时滞模糊系统的多目标控制
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摘要
模糊控制技术作为一种控制方法,能有效地处理精确数学模型难以建立的复杂系统,已引起广泛关注。本文针对当前Takagi-Sugeno(T-S)时滞模糊系统的研究现状及存在的问题,在深入研究模糊系统及时滞系统的基础上,较为系统地研究了T-S时滞模糊系统的多目标控制问题。首先,本文研究了一类T-S时滞模糊系统的H_2/H_∞控制问题,设计了模糊状态反馈控制器,保证了闭环系统稳定且满足一定的H_2/H_∞性能指标。其次,针对所考虑模糊系统的状态不完全能观测时,本文研究了基于动态输出反馈的H_2/H_∞控制问题,给出了该问题可解的充分条件。本文还研究了一类T-S模糊时滞系统的H_∞/L_2-L_∞控制问题。利用Lyapunov稳定性理论和矩阵变换技术,设计了模糊状态反馈控制器,保证了闭环系统渐近稳定且满足一定的H_∞/L_2-L_∞性能指标。此外,针对一类离散T-S模糊时滞系统,本文研究了其H_2/H_∞控制问题,得到了该问题可解的充分条件并给出了期望的模糊状态反馈控制器的参数表达式。本文中各类控制器的存在条件都通过一组线性矩阵不等式而给出,因而,所期望的控制器都可以利用Matlab软件中的LMI控制工具箱通过求解相关的线性矩阵不等式而获得。
Fuzzy logic control technique,as one of the most effective approaches to controlling complex systems which are mathematically poorly modeled,has received considerable attention during the past decades.In the light of recent work in Takagi-Sugeno(T-S)delayed fuzzy systems and with the intensive study on both the time-delay systems and fuzzy systems, this dissertation provides a systematic study on the theory of multi-objective control for T-S delayed fuzzy systems.Firstly,the problem of H_2/H_∞control is investigated;fuzzy state feedback controllers are designed to guarantee the closed-loop system is asymptotically stable and satisfies a prescribed H_2/H_∞performance level.In the case when not all states are available for feedback,the problem of H_2/H_∞control via dynamic output feedback controllers is addressed;.a sufficient condition for the solvability of the problem is provided.This dissertation also deals with the H_∞/L_2-L_∞control problem for a class of T-S delayed fuzzy systems.By the Lyapunov stability theory and the techniques on matrix transformation,fuzzy state feedback controllers are designed such that the closed-loop system is asymptotically stable while ensuring a prescribed H_∞/L_2-L_∞performace level.Finally,the problem of H_2/H_∞control for a class of discrete T-S delayed fuzzy systems is considered;a sufficient condition for the solvability of the problem is obtained and algebraic expressions of desired fuzzy state feedback controllers are also given.It is pointed out that all of the derived conditions guaranteeing the existence of controllers in the dissertation are in terms of a set of linear matrix inequalities.Therefore,desired controllers can be constructed by using the Matlab LMI Control Toolbox to solve certain linear matrix inequalities.
Fuzzy logic control technique,as one of the most effective approaches to controlling complex systems which are mathematically poorly modeled,has received considerable attention during the past decades.In the light of recent work in Takagi-Sugeno(T-S)delayed fuzzy systems and with the intensive study on both the time-delay systems and fuzzy systems, this dissertation provides a systematic study on the theory of multi-objective control for T-S delayed fuzzy systems.Firstly,the problem of H_2/H_∞control is investigated;fuzzy state feedback controllers are designed to guarantee the closed-loop system is asymptotically stable and satisfies a prescribed H_2/H_∞performance level.In the case when not all states are available for feedback,the problem of H_2/H_∞control via dynamic output feedback controllers is addressed;.a sufficient condition for the solvability of the problem is provided.This dissertation also deals with the H_∞/L_2-L_∞control problem for a class of T-S delayed fuzzy systems.By the Lyapunov stability theory and the techniques on matrix transformation,fuzzy state feedback controllers are designed such that the closed-loop system is asymptotically stable while ensuring a prescribed H_∞/L_2-L_∞performace level.Finally,the problem of H_2/H_∞control for a class of discrete T-S delayed fuzzy systems is considered;a sufficient condition for the solvability of the problem is obtained and algebraic expressions of desired fuzzy state feedback controllers are also given.It is pointed out that all of the derived conditions guaranteeing the existence of controllers in the dissertation are in terms of a set of linear matrix inequalities.Therefore,desired controllers can be constructed by using the Matlab LMI Control Toolbox to solve certain linear matrix inequalities.
