非线性扰动关联时滞广义系统的鲁棒分散控制
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摘要
关联广义系统是一类在电力系统、经济系统、网络系统等诸多方面有着广泛应用背景的动力系统,在最近的二十年里,关联广义系统理论的研究取得了长足进展和发展。
论文研究了关联广义系统的鲁棒分散控制问题,文中所研究的系统模型是已有相关文献模型的推广和改进。主要内容如下:
首先,简要的介绍了关联广义系统的产生和应用背景、关联广义系统理论的发展、研究概况及关联广义系统鲁棒控制的研究方法。其次,研究了一类带非线性扰动的关联时滞关联广义系统鲁棒分散控制问题。基于Lyapunov稳定理论,通过选取适当的Lyapunov函数,给出了该系统的鲁棒分散控制器的设计方法。
接着,针对一类参数不确定的非线性扰动关联时滞广义系统,研究了H∞状态反馈控制器以及无源状态反馈控制器的设计问题。假设其中的不确定性是范数有界的,通过构造改进的Lyapunov泛函,给出了系统二次稳定性、H∞状态反馈控制器和无源状态反馈控制器存在的条件。仅通过求解相应的线性矩阵不等式(Linear matrix inequality, LMI)就可得到相应的H∞状态反馈控制器和无源状态反馈控制器,数值算例及仿真验证了所给算法的有效性。
最后,对论文做了总结,同时,对进一步的研究工作进行了展望。
The interconnected descriptor system is a kind of dynamics of more general and extensive applied background in power system, economic system, network system and so on. In recently twenty years, it has been developed sufficiently.
This dissertation is a problem about the decentralized robust control of the interconnected descriptor systems. The system’s models are more generalized than others existing literatures.
First of all, the main background and the recent development are considered for the interconnected descriptor systems. The robust control and the research method for the robust control of the systems are also introduced.
Secondly, the problems of the decentralized passive control for the interconnected interconnected time-delay descriptor systems with nonlinear perturbations are investigated. The passive state feedback controllers are designed by selecting some approximate Lyapunov functions.
Thirdly, focuses on the interconnected interconnected time-delay descriptor systems with nonlinear perturbations and uncertainty, the research of quadratic stabilization and H∞controller and passive control are studied. Based on the modified Lyapunov functions, under the assumption that the uncertainty is norm-bounded, the existing conditions of quadratic stabilization and H∞state feedback controller are given. The controllers can be obtained by solving the corresponding linear matrix inequality. A numerical example and simulation are presented to illustrate the validity of this approach. At last, the conclusion and perspective are given.
论文研究了关联广义系统的鲁棒分散控制问题,文中所研究的系统模型是已有相关文献模型的推广和改进。主要内容如下:
首先,简要的介绍了关联广义系统的产生和应用背景、关联广义系统理论的发展、研究概况及关联广义系统鲁棒控制的研究方法。其次,研究了一类带非线性扰动的关联时滞关联广义系统鲁棒分散控制问题。基于Lyapunov稳定理论,通过选取适当的Lyapunov函数,给出了该系统的鲁棒分散控制器的设计方法。
接着,针对一类参数不确定的非线性扰动关联时滞广义系统,研究了H∞状态反馈控制器以及无源状态反馈控制器的设计问题。假设其中的不确定性是范数有界的,通过构造改进的Lyapunov泛函,给出了系统二次稳定性、H∞状态反馈控制器和无源状态反馈控制器存在的条件。仅通过求解相应的线性矩阵不等式(Linear matrix inequality, LMI)就可得到相应的H∞状态反馈控制器和无源状态反馈控制器,数值算例及仿真验证了所给算法的有效性。
最后,对论文做了总结,同时,对进一步的研究工作进行了展望。
The interconnected descriptor system is a kind of dynamics of more general and extensive applied background in power system, economic system, network system and so on. In recently twenty years, it has been developed sufficiently.
This dissertation is a problem about the decentralized robust control of the interconnected descriptor systems. The system’s models are more generalized than others existing literatures.
First of all, the main background and the recent development are considered for the interconnected descriptor systems. The robust control and the research method for the robust control of the systems are also introduced.
