不确定非线性系统的输出反馈控制
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摘要
非线性系统的控制问题是目前控制界研究的一个重要课题。总的来说,我们在有关非线性系统的状态反馈控制方面已经取得了大量的研究成果,但是相比较而言,在非线性系统的输出反馈控制方面所取得的成果却甚微,许多问题还有待于进一步研究。特别是具有严格反馈控制结构且带有未知控制方向的一类非线性系统的输出反馈控制设计问题和带有常增益率的一类不确定非线性系统的全局输出反馈稳定问题,我们更需要深一步的加以讨论与研究。本篇论文主要研究的就是这两种非线性系统的输出反馈控制问题。
论文按照以下结构组织：
第一章：介绍所研究课题的背景知识,国内外相关研究状况和本课题研究的理论意义和实际应用,并说明本文的主要工作。
第二章：介绍了本篇论文所涉及到的相关基础理论知识。主要包括一些基本的概念,相关的理论以及引理。具体来讲主要介绍了控制Lyapunov函数的定义,Nussbaum函数的定义以及相关引理。另外,重点介绍了Back-stepping设计方法在非线性系统中的应用。
第三章：研究了一类带有未知控制方向的不确定非线性系统的输出反馈自适应控制问题。由于系统的控制方向未定,因而我们引入Nussbaum函数的概念。Nussbaum函数对于解决这种系统的控制问题有很大的优势
第四章：研究了带有依赖于输出的增益率的一类不确定非线性系统的全局输出反馈稳定问题。该系统更具有一般性,通过设计高增益观测器以及相应的误差系统分析,利用递归步骤设计出了相应的控制器,从而解决了系统的全局稳定问题。
第五章：对论文内容进行总结,并提出进一步研究的方向
Nonlinear system control is an important topic in control theory. In all, we have got a lot of results in the area of state-feedback adaptive control for a class of nonlinear systems. But comparatively speaking, we have got fewer in the area of output-feedback adaptive control for a class of nonlinear systems, moreover, there are still many problems to be solved. Specially, the problem of output-feedback adaptive control for a class of nonlinear systems in strict feedback form with unknown control directions and globle output-feedback stabilization for uncertain nonlinear systems with constant incremental about witch we need to discuss and research futher. In this paper, what we will talk about these two kind of nonlinear systems.
My thesis is organized as follows:
Chapter 1, Introduce the background of this topic, internal and overseas research situations, theoretical and Practical significance, the main contributions of this dissertation.
Chapter 2, Introduce the basic theory involved in my thesis, including some basic con(?)epts, related theory and some lemmas. Specifically we mainly introduce the definition of Lyapunov function, Nussbaum function and some related lemmas. In addition we make our focus on the introduction of the application of back-stepping design in nonlinear system.
Chapter 3, Introduce the output-feedback adaptive control for a class of nonlinear systems with unknown control directions. Because of the unknown control directions, we pull in the concept of Nussbaum function witch has an advantage in solving this control problem for this kind of system.
Chapter 4, Introduce the problem of globle output-feedback stabilization for uncertain nonlinear systems with output dependent incremental. Our systems is more general than any others., by designing a dynamic high gain observer and analyzing the error system between the original system and the observer,then we give the controller based on a recursive procedure.
Chapter 5, Summarize this papers and propose the problem for further research.
论文按照以下结构组织：
第一章：介绍所研究课题的背景知识,国内外相关研究状况和本课题研究的理论意义和实际应用,并说明本文的主要工作。
第二章：介绍了本篇论文所涉及到的相关基础理论知识。主要包括一些基本的概念,相关的理论以及引理。具体来讲主要介绍了控制Lyapunov函数的定义,Nussbaum函数的定义以及相关引理。另外,重点介绍了Back-stepping设计方法在非线性系统中的应用。
第三章：研究了一类带有未知控制方向的不确定非线性系统的输出反馈自适应控制问题。由于系统的控制方向未定,因而我们引入Nussbaum函数的概念。Nussbaum函数对于解决这种系统的控制问题有很大的优势
第四章：研究了带有依赖于输出的增益率的一类不确定非线性系统的全局输出反馈稳定问题。该系统更具有一般性,通过设计高增益观测器以及相应的误差系统分析,利用递归步骤设计出了相应的控制器,从而解决了系统的全局稳定问题。
第五章：对论文内容进行总结,并提出进一步研究的方向
Nonlinear system control is an important topic in control theory. In all, we have got a lot of results in the area of state-feedback adaptive control for a class of nonlinear systems. But comparatively speaking, we have got fewer in the area of output-feedback adaptive control for a class of nonlinear systems, moreover, there are still many problems to be solved. Specially, the problem of output-feedback adaptive control for a class of nonlinear systems in strict feedback form with unknown control directions and globle output-feedback stabilization for uncertain nonlinear systems with constant incremental about witch we need to discuss and research futher. In this paper, what we will talk about these two kind of nonlinear systems.