引文
1 孙增圻等.智能控制理论与技术.第1版.北京:清华大学出版社,1997
2 诸静.模糊控制原理与应用.第1版.北京:机械工业出版社,1995
3 L.X.Wang,Adaptive Fuzzy Systems and Control:Design and stability and analysis,Englewood Cliffs,NJ:Prentice-Hall,1994
4 L.Dugard and E.I.Veriest.Stability and Control of Time-Delay Systems.Berlin:Springer,1998.
5 J.K.Hale.Theory of Functional Di.erential Equations.New York:Springer-Verlag,1977.
6 V.B.Kolmanovskii and A.D.Myshkis.Applied Theory of Functional Di.erential Equations.Dordrecht:Kluwer Academic Publishers,1992.
7 马文阁等.模糊时滞系统的输出反馈控制及其稳定性.控制与决策.2002(1):25-27
8 L.Zadeh.Outline of a new approach to the analysis of complex systems and decision processes.IEEE Trans.Syst.,Man,Cybem.,1973(3):28-44
9 T.Tanaka and M.Sugeno.Fuzzy identification of systems and its application to modeling and control.IEEE Trans.Syst.,Man,Cybem,1985(15):116-132
10 K.Tanaka and M.Sano.A robust stabilizaiton problem of fuzzy control systems and its application to backing up of a truck-trailer.IEEE Trans.Fuzzy Sys.,1994(2):119-134
11 Y.Chan and B.-S.Chen.Robust tracking designs for both holonomic and nonholonomic constrained mechanical systems:adaptive fuzzy approach.IEEE Trans.Fuzzy Syst.,2000(8):46-65
12 H.Lee and M.Tomizuka.Robust adaptive control using a universal approximator for SISO nonlinear systems.IEEE Trans.Fuzzy Syst.,2000(8):95-106
13 T.Tanaka,T.Ikeda,and H.O.Wang.Robust stabilization of a class of uncertain nonlinear systems via fuzzy control:Quadratic stability,control theory,and linear matrix inequlities.IEEE Trans.Fuzzy Sys.,1996(4):1-13
14 S.G.Cao,N.W.Rees,and G.Feng.Identification and control for a class of complex systems,Part Ⅰ:Fuzzy modelling and identification.Automatica.1997(33):1017-1028
15 S.G.Cao,N.W.Rees,and G.Feng.Analysis and design for a class of complex control systems.Part Ⅱ:Fuzzy controller design.Automatica.1997(33):1029-1039
16 X.Li and C.E.de Souza.Criteria for robust stability and stabilization of uncertain linear systems with state delay.Automatica,1997(33):1657-1662.
17 S.O.R.Moheim I.R.Petesen.Optimal quadratic guaranteed cost control of a class of uncertain time-delay systems.IEE Proc.Control Theory Appl.1997(144):183-188
18 X. Li and C. E. DE Souza. Delay-dependent robust stability and stabilization of uncertain linear delay systems: a linear matrix inequality approach. IEEE Trans. Automat. Contr. 1997(42): 1144-1148
19 H. H. Choi and M. J. Chung. Memoryless H_∞ controller design for linear systems with delayed state and control. Automatica, 1995(31):917-919
20 E. T. Jeung, D. C. Oh, J. H. Kim, and H. B. Park. Robust controller design for uncertain systems with time delays: LMI approach. Automatica, 1996(32):1229-1231
21 M. S. Mahmoud. Adaptive control of a class of time-delay systems with uncertain parameters. Int. J. Control, 2006(63):937-950
22 F. Zheng, Q.-G Wang, and T. H. Lee. Adaptive robust control of uncertain time delay systems. Automatica, 2005(40):1375-1383
23 Y.-Y. Cao and P. M. Frank. Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach. IEEE Trans. Fuzzy Syst., 2000(8):200-211
24 Y.-Y. Cao and P. M. Frank. Robust H_∞ disturbance attenuation for a class of uncertain discrete-time fuzzy systems. IEEE Trans. Fuzzy Syst., 2000(8):406-415
25 Y.-Y. Cao and P. M. Frank. Stability analysis and synthesis of nonlinear time-delay systems via linear Takagi-Sugeno fuzzy models, Fuzzy Sets and Systems, 2001(124): 213-229
26 C. Chen, G Feng and X. Guan. Delay-dependent stability analysis and controller synthesis for discrete-time T-S fuzzy systems with time delays. IEEE Trans. Fuzzy Syst., 2005(13): 630-643
27 B. S. Chen, C. S. Tseng, and H. J. Uang. Mixed fuzzy output feedback control design for nonlinear dynamic systems: An LMI approach. IEEE Trans. Fuzzy Sys., 2000(8):249-265
28 G Feng. Approaches to quadratic stabilization of uncertain fuzzy dynamic systems. IEEE Trans. Circuits Sys., 2001(48):760-769
29 G Cao, N. Rees, and G Feng, control of uncertain dynamical fuzzy discrete-time systems. IEEE Trans. Syst., Man, Cybern., 2001(31):802-812
30 T. M. Guerra and W. Perruquetti. Non-quadratic stabilisation of discrete Takagi Sugeno fuzzy models. Proc. 2001 IEEE Internat. Fuzzy Systems Conf., pages 1271—1274, April, 2001.
