非线性参数不确定系统的鲁棒控制
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摘要
本文主要研究了两类非线性参数不确定系统的鲁棒H∞自适应控制及干扰衰减问题,对于一类线性化既不可控又不稳定的非线性参数不确定系统,可能导致不存在任何光滑的静态或动态控制器.本文则通过运用参数隔离技术和改进的加幂积分器技术,成功设计出一个非光滑鲁棒自适应动态反馈控制律,使得闭环系统既具有内稳定,又达到干扰衰减.
首先,本文简要介绍了研究现状和背景.
其次,本文研究了一类具有高度非线性性且不具备严格下三角结构的非线性参数不确定系统,通过利用改进的加幂积分器方法及参数隔离技术成功给出了鲁棒H∞自适应控制干扰衰减问题的非光滑控制器,在使闭环系统全局渐近稳定的同时又达到干扰衰减.
最后,本章对具有零动态和干扰的不确定高阶非线性参数系统,通过引进新的假设条件,结合参数隔离技术及改进的幂积分器方法设计出一个非光滑的鲁棒H∞自适应反馈控制律,使得闭环系统既具有内稳定性,又使得系统干扰衰减.
This paper considers the problem of robust H∞adaptive control and disturbanceattenuation for two class of nonlinearly parameterized systems. Because of uncontrollableunstable linearization, there may not exist any smooth static or dynamic stabilizer. Basedon the tool of adding a power integrator and a new parameter separation technique, thispaper gives nonsmooth robust dynamic feedback laws to reject the disturbance and makethe systems internal stability.
Firstly, this paper introduces some related background and development situation.
Secondly, this paper studied a class of nonlinearly parameterized systems with gen-eralized lower triangular are studied. Using the tool of adding a power integrator and anew parameter separation technique, the nonsmooth robust H∞adaptive controllers areconstructed, leading to global asymptotic stability and disturbance attenuation.
Finally, in this paper, the problem of the robust adaptive H∞control is studied for aclass of nonlinearly parameterized systems with zero dynamic and disturbance uncertainty.Introducing new hypothesis, this paper gives the nonsmooth robust H∞adaptive feedbackcontrol laws on the ground of the tool of adding a power integrator and a new parameterseparation technique, leading to reject the disturbance and make the systems internal sta-bility
首先,本文简要介绍了研究现状和背景.
其次,本文研究了一类具有高度非线性性且不具备严格下三角结构的非线性参数不确定系统,通过利用改进的加幂积分器方法及参数隔离技术成功给出了鲁棒H∞自适应控制干扰衰减问题的非光滑控制器,在使闭环系统全局渐近稳定的同时又达到干扰衰减.
最后,本章对具有零动态和干扰的不确定高阶非线性参数系统,通过引进新的假设条件,结合参数隔离技术及改进的幂积分器方法设计出一个非光滑的鲁棒H∞自适应反馈控制律,使得闭环系统既具有内稳定性,又使得系统干扰衰减.
This paper considers the problem of robust H∞adaptive control and disturbanceattenuation for two class of nonlinearly parameterized systems. Because of uncontrollableunstable linearization, there may not exist any smooth static or dynamic stabilizer. Basedon the tool of adding a power integrator and a new parameter separation technique, thispaper gives nonsmooth robust dynamic feedback laws to reject the disturbance and makethe systems internal stability.
Firstly, this paper introduces some related background and development situation.
Secondly, this paper studied a class of nonlinearly parameterized systems with gen-eralized lower triangular are studied. Using the tool of adding a power integrator and anew parameter separation technique, the nonsmooth robust H∞adaptive controllers areconstructed, leading to global asymptotic stability and disturbance attenuation.
Finally, in this paper, the problem of the robust adaptive H∞control is studied for aclass of nonlinearly parameterized systems with zero dynamic and disturbance uncertainty.Introducing new hypothesis, this paper gives the nonsmooth robust H∞adaptive feedbackcontrol laws on the ground of the tool of adding a power integrator and a new parameterseparation technique, leading to reject the disturbance and make the systems internal sta-bility
引文
[1] Willems J. C. Almost invariant subspaces: An approach to hign gain feedback design-Part I: Almost controlled invariant subspaces[J]. IEEE Transaction on Automatic Control,1981,26:235-252.
