未知控制方向非线性系统的自适应控制
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摘要
近二十多年来,非线性系统控制理论成为自动化控制领域研究的热点问题之一.Backstepping技术是研究非线系统控制的一种重要方法,而自适应Backstepping控制可以使不满足匹配条件的时不变参数不确定性非线性系统,实现跟踪误差渐近收敛于零.当非线性系统中存在未知控制方向时,会使得控制器的设计变得更加复杂,而Nussbaum增益技术是处理控制方向未知问题的一种有效方法.因此如何将自适应Backstepping技术的和Nussbaum增益技术相结合,来解决控制方向未知的问题是值得研究的课题.
由以上研究思想,本文工作主要包括以下几个方面:
第一,针对一类具有未知控制方向和扰动的非线性系统,基于观测器和Backstepping方法,设计了一种自适应输出反馈控制器,控制器能够保证系统的稳定性和所有闭环系统的信号的有界性并且保证状态渐近收敛于零.最后通过数值仿真验证该控制器的有效性.
第二,针对一类具有未知控制方向的非线性级联时滞系统,首先采用部分状态反馈渐近调节的控制算法来处理系统中的不确定性,利用界化技术来处理系统中的时滞项,之后通过Nussbaum型函数来处理系统中的未知控制方向问题,最后通过Backstepping设计方法设计一种部分状态反馈控制器,通过构造合适的Lyapunov-Krasovskii泛函能够保证系统稳定性和所有闭环信号有界性,并且状态渐近收敛于零.最后通过数值仿真验证其有效性.
第三,针对一类具有未知控制方向的非线性级联系统,通过线性变换,将未知控制系数转换为一个新的未知参数,基于Backstepping方法和Nussbaum增益函数,设计了一种自适应输出反馈控制器.该控制器能够保证系统的稳定性,同时能够保证所有系统状态渐近收敛于零以及其它闭环信号的有界性.最后通过数值仿真验证该观测器和控制器的有效性.
In last two decades, the nonlinear system control theory is one of the hot topics in automatic control realm. The backstepping technique is a method to investigate the nonlinear control system,in addition, the adaptive backstepping method ensures the tracking error of the unmatched nonlinear system with time-invariant uncertainties convergences to zero asymptotically. Furthermore, when the nonlinear system with unknown control directions, the control problem becomes rather complex, in the case, the Nussbaum-gain technique is an effective way to deal with it. Thus, how to deal with the unknown control direction problem by incorporating the adaptive Backstepping control method and the Nussbaum-gain technique is worth studying.
Motivated by the above discussions, this paper mainly includes the following aspects:
Firstly, based on the state observer and the Backstepping method, a kind of adaptive output feedback controller is designed for a class of nonlinear systems with unknown control directions and unknown disturbances. The control schemes can guarantee the system is stable and all the closed-loop signals are bounded, especially, all the states converge to zero asymptotically. Finally, a simulation example is given to verify the effectiveness of the proposed controller.
Secondly, for a class of nonlinear cascade time-delay systems with unknown control directions, the partial-state feedback asymptotic regulating control scheme is introduced to deal with the uncertainties of system, and the unknown time delays terms are compensated by bouding technique. Then, Nussbaum-type functions are used to deal with the unknown control directions. Lastly, the partial-state feedback controllers are constructed by using the backstepping method. It is proven that the system is stable and its states converge to zero asymptotically by constructing appropriate Lyapunov-Krasovskii functionals, meanwhile, all the closed-loop signals are bounded. Finally, a simulation example is given to illustrate the effectiveness of the proposed controller.
Thirdly, for a class of nonlinear cascade systems with unknown control directions, through a linear state transformation, the unknown control coefficients are lumped together. Based on the Backstepping algorithm and the Nussbaum gain functions,the adaptive output-feedback controller is constructed. The controller not only guarantees the stability of the systems but also ensures the systems states converge to the origin and the boundeness of all the closed-loop signals. Lastly, a simulation example is given to show the effectiveness of the proposed controller.
由以上研究思想,本文工作主要包括以下几个方面:
第一,针对一类具有未知控制方向和扰动的非线性系统,基于观测器和Backstepping方法,设计了一种自适应输出反馈控制器,控制器能够保证系统的稳定性和所有闭环系统的信号的有界性并且保证状态渐近收敛于零.最后通过数值仿真验证该控制器的有效性.