31 H. J. Lee, J. B. Park, and G Chen. Robust fuzzy control of nonlinear systems with parametric uncertainties. IEEE Trans. Fuzzy Sys., 2001(9):369-379
32 T. Takagi, T. and M. Sugeno. Fuzzy identification of systems and its applications to modelling and control, IEEE Trans. Syst. Man Cybernet. 1985(15):116-132.
33 L. K. Wong, F. H. F. Leung and P. K. S. Tam. Fuzzy model-based control for inverted pendulum. Electron. Lett., 1996(32):1683-1685
34 H. O.Wang, K. Tanaka and M. F. Griffin. An approach to fuzzy control of nonlinear systems: stability and design issues. IEEE Trans on Fuzzy Systems, 1996(4):14-23
35 K.Tanka, T. Ikeda and H. O. Wang. Robust Stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stabilizability, H_∞ control theory, and linear matrix inequalities. IEEE Trans on Fuzzy Systems, 1996(4): 1-13
36 K.Tanka, T. Hori and H. O. Wang. A multiple Lyapunov function approach to stabilization of fuzzy control systems. IEEE Trans on Fuzzy Systems, 2003(11):582-589
37 D. Choi and P. Park. H_∞ state-feedback controller design for discrete-time fuzzy systems using fuzzy weighting dependent. Lyapunov fuctions. IEEE Trans.Fuzzy Sys., 2003(11):271-278
38 S. Zhou, G Feng, L. James, and S. Xu. Robust H_∞ control for discrete-time fuzzy systems via basis-dependent lyapunov functions. Information Sciences, 2005(174): 197-217
39 X. Liu and Q. Zhang. New approaches to H_∞, controller designs based on fuzzy observers for T-S fuzzy systems via LMI. Automatica, 2003(39): 1571 - 1582.
40 X. Liu and Q. Zhang. Approaches to quadratic stability conditions and H_∞ control designs for T-S fuzzy fystems. IEEE Trans.Fuzzy Sys. 2003(11):830—839
41 S. Xu and J. Lam. Robust H_∞ control for uncertain discrete time-delay fuzzy systems via output feedback controllers. IEEE Trans. Fuzzy Sys. 2005(13): 82-93
42 B. Chen and X. Liu. Fuzzy guaranteed cost control for nonlinear systems with time-varying delay. IEEE Trans.Fuzzy Sys. 2005(13): 238-249
43 S. Xu and J. Lam. Exponential H_∞, filter design for uncertain Takagi-Sugeno fuzzy systems with time delay. Engineering Applications of Artificial Intelligence, 2004(17): 645-659
44 M. A. Rotea and P. P. Khargonekar. H_2 optimal control with an H_∞ constraint: the state feedback case. Automatica, 1991(27): 307-316.
45 O. L. V. Costa and R. P. Marques. Mixed H_2/H_∞-control of discrete-time Markovian jump linear systems. IEEE Transactions on Automatic Control, 1998(43): 95-100.
46 P. P. Khargonekar and M. A. Rotea. Mixed H_2/H_∞ control: a convex optimization approach. IEEE Transactions on Automatic Control. 1991(36): 824-837.
47 D. J. N. Limebeer, B. D. O. Anderson, and B. A. Hendel. Nash game approach to mixed H_2/H_∞ control. IEEE Transactions on Automatic Control. 1994(39): 69-82.
