Optimality of first-order ILC among higher order ILC

Higher order iterative learning control (HO-ILC) algorithms use past system control information from more than one past iterative cycle. This class of ILC algorithms have been proposed aiming at improving the learning efficiency and performance. This paper addresses the optimality of HO-ILC in the sense of minimizing the trace of the control error covariance matrix in the presence of a class of uncorrelated random disturbances. It is shown that the optimal weighting matrices corresponding to the control information associated with more than one cycle preceding the current cycle are zero. That is, an optimal HO-ILC does not add to the optimality of standard first-order ILC in the sense of minimizing the trace of the control error covariance matrix. The system under consideration is a linear discrete-time varying systems with different relative degree between the input and each output

[1]  Pierre-Alexandre Bliman,et al.  Control of delay systems with relay , 2002 .

[2]  K. Moore,et al.  Algebraic $H_infty$ Design of Higher-Order Iterative Learning Controllers , 2005, Proceedings of the 2005 IEEE International Symposium on, Mediterrean Conference on Control and Automation Intelligent Control, 2005..

[3]  Emilia Fridman,et al.  Steady Modes in Relay Control Systems With Time Delay and Periodic Disturbances , 2000 .

[4]  Sabine Mondié,et al.  Global asymptotic stabilization of feedforward systems with delay in the input , 2004, IEEE Transactions on Automatic Control.

[5]  Zeungnam Bien,et al.  Higher-order iterative learning control algorithm , 1989 .

[6]  Shustin E.I. Fridman È.M.,et al.  Steady modes in discontinuous control systems with time delay , 1993 .

[7]  Peter Willett,et al.  Quickest detection of hidden Markov models , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[8]  Emilia Fridman,et al.  Oscillations in a second-order discontinuous system with delay , 2002 .

[9]  Eric Rogers,et al.  Higher order ILC versus alternatives applied to chain conveyor systems , 2002 .

[10]  YangQuan Chen,et al.  A high-order terminal iterative learning control scheme [RTP-CVD application] , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[11]  Wolf Bayer,et al.  Chaos proved for a second-order difference differential equation , 2002 .

[12]  Yangquan Chen,et al.  Analysis of a high-order iterative learning control algorithm for uncertain nonlinear systems with state delays , 1998, Autom..

[13]  K. Moore,et al.  ON MONOTONIC CONVERGENCE OF HIGH ORDER ITERATIVE LEARNING UPDATE LAWS , 2002 .

[14]  F. Mazenc,et al.  Global asymptotic stabilization for chains of integrators with a delay in the input , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[15]  Mingxuan Sun,et al.  Robust higher order repetitive learning control algorithm for tracking control of delayed repetitive systems , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[16]  YangQuan Chen,et al.  High-order iterative learning control of functional neuromuscular stimulation systems , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[17]  Samer S. Saab,et al.  A discrete-time stochastic learning control algorithm , 2001, IEEE Trans. Autom. Control..

[18]  Mikael Norrlöf.  Comparative study on first and second order ILC-frequency domain analysis and experiments , 2000, CDC 2000.

[19]  Suguru Arimoto,et al.  Bettering operation of Robots by learning , 1984, J. Field Robotics.

[20]  Y. Chen,et al.  A robust high-order P-type iterative learning controller using current iteration tracking error , 1997 .

[21]  S. Saab.  Stochastic P-type/D-type iterative learning control algorithms , 2003 .

[22]  M. Phan,et al.  Higher-order iterative learning control by pole placement and noise filtering , 2002 .

[23]  S. Saab.  A stochastic iterative learning control algorithm with application to an induction motor , 2004 .

[24]  Jianxin Xu,et al.  On the convergence speed of a class of higher-order ILC schemes , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[25]  Danwei W. Wang,et al.  Analysis of Nonlinear Discrete-Time Systems with Higher-Order Iterative Learning Control , 2001 .