Secondly, the problems of the decentralized passive control for the interconnected interconnected time-delay descriptor systems with nonlinear perturbations are investigated. The passive state feedback controllers are designed by selecting some approximate Lyapunov functions.
Thirdly, focuses on the interconnected interconnected time-delay descriptor systems with nonlinear perturbations and uncertainty, the research of quadratic stabilization and H∞controller and passive control are studied. Based on the modified Lyapunov functions, under the assumption that the uncertainty is norm-bounded, the existing conditions of quadratic stabilization and H∞state feedback controller are given. The controllers can be obtained by solving the corresponding linear matrix inequality. A numerical example and simulation are presented to illustrate the validity of this approach. At last, the conclusion and perspective are given.
引文
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4陈禹六.大系统理论及应用.北京:清华大学出版社, 1988
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6李人厚.邵福庆.工业大系统控制理论及应用.西安:西安交通大学出版社,西安1986
7达庆利.大系统理论与方法.南京:东南大学出版社, 1989
8 H. H. Rosenbrock. Structural Properties of Linear Dynamical Systems. Int J Control, 1974, 20(2): 191-202
9 D. C. Lenberger. Singular Dynamic Leotief Systems. Econometrica,1977,45(4): 991-995
10 S. L. Campbell. Singular Systems of Differential Equations. San Francisco: Pitman, 1980
11 I. Masubuchi, Y. Kamitane, A. Ohara, et al. H∞Control for Descriptor Systems: A Matrix Inequalities Approach. Automatic, 1997, 33(4): 669-673
12 L. Y. Dai. Singular Control Systems. Brlieng: Spriner-Verlag,1989
13 E. L. Yip, R. Sincovec. So1vability, Controllability and Observability of Continuous Descriptor Systems. IEEE Trans. On Automatic Control, 1981, 26(3): 702-707
14 A. Ailon. An Approach for Pole Assignment in Singular Systems. IEEE Trans. On Automatic Control, 1989, 34(8): 889-893
15 S. L. Campbell , N. K. Nichols and W. J. Terrel. Duality, Observability and Controllability for Linear Time-Varying Descriptor Systems. Circ. Syst. Sig. Process. 1991, 10(4): 455-470
16马跃超,张庆灵,童松.不确定广义非线性关联大系统的分散鲁棒控制.东北大学学报, 2006, 27(04): 359-361
17史国栋,沃松林,邹云.参数不确定广义大系统的保性能分散控制.控制理论与应用, 2005, 22(06): 913-917
18滕毓发,张庆灵.广义大系统的分散鲁棒镇定.东北大学学报, 2008, 29(02): 178-180
19夏小惠,王为群.非因果离散广义大系统的分散镇定.南京理工大学学报, 2006, 30(01): 65-69
20杨冬梅,印文宁,赵园园.时滞离散广义大系统的稳定性分析与镇定.辽宁师范大学学报, 2009, 32(01): 16-20
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26 M. S. Mahmoud. Adaptive Stabilization of a Class of Interconnected Systems. Boston, Birkhauser, 2003
27 F. H. Hsiao, J. D. Hwang, C. W. Chen and Z. R. Tsai. Robust Stabilization of Nonlinear Multiple Time-Delay Large Systems Via Decentralized Fuzzy Control. IEEE Transactions On Fuzzy Systems, 2005, 13(1): 152-163
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29 Z. R. Xi, D. Z. Cheng, Q. Lu, and S. W. Mei. Nonlinear Decentralized Controller Design for Multi-Machine Power Systems Using Hamiltonian Function Method, Automatic, 2002, 38: 527-534