My thesis is organized as follows:
Chapter 1, Introduce the background of this topic, internal and overseas research situations, theoretical and Practical significance, the main contributions of this dissertation.
Chapter 2, Introduce the basic theory involved in my thesis, including some basic con(?)epts, related theory and some lemmas. Specifically we mainly introduce the definition of Lyapunov function, Nussbaum function and some related lemmas. In addition we make our focus on the introduction of the application of back-stepping design in nonlinear system.
Chapter 3, Introduce the output-feedback adaptive control for a class of nonlinear systems with unknown control directions. Because of the unknown control directions, we pull in the concept of Nussbaum function witch has an advantage in solving this control problem for this kind of system.
Chapter 4, Introduce the problem of globle output-feedback stabilization for uncertain nonlinear systems with output dependent incremental. Our systems is more general than any others., by designing a dynamic high gain observer and analyzing the error system between the original system and the observer,then we give the controller based on a recursive procedure.
Chapter 5, Summarize this papers and propose the problem for further research.
引文
[1]王划一,杨西霞,林家恒,杨立才.自动控制原理[M].北京：国防工业出版社,2001.2-5.
[2]郑大钟.线性系统理论[M].北京：清华大学出版社,2002.12-16.
[3]C. Reboulet, P. Mouyon, C. Champetier. About the local linearization of nonlinear systems [J]. Algebraic and Geometric Methods in Nonlinear Control Theory, Fliess M. And Hazewinkel M. eds., Reidel,1986:311-312.
[4]R. Marino, P. V. Kokotovic. A geometric approach to nonlinear singularly perturbed control systems [J]. Automatica,1988,24(1):31-41.
[5]A. Isidori, A. J. Krener, C. G. Hiorgi, S. Monaco. Nonlinear decoupling via feedback:a differential geometric approach [J]. IEEE Trans. Aut. Contr,1981,26(2):331-345.
[6]曹建福,韩崇昭,方洋旺.非线性系统理论及应用[M].西安：西安交通大学出版社,2001.
[7]胡跃明.非线性系统理论及应用[M].北京：国防工业出版社,2001.
[8]刘桂英.自适应控制的应用[M].上海：上海电机技术高等专科学校学报.
[9]黄布毅.非线性控制系统的思想与方法[D].郑州：郑州轻工业学院学报.
[10]吴建国,张培健.非线性系统控制新方法研究[S].南通工学院学报(自然科学出版社).
[11]高莲,包曙红.关于L稳定性若干定理的推广[J].内蒙古师范大学学报(自然科学汉文版).
[12]吕玉华,徐润.L稳定性理论若干定理的推广.2006,(04)
[13]祁荣宾.基于输入输出线性化方法实现混沌系统加同步.自动化技术与应用，2004.
[14]陈谋,蒋长生.不确定非线性系统控制方法概述.南京：南京航空航天大学自动化学院.
[15]Kanellakopoulos I, Kokotovic P V, Morse A S. Systematic design of adaptive controllers for Feedback linearizable systems. IEEE Transactions on Automatic Control,1991,36(11): 1241-1253.
[16]Krstic M, Kanellakopoulos I, Kokotovic P V. Nonlinear and Adaptive Control Design. New York:John Wiley and Sons,1995.
[17]Freeman R A, Kokotovic P V. Robust Nonlinear Control Design. Boston:Birkhauser, 1996.
[18]Ge S S, Wang C. Adaptive NN control of uncertain nonlinear pure-feedback systems. Automatica,1996.
[19]Nussbaum. R D. Some remarks on a conjecture in parameter adaptive control. Systems and Control Letters,1983,3(5):243-246.
[20]Ye X D, Jiang J P. Adaptive nonlinear design without a priori knowledge of control directions. IEEE Transactions on Automatic Control,1998,43(11):1617-1621.
[21]Zhang Y, Wen C Y, Soh Y C. Adaptive backstepping control design for systems with unknown high-frequency gain. IEEE Transactions on Automatic Control,2000, 45(12):2350-2354.