[2] Marino R, Respondek W, Van der Schaft A J, etal. Nonlinear H∞almost disturbancedecoupling[J]. Syst. Contr. Lett.1994,23:159-168.
[3] Isidori A. A note on almost disturbance decoupling for nonlinear minimum-phase sys-tems[J]. Syst. Contr. Lett.1996,27:191-194.
[4] W. M. Haddad, T. Hayakawa, V. S. Chellablina. Robust adaptive control for nonlinearuncertain systems[J]. Automatica,2003,39(3):551-556.
[5] Z. P. Jiang. Decentranlized and adaptive nonlinear tracking of large-scale systems viaoutput feedback[J]. IEEE Trans. Autom. Control,2000,45(11):2122-2128.
[6] Q. Wang, R. F. Stengel. Robust control of nonlinear systems with paramatic uncertain[J].Automatic,2002,38(9):1591-1599.
[7] X. S. Wang, C. Y. Sum, H. Hong. Robust adaptive control of a class of nonlinear systemswith unknown dead-zone[J]. Automatica,2004,40(3):407-413.
[8] P. D. Christofides. Robust output feedback control of nonlinear singularly perturbed sys-tems[J]. Automatica,2000,36(1):45-52.
[9] D. Cheng, T. J. Tarn, S. K. Spurgeon. On the design of output regulators for nonlinearsystems[J]. Systems Control Letters,2001,43(3):167-179.
[10] H. J. Xu, P. A. Ioannou. Robust adaptive control for a class of mimo nonlinear systemswith guaranteed error bounds[J]. IEEE Transaction on Automatic Control,2003,48(5):728-742.
[11] Y. S. Lee, Y. S. Moon, W. H. Kwon, P. G. Park. Delay-dependent robust H∞control foruncertain systems with a state-delay[J]. Automatica,2004,40:65-72.
[12]S. Xu, T. Chen. Robust∞control for uncertain stochastic systems with state delay[J]. IEEE Trans Autom Control,2002,47:2089-2094.
[13]S. H. Song, J. K. Kim. H∞control of discrete-time linear systems with norm-bounded uncertainties and time delay in state[J]. Automatica,1998,34:137-139.
[14]W. Lin, C. J. Qian. Adding one power integrator:A tool for global stabilization of high-order lower-triangular systems [J], Syst. Control Lett,2000,39(5):339-351.
[15]W. Lin, C. J. Qian. Adaptive control of nonlinearly parameterized systems:a nonsmooth feedback frmework[J], IEEE Trans. Auto. Contr.,2002,47(5):757-774.
[16]W. Lin, C. J. Qian. A continuous feedback approach to global strong stabilization of nonlinear systems [J], IEEE Trans. Auto. Contr.,2001,46(7):1061-1079.
[17]W. Lin, C. J. Qian. Adaptive control of nonlinearly parameterized systems:the smooth feedback case[J], IEEE Trans. Auto. Contr.,2002,47(8):1249-1265.
[18]Bacciotti. Local stabilizability of nonlinear control systems [J], Singapore:World Scientific,1992.
[19]W. P. Dayawansa, C. F. Martin, G. Knowles. Asymptotic stabilization of a class of smooth two dimensional systems [J], SIAM. J. Control Optim,1990,28:1321-1349.
[20]M. Tzamtzi and J. Tsinias. Explicit formulas of feedback stabilizers for a class of triangular systems with uncontrollable linearization [J], Syst. Control Lett.,1999,38:115-126.
[21]毕卫萍,关于高阶不确定非线性系统的鲁棒适应干扰衰减问题[J].系统科学与数学,2006,26(2)：193-205.
[22]W. P. Bi. Robust H∞control for uncertain nonlinear systems [J]. Jrl Sci Complexity,2007,20:545-553.
[23]毕卫萍,张俊峰,柳瑾瑾,非线性不确定参数系统的鲁棒H∞自适应控制[J].南京市大学报(自然科学版),2010,33(4)：6-12.