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31 M. S. Mahmoud, S. Bingulac. Robust Design Of Stabilizing Controllers for Interconnected Time-Delays Systems. Automatica, 1998, 34(6): 795-800
32马跃超,张庆灵.不确定广义组合大系统的分散鲁棒镇定与脉冲分析.物理学报, 2007, 56(4): 1958-1965
33沃松林,吴建成.不确定关联时滞广义大系统的分散鲁棒镇定.电机与控制学报, 2006, 10(05): 508-512
34 S. Xu, C. Yang, Y. Niu, et al. Robust Stabilization for Uncertain Discrete Singular Systems. Automatica, 2001, 37: 769-774
35沃松林,邹云.连续广义线性大系统的稳定性.江苏工业学院学报, 2003, 15(1): 43-46
36 E. Cheres, J. Palmor and S. Gutman. Quantitative Measures of Robustness for Systems Including Delayed Perturbations. IEEE Trans. Automat. Control, 1989, 34(11): 1203-1204
37 A. Hmamed. Further Results on the Robust Stability of Uncertain Time-Delay Systems. Int. J. Systems Sci, 1991, 22(3): 605-614
38舒伟仁,张庆灵.时滞广义系统的状态反馈H∞控制.系统工程与电子技术, 2004, 26(12): 1871-1875
39 S. Yeong-Jeu Sun, H. Jer-Guang and Y. Horng-Chin. On the Stability of Uncertain Systems with Multiple Time-Varying Delays. IEEE Trans. Automat. Control, 1997, 42(1): 101-105
40冯文丽,李胜家.非线性摄动时滞系统时滞变化率最大化鲁棒控制.山西大学学报. 2005, 28(1): 8-10
41彭达洲,胥布工.带非线性扰动的不确定时滞系统的鲁棒稳定性.广东工业大学学报, 2004, 21(1): 22-25
42 Z. Zhizhong, W. Jinzhi and H. Lin. Robust Stabilization for Non-liner Discrete-time Systems . Int J Control, 2004, 77(4): 384-388
43陈东彦,许立滨,徐世杰.一类离散时滞不确定系统的鲁棒控制.电机与控制学报,2002, 6(4): 317-319
44李志虎,邵惠鹤.时滞系统输出反馈无源控制器设计.应用科学学报, 2003, 19(4): 303-307
45 M. S. Mahmoud. Passive Control Synthesis for Uncertain Time Delay Systems. Proceedings of the 37th IEEE Conference on Decision and Control. Tampa, Florida, 1998, 4139-4143
46 M. S. Mahmoud, M. Zribi. Passive Control Synthesis for Uncertain Systems with Multiple-State Delays. Computers and Electrical Engineering, 2004, 28(3): 195-216
47 C. B. Feng. Passive Analysis for Feedback Systems and Its Application. Acta Automatic Sinica,1985, 11(2): 111-117
48 C. B. Feng, K. J. Zhang and S. M. Fei. Passive Based Design of Robust Control Systems. Acta Automatic Sinica, 2003, 25(5): 577-582
49 Y. S. Lee, Y. S. Moon and W. Kwon. Delay-dependent Robust H∞Control for Uncertain Systems with A State-delay. Automatic, 2004, 40(1): 65-72
50 C. Gahinet. Multi-objective Output Feedback Control Via LMI Ptimization. IEEE Trans A C, 1997, 42(7): 896-910
51 L. H. Xie. Output Feedback H-infinite Control of Systems with Parameter Uncertain. Int J Control,1996, 63(3):741-750
52张先明,吴敏.线性时滞系统的时滞相关无源控制.控制理论与应用, 2005, 22(3): 391-401
53 Y. S. Moon, P. Park and W. H. Kwon. Delay-Dependent Robust Stabilization of Uncertain State-delayed Systems. In t. J .Control, 2003, 74(14): 1447-1452
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66 A. Hmamed. Further Results on the Robust Stability of Uncertain Time-delay Systems. Int. J. Systems Sci. 1991,22(3): 605-614
67 W. Shuenn-ahyang, C. Bor-sen and T. Pin-lin. Robust Stability of Uncertain Time-delay Systems. Int. J. Control, 1987, 46(3): 963-970