48 S. Xu and T. Chen. Robust H_∞ control for uncertain stochastic systems with state delay. IEEE Transactions on Automatic Control.2002(47):2089-2094
49 Wilson D A.Convolution and Hankel Operator Norms for Linear Systems.IEEE Trans on Automatic Control,1989(34):94-97
50 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
2 诸静.模糊控制原理与应用.第1版.北京:机械工业出版社,1995
3 L.X.Wang,Adaptive Fuzzy Systems and Control:Design and stability and analysis,Englewood Cliffs,NJ:Prentice-Hall,1994
4 L.Dugard and E.I.Veriest.Stability and Control of Time-Delay Systems.Berlin:Springer,1998.
5 J.K.Hale.Theory of Functional Di.erential Equations.New York:Springer-Verlag,1977.
6 V.B.Kolmanovskii and A.D.Myshkis.Applied Theory of Functional Di.erential Equations.Dordrecht:Kluwer Academic Publishers,1992.
7 马文阁等.模糊时滞系统的输出反馈控制及其稳定性.控制与决策.2002(1):25-27
8 L.Zadeh.Outline of a new approach to the analysis of complex systems and decision processes.IEEE Trans.Syst.,Man,Cybem.,1973(3):28-44
9 T.Tanaka and M.Sugeno.Fuzzy identification of systems and its application to modeling and control.IEEE Trans.Syst.,Man,Cybem,1985(15):116-132
10 K.Tanaka and M.Sano.A robust stabilizaiton problem of fuzzy control systems and its application to backing up of a truck-trailer.IEEE Trans.Fuzzy Sys.,1994(2):119-134
11 Y.Chan and B.-S.Chen.Robust tracking designs for both holonomic and nonholonomic constrained mechanical systems:adaptive fuzzy approach.IEEE Trans.Fuzzy Syst.,2000(8):46-65
12 H.Lee and M.Tomizuka.Robust adaptive control using a universal approximator for SISO nonlinear systems.IEEE Trans.Fuzzy Syst.,2000(8):95-106
13 T.Tanaka,T.Ikeda,and H.O.Wang.Robust stabilization of a class of uncertain nonlinear systems via fuzzy control:Quadratic stability,control theory,and linear matrix inequlities.IEEE Trans.Fuzzy Sys.,1996(4):1-13
14 S.G.Cao,N.W.Rees,and G.Feng.Identification and control for a class of complex systems,Part Ⅰ:Fuzzy modelling and identification.Automatica.1997(33):1017-1028
15 S.G.Cao,N.W.Rees,and G.Feng.Analysis and design for a class of complex control systems.Part Ⅱ:Fuzzy controller design.Automatica.1997(33):1029-1039
16 X.Li and C.E.de Souza.Criteria for robust stability and stabilization of uncertain linear systems with state delay.Automatica,1997(33):1657-1662.
17 S.O.R.Moheim I.R.Petesen.Optimal quadratic guaranteed cost control of a class of uncertain time-delay systems.IEE Proc.Control Theory Appl.1997(144):183-188
18 X. Li and C. E. DE Souza. Delay-dependent robust stability and stabilization of uncertain linear delay systems: a linear matrix inequality approach. IEEE Trans. Automat. Contr. 1997(42): 1144-1148
19 H. H. Choi and M. J. Chung. Memoryless H_∞ controller design for linear systems with delayed state and control. Automatica, 1995(31):917-919
20 E. T. Jeung, D. C. Oh, J. H. Kim, and H. B. Park. Robust controller design for uncertain systems with time delays: LMI approach. Automatica, 1996(32):1229-1231
21 M. S. Mahmoud. Adaptive control of a class of time-delay systems with uncertain parameters. Int. J. Control, 2006(63):937-950
22 F. Zheng, Q.-G Wang, and T. H. Lee. Adaptive robust control of uncertain time delay systems. Automatica, 2005(40):1375-1383
23 Y.-Y. Cao and P. M. Frank. Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach. IEEE Trans. Fuzzy Syst., 2000(8):200-211
24 Y.-Y. Cao and P. M. Frank. Robust H_∞ disturbance attenuation for a class of uncertain discrete-time fuzzy systems. IEEE Trans. Fuzzy Syst., 2000(8):406-415
25 Y.-Y. Cao and P. M. Frank. Stability analysis and synthesis of nonlinear time-delay systems via linear Takagi-Sugeno fuzzy models, Fuzzy Sets and Systems, 2001(124): 213-229
26 C. Chen, G Feng and X. Guan. Delay-dependent stability analysis and controller synthesis for discrete-time T-S fuzzy systems with time delays. IEEE Trans. Fuzzy Syst., 2005(13): 630-643
27 B. S. Chen, C. S. Tseng, and H. J. Uang. Mixed fuzzy output feedback control design for nonlinear dynamic systems: An LMI approach. IEEE Trans. Fuzzy Sys., 2000(8):249-265
28 G Feng. Approaches to quadratic stabilization of uncertain fuzzy dynamic systems. IEEE Trans. Circuits Sys., 2001(48):760-769
29 G Cao, N. Rees, and G Feng, control of uncertain dynamical fuzzy discrete-time systems. IEEE Trans. Syst., Man, Cybern., 2001(31):802-812
30 T. M. Guerra and W. Perruquetti. Non-quadratic stabilisation of discrete Takagi Sugeno fuzzy models. Proc. 2001 IEEE Internat. Fuzzy Systems Conf., pages 1271—1274, April, 2001.
