迭代学习控制的参考信号初始修正方法
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摘要
针对一类非参数不确定系统,提出状态受限迭代学习控制的参考信号初始修正方法,以解决任意初态下的状态受限轨迹跟踪问题.通过构造修正参考信号,利用一种新型的障碍Lyapunov函数设计迭代学习控制系统,采用鲁棒方法与学习方法相结合的策略处理非参数不确定性,经过足够多次迭代后,可实现系统状态在整个作业区间上对修正参考信号的零误差跟踪,以及在预设作业区间上对参考信号的零误差跟踪.同时,将滤波误差约束于预设的界内,并由此实现对系统状态在各次迭代运行过程中的约束.仿真结果表明了本文所提控制方法的有效性.
This paper presents a reference-signal rectifying method of iterative learning control to address the trajectorytracking problem for a class of state-constrained uncertain systems, in the presence of arbitrary initial states. For design of the iterative learning control scheme, a rectified reference signal is constructed and a new type of barrier Lyapunov function is used. In order to deal with the nonparametric uncertainties, a robust learning approach is applied. It is shown that the closedloop system s state follows the rectified reference signal perfectly over the entire time interval as iteration increases. In turn, the system state tracks the reference signal on the specified interval.During each iteration, the filtering-error is constrained in the pre-specified region, and the system state is thus constrained.Numerical results are presented to demonstrate the effectiveness of the learning control scheme.
This paper presents a reference-signal rectifying method of iterative learning control to address the trajectorytracking problem for a class of state-constrained uncertain systems, in the presence of arbitrary initial states. For design of the iterative learning control scheme, a rectified reference signal is constructed and a new type of barrier Lyapunov function is used. In order to deal with the nonparametric uncertainties, a robust learning approach is applied. It is shown that the closedloop system s state follows the rectified reference signal perfectly over the entire time interval as iteration increases. In turn, the system state tracks the reference signal on the specified interval.During each iteration, the filtering-error is constrained in the pre-specified region, and the system state is thus constrained.Numerical results are presented to demonstrate the effectiveness of the learning control scheme.
引文
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2 Dixon W E,Zergeroglu E,Dawson D M,Costic B T.Repetitive learning control:a Lyapunov-based approach.IEEETransactions on Systems,Man,and Cybernetics,Part B(Cybernetics),2002,32(4):538-545
3 Xu J X,Tan Y.A composite energy function-based learning control approach for nonlinear systems with time-varying parametric uncertainties.IEEE Transactions on Automatic Control,2002,47(11):1940-1945
4 Zhang Yu-Dong,Fang Yong-Chun.Learning control for systems with saturated output.Acta Automatica Sinica,2011,37(1):92-98(张玉东,方勇纯.一类输出饱和系统的学习控制算法研究.自动化学报,2011,37(1):92-98)
5 Zhang Li,Liu Shan.Basis function based adaptive iterative learning control for non-minimum phase systems.Acta Automatica Sinica,2014,40(12):2716-2725(张黎,刘山.非最小相位系统的基函数型自适应迭代学习控制.自动化学报,2014,40(12):2716-2725)
6 Bu Xu-Hui,Hou Zhong-Sheng,Yu Fa-Shan,Fu Zi-Yi.Iterative learning control for trajectory tracking of farm vehicles.Acta Automatica Sinica,2014,40(2):368-372(卜旭辉,侯忠生,余发山,付子义.基于迭代学习的农业车辆路径跟踪控制.自动化学报,2014,40(2):368-372)
7 French M,Rogers E.Non-linear iterative learning by an adaptive Lyapunov technique.International Journal of Control,2000,73(10):840-850
