptimal Tracker for Two-Dimensional Systems
7.1 Introduction
7.2 The discretized cost function
7.3 Linear quadratic tracker for discretized continuous-time two-dimensional systems
7.4 An illustrative example
7.5 Summary
Chapter 8 Conclusions

[1] Attasi, S., “Systémes Lineaires Homogènes à Deux Indices,” IRIA Rapport Laboria, 1973.
[2] Attasi, S., “Modélisation et Traitement des Suites à Deux Indices,” IRIA Rapport Laboria, 1975.
[3] Bellman, R., Adaptive Control Process: A Guided Tour. Princeton, NJ: Princeton University Press, 1961.
[4] Bellman, R., “Bellman Special Issue,” IEEE Trans. Automat. Contr., Vol. 26, 1981.
[5] Bryson, A. E. and Y. C. Ho, Applied Optimal Control, Washington D.C., Halsted Press, 1975.
[6] Chen, C. W., J. S. H. Tsai and L. S. Shieh, “Two-dimensional discrete-continuous model conversion,” Circuits, Systems, and Signal Processing, Vol. 18, pp. 565-585, 2000.
[7] Chen, T. and B. A. Francis, Optimal sampled-data control systems, Springer-Verlag, New York, 1995.
[8] Du, C., L. Xie and C. Zhang, “ control and robust stabilization of two- dimensional systems in Roesser models,” Automatica, Vol. 37, pp. 205-211, 2001.
[9] Eising, R., “Controllability and observability of 2-D systems,” IEEE Trans. Automat. Contr., Vol. 24, pp. 132-133, 1979.
[10] Fornasini, E. and G. Marchesini, “State-Space Realization Theory of Two- Dimensional Filters,” IEEE Trans. Automat. Contr., Vol. 2, pp. 484-491, 1976.
[11] Fornasini, E. and G. Marchesini, “Doubly Indexed Dynamical Systems: State Space Models and Structural Properties,” Math. Syst. Theory, Vol. 12, pp. 59-72, 1978.
[12] Fornasini, E. and G. Marchesini, “On the internal stability of two-dimensional filters,” IEEE Trans. Automat. Contr., Vol. 27, pp. 129-130, 1979.
[13] Galkowski, K., "High order discretization of 2-D systems," IEEE Trans. on Circuits and Systems-I: Fundamental Theory and Applications, Vol. 47, pp. 713-722, 2000.
[14] Jagannathan, M and V. L. Syrmos, “ A Linear-Quadratic Optimal Regulator for Two-Dimensional Systems,” IEEE Conf. Decis. Contr., pp. 4172-4177, 1996.
[15] Kaczorek, T., Lecture Notes in Control and Information Sciences 68: Two- Dimensional Linear System, Springer-Verlag, New York, 1985.
[16] Kaczorek, T., “The Linear-Quadratic Optimal Regulator for Singular 2-D Systems with Variable Coefficients,” IEEE Trans. Automat. Contr., Vol. 34, pp. 565-566, 1989.
[17] Kaczorek, T., “General Response Formula and Minimum Energy Control for the General Singular Model of 2-D Systems,” IEEE Trans. Automat. Contr., Vol. 35, pp. 433-436, 1990.
[18] Kaczorek, T., Linear Control Systems. Vol. 2, N.Y., T. Wiley Press, 1992.
[19] Kaczorek, T. and J. Klamka, “Minimum Energy Control of 2-D Linear Systems with Variable Coefficients,” Int. J. Contr., Vol. 44, pp. 645-650, 1986.
[20] Kaczorek, T. and M. Swierkosz, “General Model of n-D System with Variable Coefficients and Its Reduction to 1-D Systems with Variable Structure,” Int. J. Contr., Vol. 48, pp. 609-623, 1988.
[21] Keller, J. P. and B. D. O. Anderson, “A new approach to the discretization of continuous-time controllers,” IEEE Trans. Automat. Contr., Vol. AC-37, pp. 214-223, 1992.
[22] Klamka, J., “Controllability and Minimum Energy Control of 2-D Linear Systems,” Proc. Amer. Contr. Conf., Albuquerque, NM, pp. 3141-3142, 1997.
[23] Koo, C. S. and C. T. Chen, “Fadeeva’s Algorithm for Spatial Dynamical Equations,” Proc. IEEE, Vol. 65, pp. 975-976, 1977.
[24] Kuo, B. C., Digital Control Systems, Holt, Rinehart and Winston, New York, 1992.