31 H. J. Lee, J. B. Park, and G Chen. Robust fuzzy control of nonlinear systems with parametric uncertainties. IEEE Trans. Fuzzy Sys., 2001(9):369-379
32 T. Takagi, T. and M. Sugeno. Fuzzy identification of systems and its applications to modelling and control, IEEE Trans. Syst. Man Cybernet. 1985(15):116-132.
33 L. K. Wong, F. H. F. Leung and P. K. S. Tam. Fuzzy model-based control for inverted pendulum. Electron. Lett., 1996(32):1683-1685
34 H. O.Wang, K. Tanaka and M. F. Griffin. An approach to fuzzy control of nonlinear systems: stability and design issues. IEEE Trans on Fuzzy Systems, 1996(4):14-23
35 K.Tanka, T. Ikeda and H. O. Wang. Robust Stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stabilizability, H_∞ control theory, and linear matrix inequalities. IEEE Trans on Fuzzy Systems, 1996(4): 1-13
36 K.Tanka, T. Hori and H. O. Wang. A multiple Lyapunov function approach to stabilization of fuzzy control systems. IEEE Trans on Fuzzy Systems, 2003(11):582-589
37 D. Choi and P. Park. H_∞ state-feedback controller design for discrete-time fuzzy systems using fuzzy weighting dependent. Lyapunov fuctions. IEEE Trans.Fuzzy Sys., 2003(11):271-278
38 S. Zhou, G Feng, L. James, and S. Xu. Robust H_∞ control for discrete-time fuzzy systems via basis-dependent lyapunov functions. Information Sciences, 2005(174): 197-217
39 X. Liu and Q. Zhang. New approaches to H_∞, controller designs based on fuzzy observers for T-S fuzzy systems via LMI. Automatica, 2003(39): 1571 - 1582.
40 X. Liu and Q. Zhang. Approaches to quadratic stability conditions and H_∞ control designs for T-S fuzzy fystems. IEEE Trans.Fuzzy Sys. 2003(11):830—839
41 S. Xu and J. Lam. Robust H_∞ control for uncertain discrete time-delay fuzzy systems via output feedback controllers. IEEE Trans. Fuzzy Sys. 2005(13): 82-93
42 B. Chen and X. Liu. Fuzzy guaranteed cost control for nonlinear systems with time-varying delay. IEEE Trans.Fuzzy Sys. 2005(13): 238-249
43 S. Xu and J. Lam. Exponential H_∞, filter design for uncertain Takagi-Sugeno fuzzy systems with time delay. Engineering Applications of Artificial Intelligence, 2004(17): 645-659
44 M. A. Rotea and P. P. Khargonekar. H_2 optimal control with an H_∞ constraint: the state feedback case. Automatica, 1991(27): 307-316.
45 O. L. V. Costa and R. P. Marques. Mixed H_2/H_∞-control of discrete-time Markovian jump linear systems. IEEE Transactions on Automatic Control, 1998(43): 95-100.
46 P. P. Khargonekar and M. A. Rotea. Mixed H_2/H_∞ control: a convex optimization approach. IEEE Transactions on Automatic Control. 1991(36): 824-837.
47 D. J. N. Limebeer, B. D. O. Anderson, and B. A. Hendel. Nash game approach to mixed H_2/H_∞ control. IEEE Transactions on Automatic Control. 1994(39): 69-82.
48 S. Xu and T. Chen. Robust H_∞ control for uncertain stochastic systems with state delay. IEEE Transactions on Automatic Control.2002(47):2089-2094
49 Wilson D A.Convolution and Hankel Operator Norms for Linear Systems.IEEE Trans on Automatic Control,1989(34):94-97
50 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