8 Tayebi A,Chien C J.A unified adaptive iterative learning control framework for uncertain nonlinear systems.IEEE Transactions on Automatic Control,2007,52(10):1907-1913
9 Chen Wei-Sheng,Wang Yuan-Liang,Li Jun-Min.Adaptive learning control for nonlinearly parameterized systems with periodically time-varying delays.Acta Automatica Sinica,2008,34(12):1556-1560(陈为胜,王元亮,李俊民.周期时变时滞非线性参数化系统的自适应学习控制.自动化学报,2008,34(12):1556-1560)
10 Yin C K,Xu J X,Hou Z S.A high-order internal model based iterative learning control scheme for nonlinear systems with time-iteration-varying parameters.IEEE Transactions on Automatic Control,2010,55(11):2665-2670
11 Ham C,Qu Z.A new learning control based on the Lyapunov direct method.In:Proceedings of Southcon/94 Conference Record.Orlando,USA:IEEE,1994.121-125
12 Xu J X,Yan R.On repetitive learning control for periodic tracking tasks.IEEE Transactions on Automatic Control,2006,51(11):1842-1848
13 Marino R,Tomei P,Verrelli C M.Robust adaptive learning control for nonlinear systems with extended matching unstructured uncertainties.International Journal of Robust and Nonlinear Control,2012,22(6):645-675
14 Chen Peng-Nian,Qin Hua-Shu,Fang Xue-Yi.Iterative learning control for uncertain nonlinear systems with time-varying control gain.Journal of Systems Science and Mathematical Sciences,2012,32(6):693-704(陈彭年,秦化淑,方学毅.控制增益时变的非线性系统的迭代学习控制.系统科学与数学,2012,32(6):693-704)
15 Liuzzo S,Marino R,Tomei P.Adaptive learning control of nonlinear systems by output error feedback.IEEE Transactions on Automatic Control,2007,52(7):1232-1248
16 Chien C J,Hsu C T,Yao C Y.Fuzzy system-based adaptive iterative learning control for nonlinear plants with initial state errors.IEEE Transactions on Fuzzy Systems,2004,12(5):724-732
17 Sun M X,Yan Q Z.Error tracking of iterative learning control systems.Acta Automatica Sinica,2013,39(3):251-262
18 Sun Ming-Xuan,Huang Bao-Jian.Iterative Learning Control.Beijing:National Defence Industry Press,1999.182-184(孙明轩,黄宝健.迭代学习控制.北京:国防工业出版社,1999.182-184)
19 Yan Qiu-Zhen,Sun Ming-Xuan,Li He.Iterative learning control for nonlinear uncertain systems with arbitrary initial state.Acta Automatica Sinica,2016,42(4):545-555(严求真,孙明轩,李鹤.任意初值非线性不确定系统的迭代学习控制.自动化学报,2016,42(4):545-555)
20 Li X D,Chow T W S,Cheng L L.Adaptive iterative learning control of non-linear MIMO continuous systems with iteration-varying initial error and reference trajectory.International Journal of Systems Science,2013,44(4):786-794
21 Li Xiang-Yang.Iterative learning control for a class of nonlinear time-varying system.Control Theory&Applications,2014,31(8):1087-1093(李向阳.一类非线性时变系统的迭代学习控制.控制理论与应用,2014,31(8):1087-1093)
22 Li Xiang-Yang.Iterative learning control based on finite time tracking differentiator.Acta Automatica Sinica,2014,40(7):1366-1375(李向阳.基于有限时间跟踪微分器的迭代学习控制.自动化学报,2014,40(7):1366-1375)
23 Jin X,Xu J X.Iterative learning control for outputconstrained systems with both parametric and nonparametric uncertainties.Automatica,2013,49(8):2508-2516
24 Xu J X,Jin X.State-constrained iterative learning control for a class of MIMO systems.IEEE Transactions on Automatic Control,2013,58(5):1322-1327
25 Sun Ming-Xuan,Zhang Wei-Bo,Yan Qiu-Zhen.Constrained iterative learning control of a class of non-parametric uncertain systems.Control Theory&Applications,2014,31(4):479-484(孙明轩,张伟博,严求真.非参数不确定系统约束迭代学习控制.控制理论与应用,2014,31(4):479-484)