第二,针对一类具有未知控制方向的非线性级联时滞系统,首先采用部分状态反馈渐近调节的控制算法来处理系统中的不确定性,利用界化技术来处理系统中的时滞项,之后通过Nussbaum型函数来处理系统中的未知控制方向问题,最后通过Backstepping设计方法设计一种部分状态反馈控制器,通过构造合适的Lyapunov-Krasovskii泛函能够保证系统稳定性和所有闭环信号有界性,并且状态渐近收敛于零.最后通过数值仿真验证其有效性.
第三,针对一类具有未知控制方向的非线性级联系统,通过线性变换,将未知控制系数转换为一个新的未知参数,基于Backstepping方法和Nussbaum增益函数,设计了一种自适应输出反馈控制器.该控制器能够保证系统的稳定性,同时能够保证所有系统状态渐近收敛于零以及其它闭环信号的有界性.最后通过数值仿真验证该观测器和控制器的有效性.
In last two decades, the nonlinear system control theory is one of the hot topics in automatic control realm. The backstepping technique is a method to investigate the nonlinear control system,in addition, the adaptive backstepping method ensures the tracking error of the unmatched nonlinear system with time-invariant uncertainties convergences to zero asymptotically. Furthermore, when the nonlinear system with unknown control directions, the control problem becomes rather complex, in the case, the Nussbaum-gain technique is an effective way to deal with it. Thus, how to deal with the unknown control direction problem by incorporating the adaptive Backstepping control method and the Nussbaum-gain technique is worth studying.
Motivated by the above discussions, this paper mainly includes the following aspects:
Firstly, based on the state observer and the Backstepping method, a kind of adaptive output feedback controller is designed for a class of nonlinear systems with unknown control directions and unknown disturbances. The control schemes can guarantee the system is stable and all the closed-loop signals are bounded, especially, all the states converge to zero asymptotically. Finally, a simulation example is given to verify the effectiveness of the proposed controller.
Secondly, for a class of nonlinear cascade time-delay systems with unknown control directions, the partial-state feedback asymptotic regulating control scheme is introduced to deal with the uncertainties of system, and the unknown time delays terms are compensated by bouding technique. Then, Nussbaum-type functions are used to deal with the unknown control directions. Lastly, the partial-state feedback controllers are constructed by using the backstepping method. It is proven that the system is stable and its states converge to zero asymptotically by constructing appropriate Lyapunov-Krasovskii functionals, meanwhile, all the closed-loop signals are bounded. Finally, a simulation example is given to illustrate the effectiveness of the proposed controller.
Thirdly, for a class of nonlinear cascade systems with unknown control directions, through a linear state transformation, the unknown control coefficients are lumped together. Based on the Backstepping algorithm and the Nussbaum gain functions,the adaptive output-feedback controller is constructed. The controller not only guarantees the stability of the systems but also ensures the systems states converge to the origin and the boundeness of all the closed-loop signals. Lastly, a simulation example is given to show the effectiveness of the proposed controller.
引文
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[2] Kaloust J, Qu Z. Continuous robust control design for nonlinear uncertain systems without a priori knowledge of control direction[J]. IEEE Transactions on Automatic Control, 1995, 40(2): 276-282.
[3] Ye X., Jiang J. Adaptive nonlinear design without a priori knowledge of control directions[J].IEEE Transactions on Automatic Control, 1998, 43(11):1617-1621.
[4] Ye X. Asymptotic regulation of time-varying uncertain nonlinear systems with unknown control directions[J]. Automatica, 1999,35(5): 929-935.
[5] Ding Z. Adaptive control of nonlinear systems with unknown virtual control coefficients [J]. International Journal of Adaptive Control Signal Processing, 2000, 14(5): 505-517.
[6] Ye X. Adaptive nonlinear output-feedback control with unknown high-frequency gain sign[J]. IEEE Transactions on Automatic Control, 2001, 43(1): 112-115.
[7] Ge S S, WANG J. Robust adaptive neural control for a class of perturbed strict feedback nonlinear systems[J]. IEEE Transactions on Neural Networks, 2002, 13(6): 1409-1419.
[8] Ge S S, WANG J. Robust adaptive tracking for time-varying uncertain nonlinear systems with unknown control coefficients[J]. IEEE Transactions on Automatic Control, 2003, 48(8): 423-427.