[24]Marino R, Respondek W, Van der Schaft A J. Almost disturbance decoupling for single-input single-output nonlinear systems. IEEE Trans. Automat. Contr.,1989,34:1013-1017.
[25]Marino R, Respondek W, Van der Schaft A J, et al. Nonlinear H∞almost disturbance decoupling. Syst. Contr. Lett.,1994,23:159-168.
[26]C. J. Qian, W. Lin. Almost disturbance decoupling for a class of high-order nonlinear systems [J]. IEEE Trans. Auto. Contr.,2000,45:1208-1214.
[27]C. I. Bymes, A. Isidori. Asymptotic stabilization of minimum phase nonlinear systems [J]. IEEE Trans. Automat. Contr.,1991,36:1122-1137.
A. Isidori. Nonlinear control systems3rd ed[M]. New York:Springer-Verlag,1995.
A. Isidori. Nonlinear control systems II[M]. New York:Springer-Verlag,1999.
H. Nijmeijer, A. J. van der Schaft. Nonlinear dynamical control systems[M]. New York: Springer-Verlag,1990.
[31]Ezal K, Kokotovic P V. Locally optimal backstepping design [J]. IEEE Trans on Automatic Control,2000,45(2):260-271.
[32]Kanellakopoulos I, Kokotovic P V, Morse S. Syestematic design of adaptive controllers for feedback linearizable systems [J]. IEEE Trans on Automatic Control,1991,36(11):1241-1253.
[33]W. Lin, C. J. Qian. Adaptive regulation of high-order lower-triangular systems:an adding a power integrator technique[J], Syst. Control Lett,2000,39(5):353-364.
[34]C. J. Qian, W. Lin. Recursive observer design, homogeneous approximation and nons-mooth output feedback stabilization of nonlinear system[J]. IEEE Trans. Auto. Contr.2006,51(9):1457-1471.
[35]孙宗耀,刘允刚.一类虚拟控制系数未知但等同高阶非线性系统的状态反馈稳定控制设计[J].自动化学报,2007,33(3)：331-334.
[36]孙宗耀,刘允刚.一类高阶非线性不确定系统自适应稳定控制[J].控制理论与应用,2008,25(1)：40-56.
[2] Marino R, Respondek W, Van der Schaft A J, etal. Nonlinear H∞almost disturbancedecoupling[J]. Syst. Contr. Lett.1994,23:159-168.
[3] Isidori A. A note on almost disturbance decoupling for nonlinear minimum-phase sys-tems[J]. Syst. Contr. Lett.1996,27:191-194.
[4] W. M. Haddad, T. Hayakawa, V. S. Chellablina. Robust adaptive control for nonlinearuncertain systems[J]. Automatica,2003,39(3):551-556.
[5] Z. P. Jiang. Decentranlized and adaptive nonlinear tracking of large-scale systems viaoutput feedback[J]. IEEE Trans. Autom. Control,2000,45(11):2122-2128.
[6] Q. Wang, R. F. Stengel. Robust control of nonlinear systems with paramatic uncertain[J].Automatic,2002,38(9):1591-1599.
[7] X. S. Wang, C. Y. Sum, H. Hong. Robust adaptive control of a class of nonlinear systemswith unknown dead-zone[J]. Automatica,2004,40(3):407-413.
[8] P. D. Christofides. Robust output feedback control of nonlinear singularly perturbed sys-tems[J]. Automatica,2000,36(1):45-52.
[9] D. Cheng, T. J. Tarn, S. K. Spurgeon. On the design of output regulators for nonlinearsystems[J]. Systems Control Letters,2001,43(3):167-179.
[10] H. J. Xu, P. A. Ioannou. Robust adaptive control for a class of mimo nonlinear systemswith guaranteed error bounds[J]. IEEE Transaction on Automatic Control,2003,48(5):728-742.
[11] Y. S. Lee, Y. S. Moon, W. H. Kwon, P. G. Park. Delay-dependent robust H∞control foruncertain systems with a state-delay[J]. Automatica,2004,40:65-72.
[12]S. Xu, T. Chen. Robust∞control for uncertain stochastic systems with state delay[J]. IEEE Trans Autom Control,2002,47:2089-2094.