68 S. Yeong-Jeu Sun, H. Jer-Guang and Y. Horng-Chin. On the Stability of Uncertain Systems with Multiple Time-Varying Delays. IEEE Trans. Control, 1997, 42(1): 101-105
69单伟,王玉田.带非线性扰动的时滞大系统的分散输出反馈镇定.航天返回与遥感, 2003, 3(03): 10-13
70董心壮,张庆灵.时变不确定广义系统的鲁棒无源控制.控制理论于应用, 2004, 21(4): 517-520
71冯纯伯,张侃健,费树岷.基于无源性分析的鲁棒控制系统设计.自动化学报, 1999, 25(5): 577-582
72董心壮,张庆灵,郭凯.具滞后的离散广义系统的无源控制.电机与控制学报,2003, 08(03): 232-234
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2 M. G. Singh, A. Titlti. Systems: Decomposition, Optimization and Control. Pergamon Press, Oxford, 1978
3桂卫华,王鸿贵,沈德耀,吴敏.工业大系统控制理论及应用.长沙:中南工业大学出版社, 1993
4陈禹六.大系统理论及应用.北京:清华大学出版社, 1988
5席裕庚.动态大系统方法导论.北京:国防工业出版社, 1988
6李人厚.邵福庆.工业大系统控制理论及应用.西安:西安交通大学出版社,西安1986
7达庆利.大系统理论与方法.南京:东南大学出版社, 1989
8 H. H. Rosenbrock. Structural Properties of Linear Dynamical Systems. Int J Control, 1974, 20(2): 191-202
9 D. C. Lenberger. Singular Dynamic Leotief Systems. Econometrica,1977,45(4): 991-995
10 S. L. Campbell. Singular Systems of Differential Equations. San Francisco: Pitman, 1980
11 I. Masubuchi, Y. Kamitane, A. Ohara, et al. H∞Control for Descriptor Systems: A Matrix Inequalities Approach. Automatic, 1997, 33(4): 669-673
12 L. Y. Dai. Singular Control Systems. Brlieng: Spriner-Verlag,1989
13 E. L. Yip, R. Sincovec. So1vability, Controllability and Observability of Continuous Descriptor Systems. IEEE Trans. On Automatic Control, 1981, 26(3): 702-707
14 A. Ailon. An Approach for Pole Assignment in Singular Systems. IEEE Trans. On Automatic Control, 1989, 34(8): 889-893
15 S. L. Campbell , N. K. Nichols and W. J. Terrel. Duality, Observability and Controllability for Linear Time-Varying Descriptor Systems. Circ. Syst. Sig. Process. 1991, 10(4): 455-470
16马跃超,张庆灵,童松.不确定广义非线性关联大系统的分散鲁棒控制.东北大学学报, 2006, 27(04): 359-361
17史国栋,沃松林,邹云.参数不确定广义大系统的保性能分散控制.控制理论与应用, 2005, 22(06): 913-917
18滕毓发,张庆灵.广义大系统的分散鲁棒镇定.东北大学学报, 2008, 29(02): 178-180
19夏小惠,王为群.非因果离散广义大系统的分散镇定.南京理工大学学报, 2006, 30(01): 65-69
20杨冬梅,印文宁,赵园园.时滞离散广义大系统的稳定性分析与镇定.辽宁师范大学学报, 2009, 32(01): 16-20
21 R. Sepulchre, M. Jankovic and P. V. Kokotovic. Constructive Nonlinear Control, Springer, London, 1997
22 K. Gu, V. L. Kharitonov and J. Chen. Stability of Time-Delay Systems, Boston, Birkhauser, 2003
23 Y. Wang, L. Xie and C. E. De Souza. Robust Control Of a Class of Uncertain Nonlinear Systems. Systems Control Lett, 1992, 19: 139-149
24 P. L. Liu. Robust Stability of Multiple-Time-Delay Uncertain Systems With Series Nonlinearities. International Journal Of Systems Science, 2001, 32(2): 185-193
25 M. Jankovic. Stabilization of Nonlinear Time-Delay Systems With Delay-Independent Feedback. Proceeding of American Control Conference, 2005, 4253-4258
26 M. S. Mahmoud. Adaptive Stabilization of a Class of Interconnected Systems. Boston, Birkhauser, 2003
27 F. H. Hsiao, J. D. Hwang, C. W. Chen and Z. R. Tsai. Robust Stabilization of Nonlinear Multiple Time-Delay Large Systems Via Decentralized Fuzzy Control. IEEE Transactions On Fuzzy Systems, 2005, 13(1): 152-163