[22]Martesson B. Remarks on adaptive stabilization of first order nonlinear systems. Systems and Control Letters,1990,14(1):1-7
[23]Kaloust J, Qu Z. Continuous robust control design for nonlinear uncertain systems without a priori knowledge of control design. IEEE Transactions on Automatic Control,1995,40(2): 276-281.
[24]Ye X D. Adaptive nonlinear output feedback control with unknown high-frequency gain sign. IEEE Transactions on Automatic Control,2001,56(1):112-115.
[25]Jiang Z P, Mareels I, Hill D J, Huang J. A unifying framework for global regulation via nonlinear output feedback:from ISS to iISS. IEEE Transactions on Automatic Control, 2004,49(4):549-562.
[26]Ding Z T. Global adaptive output feedback stabilization of nonlinear systems of any relative degree with unknown high-frequency gains. IEEE Transaction on Automatic Control,1998,43(10):1442-1446.
[27]Liu Yun-Gang. Output-feedback Adaptive Control for a class of Nonlinear Systems with Unknown Control Directions. Acta Automatica Sinica,2007.
[28]Wu Zhao-Jing, Xie Xue-Jun, Zhang Si-Ying. The reduced-order design of robust adaptive backstepping controller. Acta Automatica Sinica,2005,31 (4):543-548(in Chinese).
[29]J.P. Gauthier and I. Kupka, "A separation principle for bilinear systems with dissipative drift," IEEE Trans. Automat. Contr, vol.37, pp.1970-1974, Dec.1992.
[30]W.Lin, "Input saturation and globle stabilization of nonlinear systems via state and output feedback," IEEE Trans. Automat. Contr, vol.40, pp.776-782, Apr.1995.
[31]＿, "Bounded smooth state feedback and a globle separation principle for nonaffine nonlinear systems," Syst. Control Lett, vol.26, pp.41-53,1995.
[32]L. Praly, "Asymptotic stabilization via output feedback for loeer triangular systems with output dependent incrementalrate," IEEE Transactions on Automatic Control, vol.48, pp. 1103-1108,2003.
[33]C.Qian and W. Lin, "Output feedback control of a class of nonlinear systems:a nonseparation principle paradigm," IEEE Transactions on Automayic Control, vol.47, pp. 1710-1715,2002.
[34]Z. Chen and J. Huang, "Globle output feedback stabilization for uncertain nonlinear systems with output dependent incremental rate," IEEE Transactions on Automatic Control, vol.23,pp.119-125,2004.
[35]A.J.Krener and A. Isidori, "Linearization by output injection and nonlinear observer," Syst. Control Lett, vol.3,pp.47-52,1983.
[36]H.Khalil and A. Saberi. "Adaptive stabilization of a class of nonlinear systems using high-gain feedback." IEEE Transaction on Automatic Control,vol.32, pp.1031-1035,1987.
[37]F. Mazenc, L.Praly, W. P. Dayawansa, "Globle stabilization by output feedback example & counterexample," Systems and Control Letters,vol.23, pp.119-125,1994.
[2]郑大钟.线性系统理论[M].北京：清华大学出版社,2002.12-16.
[3]C. Reboulet, P. Mouyon, C. Champetier. About the local linearization of nonlinear systems [J]. Algebraic and Geometric Methods in Nonlinear Control Theory, Fliess M. And Hazewinkel M. eds., Reidel,1986:311-312.
[4]R. Marino, P. V. Kokotovic. A geometric approach to nonlinear singularly perturbed control systems [J]. Automatica,1988,24(1):31-41.
[5]A. Isidori, A. J. Krener, C. G. Hiorgi, S. Monaco. Nonlinear decoupling via feedback:a differential geometric approach [J]. IEEE Trans. Aut. Contr,1981,26(2):331-345.
[6]曹建福,韩崇昭,方洋旺.非线性系统理论及应用[M].西安：西安交通大学出版社,2001.
[7]胡跃明.非线性系统理论及应用[M].北京：国防工业出版社,2001.
[8]刘桂英.自适应控制的应用[M].上海：上海电机技术高等专科学校学报.
[9]黄布毅.非线性控制系统的思想与方法[D].郑州：郑州轻工业学院学报.
[10]吴建国,张培健.非线性系统控制新方法研究[S].南通工学院学报(自然科学出版社).
[11]高莲,包曙红.关于L稳定性若干定理的推广[J].内蒙古师范大学学报(自然科学汉文版).