[9] Ge S S, F Hong, Lee T H. Robust adaptive control of nonlinear systems with unknown time delays [J]. Automatica, 2005, 41(7): 499-516.
[10]Liu Y G, Output-feedback Adaptive control for a class of nonlinear systems with unknown control directions[J].Acta Automatic Sinica, 2007, 33(12): 1306-1312.
[11]Lu Liu, Jie Huang. Global robust output regulation of lower triangular systems with unknown control direction[J]. Automatica, 2008, 44(5): 1278-1284.
[12]Wang Qiangde, Wei Chunling, Asymptotic regulation of cascade systems with unknown control directions and nonlinear parameterization[J]. J Control Theory Apply, 2009,7(1): 1-56.
[13]Shang Fang, Liu Yun-Gang. Output-feedback control for a class of uncertainnonlinear systems with linearly unmeasured states dependent growth[J].Acta Automatic Sinica, 2009, 35(3): 272-280.
[14]Shang Fang, Liu Yungang, Zhang Chenghui. Adaptive output-feedback control for a class of planar nonlinear systems[J]. Asian Journal of Control, 2009, 11(5): 578-586.
[15]陈卫田,施颂椒,张钟俊.不确定非线性系统的鲁棒自适应控制[J].上海交通大学学报,1998, 32(6): 88-93.
[16]黄长水,阮荣耀.一类不确定性非线性系统的鲁棒自适应控制[J].自动化学报,2001, 27(1): 82-88.
[17]Ye X D. Global adaptive control of nonlinear parameterized systems[J].IEEE Transactions on Automatic Control, 2003, 48(1): 169-173.
[18]Qu Z. H., Hull R. A. and Wang J. Global stabilizing adaptive control design for nonlinearly parameterized systems[J].IEEE Transactions on Automatic Control, 2006, 51(6): 1073-1079.
[19]Nussbaum. R. D. Some remarks on a conjecture in parameter adaptive control[J]. Systems and Control Letters, 1983, 3(5): 243-246.
[20]Zhang Y, Wen C. Adaptive Backstepping control design for systems with unknown high-frequency gain[J]. IEEE Transactions on Automatic Control, 2000, 45 (12): 2350-2354.
[21]Zheng Y, Yang Y. Adaptive output feedback control for a class of nonlinear systems with unknown virtual control coefficients signs[J].International Journal of Adaptive Control and Signal Processing, 2007, 21: 77-89.
[22]Ge S. S, Yang C.G., Lee T. H. Adaptive robust control of a class of nonlinear strict-feedback discrete-time systems with unknown control directions[J]. Systems & Control Letters, 2008, 57(11): 888–895.
[23]Yang C.G., Ge S. S, Lee T. H. Output feedback adaptive control of a class of nonlinear discrete-time systems with unknown control directions[J]. Automatica, 2009, 45(1): 270-276.
[24]陆东先,魏振国,高庆争,解学军.一类具有未知控制方向非线性时滞系统的输出反馈镇定[J].曲阜师范大学学报,2008, 34(3): 19-24.
[25]伏玉笋,田作华,施颂椒.非线性时滞系统输出反馈镇定[J].自动化学报,2002, 28(5): 802-805.
[26]伏玉笋,田作华,施颂椒.非线性随机时滞系统输出反馈镇定[J].控制理论与应用,2003,20(5): 749-752.
[27]杜佳璐,于双和,郭晨,赵永生.一类具有未知控制方向的不确定非线性系统自适应控制[C].Proceedings of the 26th Chinese Control Conference,July 26-31, Zhangjiajie,2007, 835-839.
[28]Ge S S, Hong F, Lee T H. Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients[J]. IEEE Transactions on Systems, Man, and Cybernetics-Part B, 2004, 34(1): 499-516.
[29]叶旭东,陈彭年.具有未知控制方向非线性系统的全局自适应控制[J].中国计量学院学报,2005,16(1): 24-41.
[30]陈刚,王树青.控制方向未知的时变非线性系统鲁棒控制[J].控制与决策,2005,20(12): 1397-1400.
[31]王强德,井元伟,张嗣瀛.控制方向未知的非线性系统的自适应输出跟踪控制[J].控制与决策,2006,21(3): 248-252.
[32]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.
[33]李铁山,杨盐生,杜嘉立,洪碧光.一类不确定非线性系统的鲁棒自适应跟踪控制[J].哈尔滨工程大学学报,2005,26(2): 152-155.
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