[13]S. H. Song, J. K. Kim. H∞control of discrete-time linear systems with norm-bounded uncertainties and time delay in state[J]. Automatica,1998,34:137-139.
[14]W. Lin, C. J. Qian. Adding one power integrator:A tool for global stabilization of high-order lower-triangular systems [J], Syst. Control Lett,2000,39(5):339-351.
[15]W. Lin, C. J. Qian. Adaptive control of nonlinearly parameterized systems:a nonsmooth feedback frmework[J], IEEE Trans. Auto. Contr.,2002,47(5):757-774.
[16]W. Lin, C. J. Qian. A continuous feedback approach to global strong stabilization of nonlinear systems [J], IEEE Trans. Auto. Contr.,2001,46(7):1061-1079.
[17]W. Lin, C. J. Qian. Adaptive control of nonlinearly parameterized systems:the smooth feedback case[J], IEEE Trans. Auto. Contr.,2002,47(8):1249-1265.
[18]Bacciotti. Local stabilizability of nonlinear control systems [J], Singapore:World Scientific,1992.
[19]W. P. Dayawansa, C. F. Martin, G. Knowles. Asymptotic stabilization of a class of smooth two dimensional systems [J], SIAM. J. Control Optim,1990,28:1321-1349.
[20]M. Tzamtzi and J. Tsinias. Explicit formulas of feedback stabilizers for a class of triangular systems with uncontrollable linearization [J], Syst. Control Lett.,1999,38:115-126.
[21]毕卫萍,关于高阶不确定非线性系统的鲁棒适应干扰衰减问题[J].系统科学与数学,2006,26(2)：193-205.
[22]W. P. Bi. Robust H∞control for uncertain nonlinear systems [J]. Jrl Sci Complexity,2007,20:545-553.
[23]毕卫萍,张俊峰,柳瑾瑾,非线性不确定参数系统的鲁棒H∞自适应控制[J].南京市大学报(自然科学版),2010,33(4)：6-12.
[24]Marino R, Respondek W, Van der Schaft A J. Almost disturbance decoupling for single-input single-output nonlinear systems. IEEE Trans. Automat. Contr.,1989,34:1013-1017.
[25]Marino R, Respondek W, Van der Schaft A J, et al. Nonlinear H∞almost disturbance decoupling. Syst. Contr. Lett.,1994,23:159-168.
[26]C. J. Qian, W. Lin. Almost disturbance decoupling for a class of high-order nonlinear systems [J]. IEEE Trans. Auto. Contr.,2000,45:1208-1214.
[27]C. I. Bymes, A. Isidori. Asymptotic stabilization of minimum phase nonlinear systems [J]. IEEE Trans. Automat. Contr.,1991,36:1122-1137.
A. Isidori. Nonlinear control systems3rd ed[M]. New York:Springer-Verlag,1995.
A. Isidori. Nonlinear control systems II[M]. New York:Springer-Verlag,1999.
H. Nijmeijer, A. J. van der Schaft. Nonlinear dynamical control systems[M]. New York: Springer-Verlag,1990.
[31]Ezal K, Kokotovic P V. Locally optimal backstepping design [J]. IEEE Trans on Automatic Control,2000,45(2):260-271.
[32]Kanellakopoulos I, Kokotovic P V, Morse S. Syestematic design of adaptive controllers for feedback linearizable systems [J]. IEEE Trans on Automatic Control,1991,36(11):1241-1253.
[33]W. Lin, C. J. Qian. Adaptive regulation of high-order lower-triangular systems:an adding a power integrator technique[J], Syst. Control Lett,2000,39(5):353-364.
[34]C. J. Qian, W. Lin. Recursive observer design, homogeneous approximation and nons-mooth output feedback stabilization of nonlinear system[J]. IEEE Trans. Auto. Contr.2006,51(9):1457-1471.
[35]孙宗耀,刘允刚.一类虚拟控制系数未知但等同高阶非线性系统的状态反馈稳定控制设计[J].自动化学报,2007,33(3)：331-334.
[36]孙宗耀,刘允刚.一类高阶非线性不确定系统自适应稳定控制[J].控制理论与应用,2008,25(1)：40-56.