28 C. C. Hua, C. N. Long and X. P. Guan. Decentralized Output Feedback Control For Large-Scale Systems With Time-Delays. Chinese Control Conference, 2005, 964-968
29 Z. R. Xi, D. Z. Cheng, Q. Lu, and S. W. Mei. Nonlinear Decentralized Controller Design for Multi-Machine Power Systems Using Hamiltonian Function Method, Automatic, 2002, 38: 527-534
30 Y. Guo, D. J. Hill and Y. Y. Wang. Nonlinear Decentralized Control of Large-Scale Power Systems, Automatic, 2000, 36: 1275-1289
31 M. S. Mahmoud, S. Bingulac. Robust Design Of Stabilizing Controllers for Interconnected Time-Delays Systems. Automatica, 1998, 34(6): 795-800
32马跃超,张庆灵.不确定广义组合大系统的分散鲁棒镇定与脉冲分析.物理学报, 2007, 56(4): 1958-1965
33沃松林,吴建成.不确定关联时滞广义大系统的分散鲁棒镇定.电机与控制学报, 2006, 10(05): 508-512
34 S. Xu, C. Yang, Y. Niu, et al. Robust Stabilization for Uncertain Discrete Singular Systems. Automatica, 2001, 37: 769-774
35沃松林,邹云.连续广义线性大系统的稳定性.江苏工业学院学报, 2003, 15(1): 43-46
36 E. Cheres, J. Palmor and S. Gutman. Quantitative Measures of Robustness for Systems Including Delayed Perturbations. IEEE Trans. Automat. Control, 1989, 34(11): 1203-1204
37 A. Hmamed. Further Results on the Robust Stability of Uncertain Time-Delay Systems. Int. J. Systems Sci, 1991, 22(3): 605-614
38舒伟仁,张庆灵.时滞广义系统的状态反馈H∞控制.系统工程与电子技术, 2004, 26(12): 1871-1875
39 S. Yeong-Jeu Sun, H. Jer-Guang and Y. Horng-Chin. On the Stability of Uncertain Systems with Multiple Time-Varying Delays. IEEE Trans. Automat. Control, 1997, 42(1): 101-105
40冯文丽,李胜家.非线性摄动时滞系统时滞变化率最大化鲁棒控制.山西大学学报. 2005, 28(1): 8-10
41彭达洲,胥布工.带非线性扰动的不确定时滞系统的鲁棒稳定性.广东工业大学学报, 2004, 21(1): 22-25
42 Z. Zhizhong, W. Jinzhi and H. Lin. Robust Stabilization for Non-liner Discrete-time Systems . Int J Control, 2004, 77(4): 384-388
43陈东彦,许立滨,徐世杰.一类离散时滞不确定系统的鲁棒控制.电机与控制学报,2002, 6(4): 317-319
44李志虎,邵惠鹤.时滞系统输出反馈无源控制器设计.应用科学学报, 2003, 19(4): 303-307
45 M. S. Mahmoud. Passive Control Synthesis for Uncertain Time Delay Systems. Proceedings of the 37th IEEE Conference on Decision and Control. Tampa, Florida, 1998, 4139-4143
46 M. S. Mahmoud, M. Zribi. Passive Control Synthesis for Uncertain Systems with Multiple-State Delays. Computers and Electrical Engineering, 2004, 28(3): 195-216
47 C. B. Feng. Passive Analysis for Feedback Systems and Its Application. Acta Automatic Sinica,1985, 11(2): 111-117
48 C. B. Feng, K. J. Zhang and S. M. Fei. Passive Based Design of Robust Control Systems. Acta Automatic Sinica, 2003, 25(5): 577-582
49 Y. S. Lee, Y. S. Moon and W. Kwon. Delay-dependent Robust H∞Control for Uncertain Systems with A State-delay. Automatic, 2004, 40(1): 65-72
50 C. Gahinet. Multi-objective Output Feedback Control Via LMI Ptimization. IEEE Trans A C, 1997, 42(7): 896-910
51 L. H. Xie. Output Feedback H-infinite Control of Systems with Parameter Uncertain. Int J Control,1996, 63(3):741-750
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