[12]吕玉华,徐润.L稳定性理论若干定理的推广.2006,(04)
[13]祁荣宾.基于输入输出线性化方法实现混沌系统加同步.自动化技术与应用，2004.
[14]陈谋,蒋长生.不确定非线性系统控制方法概述.南京：南京航空航天大学自动化学院.
[15]Kanellakopoulos I, Kokotovic P V, Morse A S. Systematic design of adaptive controllers for Feedback linearizable systems. IEEE Transactions on Automatic Control,1991,36(11): 1241-1253.
[16]Krstic M, Kanellakopoulos I, Kokotovic P V. Nonlinear and Adaptive Control Design. New York:John Wiley and Sons,1995.
[17]Freeman R A, Kokotovic P V. Robust Nonlinear Control Design. Boston:Birkhauser, 1996.
[18]Ge S S, Wang C. Adaptive NN control of uncertain nonlinear pure-feedback systems. Automatica,1996.
[19]Nussbaum. R D. Some remarks on a conjecture in parameter adaptive control. Systems and Control Letters,1983,3(5):243-246.
[20]Ye X D, Jiang J P. Adaptive nonlinear design without a priori knowledge of control directions. IEEE Transactions on Automatic Control,1998,43(11):1617-1621.
[21]Zhang Y, Wen C Y, Soh Y C. Adaptive backstepping control design for systems with unknown high-frequency gain. IEEE Transactions on Automatic Control,2000, 45(12):2350-2354.
[22]Martesson B. Remarks on adaptive stabilization of first order nonlinear systems. Systems and Control Letters,1990,14(1):1-7
[23]Kaloust J, Qu Z. Continuous robust control design for nonlinear uncertain systems without a priori knowledge of control design. IEEE Transactions on Automatic Control,1995,40(2): 276-281.
[24]Ye X D. Adaptive nonlinear output feedback control with unknown high-frequency gain sign. IEEE Transactions on Automatic Control,2001,56(1):112-115.
[25]Jiang Z P, Mareels I, Hill D J, Huang J. A unifying framework for global regulation via nonlinear output feedback:from ISS to iISS. IEEE Transactions on Automatic Control, 2004,49(4):549-562.
[26]Ding Z T. Global adaptive output feedback stabilization of nonlinear systems of any relative degree with unknown high-frequency gains. IEEE Transaction on Automatic Control,1998,43(10):1442-1446.
[27]Liu Yun-Gang. Output-feedback Adaptive Control for a class of Nonlinear Systems with Unknown Control Directions. Acta Automatica Sinica,2007.
[28]Wu Zhao-Jing, Xie Xue-Jun, Zhang Si-Ying. The reduced-order design of robust adaptive backstepping controller. Acta Automatica Sinica,2005,31 (4):543-548(in Chinese).
[29]J.P. Gauthier and I. Kupka, "A separation principle for bilinear systems with dissipative drift," IEEE Trans. Automat. Contr, vol.37, pp.1970-1974, Dec.1992.
[30]W.Lin, "Input saturation and globle stabilization of nonlinear systems via state and output feedback," IEEE Trans. Automat. Contr, vol.40, pp.776-782, Apr.1995.
[31]＿, "Bounded smooth state feedback and a globle separation principle for nonaffine nonlinear systems," Syst. Control Lett, vol.26, pp.41-53,1995.
[32]L. Praly, "Asymptotic stabilization via output feedback for loeer triangular systems with output dependent incrementalrate," IEEE Transactions on Automatic Control, vol.48, pp. 1103-1108,2003.
[33]C.Qian and W. Lin, "Output feedback control of a class of nonlinear systems:a nonseparation principle paradigm," IEEE Transactions on Automayic Control, vol.47, pp. 1710-1715,2002.
[34]Z. Chen and J. Huang, "Globle output feedback stabilization for uncertain nonlinear systems with output dependent incremental rate," IEEE Transactions on Automatic Control, vol.23,pp.119-125,2004.
[35]A.J.Krener and A. Isidori, "Linearization by output injection and nonlinear observer," Syst. Control Lett, vol.3,pp.47-52,1983.
[36]H.Khalil and A. Saberi. "Adaptive stabilization of a class of nonlinear systems using high-gain feedback." IEEE Transaction on Automatic Control,vol.32, pp.1031-1035,1987.
[37]F. Mazenc, L.Praly, W. P. Dayawansa, "Globle stabilization by output feedback example & counterexample," Systems and Control Letters,vol.23, pp.119-125,1994.