26 Yan Qiu-Zhen,Sun Ming-Xuan.Error-tracking iterative learning control with state constrained for nonparametric uncertain systems.Control Theory&Applications,2015,32(7):895-901(严求真,孙明轩.非参数不确定系统状态受限误差跟踪学习控制方法.控制理论与应用,2015,32(7):895-901)
27 Yu Qiong-Xia,Hou Zhong-Sheng.Adaptive iterative learning control for a class of non-parametric uncertain systems.Journal of Systems Science and Mathematical Sciences,2016,36(1):1-13(余琼霞,侯忠生.非参数不确定系统的自适应迭代学习控制.系统科学与数学,2016,36(1):1-13)
28 Zhuang Kai-Yu,Zhang Ke-Qin,Su Hong-Ye,Chu Jian.Terminal sliding mode control for high-order nonlinear dynamic systems.Journal of Zhejiang University(Engineering Science),2002,36(5):482-485,539(庄开宇,张克勤,苏宏业,褚健.高阶非线性系统的Terminal滑模控制.浙江大学学报(工学版),2002,36(5):482-485,539)
29 Xie Hua-Ying,Sun Ming-Xuan,Jin Kui.Iterative learning controller designs with finite-time convergence performance.In:Proceedings of the 29th Chinese Control Conference.Beijing,China:TCCT,2010.5845-5850(谢华英,孙明轩,金奎.有限时间收敛迭代学习控制器设计.见:第29届中国控制会议论文集.北京:中国自动化学会,2010.5845-5850)
2 Dixon W E,Zergeroglu E,Dawson D M,Costic B T.Repetitive learning control:a Lyapunov-based approach.IEEETransactions on Systems,Man,and Cybernetics,Part B(Cybernetics),2002,32(4):538-545
3 Xu J X,Tan Y.A composite energy function-based learning control approach for nonlinear systems with time-varying parametric uncertainties.IEEE Transactions on Automatic Control,2002,47(11):1940-1945
4 Zhang Yu-Dong,Fang Yong-Chun.Learning control for systems with saturated output.Acta Automatica Sinica,2011,37(1):92-98(张玉东,方勇纯.一类输出饱和系统的学习控制算法研究.自动化学报,2011,37(1):92-98)
5 Zhang Li,Liu Shan.Basis function based adaptive iterative learning control for non-minimum phase systems.Acta Automatica Sinica,2014,40(12):2716-2725(张黎,刘山.非最小相位系统的基函数型自适应迭代学习控制.自动化学报,2014,40(12):2716-2725)
6 Bu Xu-Hui,Hou Zhong-Sheng,Yu Fa-Shan,Fu Zi-Yi.Iterative learning control for trajectory tracking of farm vehicles.Acta Automatica Sinica,2014,40(2):368-372(卜旭辉,侯忠生,余发山,付子义.基于迭代学习的农业车辆路径跟踪控制.自动化学报,2014,40(2):368-372)
7 French M,Rogers E.Non-linear iterative learning by an adaptive Lyapunov technique.International Journal of Control,2000,73(10):840-850
8 Tayebi A,Chien C J.A unified adaptive iterative learning control framework for uncertain nonlinear systems.IEEE Transactions on Automatic Control,2007,52(10):1907-1913
9 Chen Wei-Sheng,Wang Yuan-Liang,Li Jun-Min.Adaptive learning control for nonlinearly parameterized systems with periodically time-varying delays.Acta Automatica Sinica,2008,34(12):1556-1560(陈为胜,王元亮,李俊民.周期时变时滞非线性参数化系统的自适应学习控制.自动化学报,2008,34(12):1556-1560)
10 Yin C K,Xu J X,Hou Z S.A high-order internal model based iterative learning control scheme for nonlinear systems with time-iteration-varying parameters.IEEE Transactions on Automatic Control,2010,55(11):2665-2670
11 Ham C,Qu Z.A new learning control based on the Lyapunov direct method.In:Proceedings of Southcon/94 Conference Record.Orlando,USA:IEEE,1994.121-125
12 Xu J X,Yan R.On repetitive learning control for periodic tracking tasks.IEEE Transactions on Automatic Control,2006,51(11):1842-1848
13 Marino R,Tomei P,Verrelli C M.Robust adaptive learning control for nonlinear systems with extended matching unstructured uncertainties.International Journal of Robust and Nonlinear Control,2012,22(6):645-675