[25] Kung, S. T., B. C. Levy, M. Morf and T. Kailath, “New results in 2-D systems theory, Part I: 2-D state-space models — realization and the notions of controllability, observability and minimality,” Proc. IEEE, Vol. 65, pp.945-961, 1977.
[26] Lewis, F. L., “A review of 2-D implicit systems, Automatica, Vol. 28, pp. 345-354, 1992.
[27] Lewis, F. L. and B. G. Mertzios, “On the Analysis of Discrete Linear Time-Invariant Singular Systems,” IEEE Trans. Automat. Contr., Vol. AC-35, 1990.
[28] Lewis, L., Applied Optimal Control and Estimation, Prentice-Hall, New Jersey, 1992.
[29] Li, C. and M. S. Fadali, “Optimal Control of 2-D Systems,” IEEE Trans. Automat. Contr., Vol. 36, pp. 223-228, 1991.
[30] Li, J. S., J. S. H. Tsai and L. S. Shieh, “Optimal control for two-dimensional linear systems with variable coefficients,” Asian Journal of Cont., Vol. 1, pp. 245-257, 1999.
[31] Lu, W. S. and E. B. Lee, “Stability analysis for two-dimensional systems,” IEEE Trans. on Circuits and Systems, Vol. 30, pp. 455-461, 1983.
[32] Marszalek, W., “Two-dimensional state-space discrete models for hyperbolic partial differential equations,” Applied Mathematical Modeling, Vol. 8, pp. 11-14, 1984.
[33] Marszalek, W., “On solving of some heat exchangers problems via image processing equations,” Archiwum Termodynamiki, Vol. 8, No. 1-2, pp. 55-72, 1987.
[34] Marszalek, W., “On modelling of distributed processed with two-dimensional discrete linear equation,” Rozprawy Elektrotechniczne, Vol. 33, pp. 627-640, 1987.
[35] Marszalek, W. and J. Sandecki, “Dynamic Programming for 2-D Discrete Linear Systems,” IEEE Trans. Automat. Contr., Vol. 34, pp. 181-184, 1989.
[36] Nikoukali, R., B. C. Levy and A. S. Willsky, “Control of Discrete-Time Descriptor Systems,” SIAM Conf. Sign. Syst. Contr., 1990.
[37] Pandolfi L., “Exponential stability of 2-D systems,” Systems and Control Letters, Vol. 4, pp. 381-385, 1984.
[38] Paraskevopoulos, P. N. and B. G. Mertzios, “Transfer Function Factorization of SISO 2-D Systems Using State Feedback,” Int. J. Systems Sci., Vol. 12, pp. 1135-1147, 1981.
[39] Rafael, C. G. and E. W. Richard, Digital image processing, Addison-Wesley, Reading, MA, 1993.
[40] Rafee, N., T. Chen and O. P. Malik, “A technique for optimal digital redesign of analog controllers,” IEEE Trans. Contr. Syst. Technology, Vol. 5, pp.89-99, 1995.
[41] Rosenbrock, H. H. State Space and Multivariable Theory. John Wiley, New York, 1970.
[42] Roesser, R. P., “A Discrete State-Space Model for Linear Image Processing,” IEEE Trans. Automat. Contr., Vol. 20, pp. 1-10, 1975.
[43] Rostan, M. and E. B. Lee, “Optimal Control (Quadratic Performance) for Linear Two-Dimensional Systems,” IEEE Conf. Decis. Contr., pp. 307-309, 1989.
[44] Shafiee, M. and M. Haji-Ramazanali, “Solution to the LQR Problem of Variable Coefficients Singular 2-D Systems Using the Wave Advanced Model,” IEE Coll. Multidim. Syst., pp. 12/1-12/8, 1998.
[45] Shieh, L. S., X. M. Zhao and J. L. Zhang, “Locally optimal-digital redesign of continuous-time systems,” IEEE Trans. Indus. Electro., Vol. 36, pp. 511-515, 1989.
[46] Tsai, J. S. H., L. S. Shieh and J. L. Zhang, “An improvement on the digital redesign method based on the block-pulse function approximation,” Circuits Systems Signal Process, Vol. 12, pp. 37-49, 1993.
[47] Turhan, C and Y. Onder, “Sufficient or necessary conditions for modal controllability and observability of Roesser’s 2-D system model,” IEEE Trans. Automat. Contr., Vol. 28, 1983.
[48] Tzafestas, S. G., Multidimensional Systems Techniques and Applications, Marcel Dekker, New York, 1986.

QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top