任意初态下的迭代学习控制策略
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摘要
针对一类在有限区间上执行重复任务的动态系统,本文提出一种迭代学习初始修正算法,用于解决各次迭代过程中的任意初态问题.通过构造一个虚拟误差函数来分析算法的收敛性,分析结果表明该算法可在指定区间上实现对期望轨迹的一致性跟踪,并通过求解线性矩阵不等式的方法获得具体的矩阵型控制增益.最后,通过数值结果,验证了算法的有效性.
In this paper, we present an iterative learning initial rectifying algorithm for a class of dynamic systems, where the initial state of every iteration can be arbitrary. The convergence analysis results are addressed through a virtual error function. Furthermore, the matrix type control gains can be obtained via solving the linear matrix inequality. Finally, the effectiveness of the stated algorithm are demonstrated by some simulation results.
In this paper, we present an iterative learning initial rectifying algorithm for a class of dynamic systems, where the initial state of every iteration can be arbitrary. The convergence analysis results are addressed through a virtual error function. Furthermore, the matrix type control gains can be obtained via solving the linear matrix inequality. Finally, the effectiveness of the stated algorithm are demonstrated by some simulation results.
引文
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[19]谢华英,孙明轩.有限时间死区修正迭代学习控制器的设计[J].控制理论与应用,2009,26(11):1225-1231.
[20]齐丽强.非参数不确定系统的有限时间迭代学习控制[J].自动化学报,2014,40(7):1320-1327.
[21]CHI R,HOU Z,XU J.Adaptive ILC for a class of discrete-time systems with iteration-varying trajectory and random initial condition.Automatica,2008,44(8):2207-2213.
[22]XU J.On iterative learning from different tracking tasks in the presence of time-varying uncertainties[J].IEEE Transactions on Systems Man and Cybernetics Part B,2004,34(1):589-597.
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[24]MARINO R.An iterative learning control for a class of partially feedback linearizable systems[J].IEEE Transactions on Automatic Control,2009,54(8):1991-1996.
[25]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[J].系统科学与数学,2012,32(6):693-704.
[26]MENG D,JIA Y,DU J,et al.Data-driven control for relative degree systems via iterative learning[J].IEEE Transactions on Neural Networks,2011,22(12):2213-2225.
[2]BRISTOW D,THARAYIL M,ALLEYNE A.A survey of iterative learning control[J].IEEE Control Systems Magazine,2006,26(3):96-114.
[3]ISHIHARA T,ABE K,TAKEDA H.A discrete-time design of robust iterative learning controllers[J].IEEE Transactions on Systems Man and Cybernetics Part B,1992,22(1):74-84.
[4]SAAB S,VOGT W,MICKLE M.Learning control algorithms for tracking’slowly’varying trajectories[J].IEEE Transactions on Systems Man and Cybernetics Part B,1997,27(4):657-670.
[5]HEINZINGER G,FENWICK D,PADEN B,et al.Stability of learning control with disturbances and uncertain initial conditions[J].IEEE Transactions on Automatic Control,1992,37(1):110-114.
[6]WANG D.Convergence and robustness of discrete time nonlinear systems with iterative learning control[J].Automatica,1998,34(11):1445-1448
[7]ARIMOTO S.Learning control theory for robotic motion[J].International Journal of Adaptive Control and Signal Processing,1990,6(4):543-564.
[8]LEE H,BIEN Z.Study on robustness of iterative learning control with nonzero initial error[J].International Journal of Control,1996,64(3):345-359.
[9]PARK P,BIEN Z,HWANG D.A study on the robustness of a PID-type iterative learning controller against initial state error[J].International Journal of Systems Science,1999,30(1):49-59.
[10]SUN M,WANG D.Initial condition issues on iterative learning control for nonlinear systems with time delay[J].International Journal of Systems Science,2001,32(11):1365-1375.
[11]SUN M,WANG D.Closed-loop iterative learning control for nonlinear systems with initial shifts[J].International Journal of Adaptive Control and Signal Processing,2002,16(7):515-538.
[12]SUN M,WANG D.Iterative learning control with initial rectifying action[J].Automatica,2002,38(7):1177-1182.
[13]LI X,CHOW T,HO J,et al.Iterative learning control with initial rectifying action for nonlinear continuous systems[J].IET Control Theory&Applications,2009,3(1):49-55.
[14]XU J,TAN Y.A composite energy function-based learning control approach for nonlinear systems with time-varying parametric uncertainties[J].IEEE Transactions on Automatic Control,2002,47(11):1940-1945.
[15]QU Z,XU J.Asymptotic learning control for a class of cascaded nonlinear uncertain systems[J].IEEETransactions on Automatic Control,2002,47(8):1369-1376.
[16]TAYEBI A,CHIEN C.A unified adaptive iterative learning control framework for uncertain nonlinear systems[J].IEEE Transactions on Automatic Control,2007,52(10):1907-1913.
[17]CHIEN C,HSU C,YAO C.Fuzzy system-based adaptive iterative learning control for nonlinear plants with initial state errors[J].IEEE Transactions on Fuzzy Systems,2004,12(5):724-732.
[18]孙明轩.有限时间迭代学习控制[J].系统科学与数学,2010,30(6):733-741.
[19]谢华英,孙明轩.有限时间死区修正迭代学习控制器的设计[J].控制理论与应用,2009,26(11):1225-1231.
[20]齐丽强.非参数不确定系统的有限时间迭代学习控制[J].自动化学报,2014,40(7):1320-1327.
[21]CHI R,HOU Z,XU J.Adaptive ILC for a class of discrete-time systems with iteration-varying trajectory and random initial condition.Automatica,2008,44(8):2207-2213.
[22]XU J.On iterative learning from different tracking tasks in the presence of time-varying uncertainties[J].IEEE Transactions on Systems Man and Cybernetics Part B,2004,34(1):589-597.
[23]YIN C,XU J,HOU Z.A high-order internal model based iterative learning control scheme for nonlinear systems with time-iteration-varying parameters[J].IEEE Transactions on Automatic Control,2010,55(11):2665-2670.
[24]MARINO R.An iterative learning control for a class of partially feedback linearizable systems[J].IEEE Transactions on Automatic Control,2009,54(8):1991-1996.
[25]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[J].系统科学与数学,2012,32(6):693-704.
[26]MENG D,JIA Y,DU J,et al.Data-driven control for relative degree systems via iterative learning[J].IEEE Transactions on Neural Networks,2011,22(12):2213-2225.