14 Chen Peng-Nian,Qin Hua-Shu,Fang Xue-Yi.Iterative learning control for uncertain nonlinear systems with time-varying control gain.Journal of Systems Science and Mathematical Sciences,2012,32(6):693-704(陈彭年,秦化淑,方学毅.控制增益时变的非线性系统的迭代学习控制.系统科学与数学,2012,32(6):693-704)
15 Liuzzo S,Marino R,Tomei P.Adaptive learning control of nonlinear systems by output error feedback.IEEE Transactions on Automatic Control,2007,52(7):1232-1248
16 Chien C J,Hsu C T,Yao C Y.Fuzzy system-based adaptive iterative learning control for nonlinear plants with initial state errors.IEEE Transactions on Fuzzy Systems,2004,12(5):724-732
17 Sun M X,Yan Q Z.Error tracking of iterative learning control systems.Acta Automatica Sinica,2013,39(3):251-262
18 Sun Ming-Xuan,Huang Bao-Jian.Iterative Learning Control.Beijing:National Defence Industry Press,1999.182-184(孙明轩,黄宝健.迭代学习控制.北京:国防工业出版社,1999.182-184)
19 Yan Qiu-Zhen,Sun Ming-Xuan,Li He.Iterative learning control for nonlinear uncertain systems with arbitrary initial state.Acta Automatica Sinica,2016,42(4):545-555(严求真,孙明轩,李鹤.任意初值非线性不确定系统的迭代学习控制.自动化学报,2016,42(4):545-555)
20 Li X D,Chow T W S,Cheng L L.Adaptive iterative learning control of non-linear MIMO continuous systems with iteration-varying initial error and reference trajectory.International Journal of Systems Science,2013,44(4):786-794
21 Li Xiang-Yang.Iterative learning control for a class of nonlinear time-varying system.Control Theory&Applications,2014,31(8):1087-1093(李向阳.一类非线性时变系统的迭代学习控制.控制理论与应用,2014,31(8):1087-1093)
22 Li Xiang-Yang.Iterative learning control based on finite time tracking differentiator.Acta Automatica Sinica,2014,40(7):1366-1375(李向阳.基于有限时间跟踪微分器的迭代学习控制.自动化学报,2014,40(7):1366-1375)
23 Jin X,Xu J X.Iterative learning control for outputconstrained systems with both parametric and nonparametric uncertainties.Automatica,2013,49(8):2508-2516
24 Xu J X,Jin X.State-constrained iterative learning control for a class of MIMO systems.IEEE Transactions on Automatic Control,2013,58(5):1322-1327
25 Sun Ming-Xuan,Zhang Wei-Bo,Yan Qiu-Zhen.Constrained iterative learning control of a class of non-parametric uncertain systems.Control Theory&Applications,2014,31(4):479-484(孙明轩,张伟博,严求真.非参数不确定系统约束迭代学习控制.控制理论与应用,2014,31(4):479-484)
26 Yan Qiu-Zhen,Sun Ming-Xuan.Error-tracking iterative learning control with state constrained for nonparametric uncertain systems.Control Theory&Applications,2015,32(7):895-901(严求真,孙明轩.非参数不确定系统状态受限误差跟踪学习控制方法.控制理论与应用,2015,32(7):895-901)
27 Yu Qiong-Xia,Hou Zhong-Sheng.Adaptive iterative learning control for a class of non-parametric uncertain systems.Journal of Systems Science and Mathematical Sciences,2016,36(1):1-13(余琼霞,侯忠生.非参数不确定系统的自适应迭代学习控制.系统科学与数学,2016,36(1):1-13)
28 Zhuang Kai-Yu,Zhang Ke-Qin,Su Hong-Ye,Chu Jian.Terminal sliding mode control for high-order nonlinear dynamic systems.Journal of Zhejiang University(Engineering Science),2002,36(5):482-485,539(庄开宇,张克勤,苏宏业,褚健.高阶非线性系统的Terminal滑模控制.浙江大学学报(工学版),2002,36(5):482-485,539)
29 Xie Hua-Ying,Sun Ming-Xuan,Jin Kui.Iterative learning controller designs with finite-time convergence performance.In:Proceedings of the 29th Chinese Control Conference.Beijing,China:TCCT,2010.5845-5850(谢华英,孙明轩,金奎.有限时间收敛迭代学习控制器设计.见:第29届中国控制会议论文集.北京:中国自动化学会,2010.5845-5850)