On the PDα-type iterative learning control for the fractional-order nonlinear systems

In this paper, we discuss in time domain the convergence of the iterative process for fractional-order nonlinear systems. The PDα-type iterative learning updating laws are considered. Most of the classical fractional-order cases for linear or nonlinear systems fall into the scheme of this paper. A number of numerical simulations are illustrated to validate the concepts.

[1]  Peter J. Torvik,et al.  Fractional calculus-a di erent approach to the analysis of viscoelastically damped structures , 1983 .

[2]  Danwei Wang,et al.  Higher Relative Degree Nonlinear Systems With ilc Using Lower‐order Differentiations , 2002 .

[3]  Krzysztof Galkowski,et al.  PI output feedback control of differential linear repetitive processes , 2008, Autom..

[4]  O. Agrawal,et al.  Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering , 2007 .

[5]  R. Bagley,et al.  On the Fractional Calculus Model of Viscoelastic Behavior , 1986 .

[6]  YangQuan Chen,et al.  Iterative learning control strategy for functional neuromuscular stimulation , 1996, Proceedings of 18th Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[7]  Yongqiang Ye,et al.  Simple LMI based learning control design , 2009 .

[8]  Eric Rogers,et al.  Identification of electrically stimulated muscle models of stroke patients , 2010 .

[9]  Chiang-Ju Chien,et al.  APPLICATION OF A MODEL‐BASED ITERATIVE LEARNING TECHNIQUE TO TRACKING CONTROL OF A PIEZOELECTRIC SYSTEM , 2005 .

[10]  Mikael Norrlöf,et al.  DISTURBANCE REJECTION USING AN ILC ALGORITHM WITH ITERATION VARYING FILTERS , 2004 .

[11]  M. E. Bise,et al.  Fractional calculus application in control systems , 1990, IEEE Conference on Aerospace and Electronics.

[12]  Hikaru Inooka,et al.  Incorporation of experience in iterative learning controllers using locally weighted learning , 2001, Autom..

[13]  Kok Kiong Tan,et al.  ITERATIVE LEARNING CONTROL VIA WEIGHTED LOCAL-SYMMETRICAL-INTEGRATION , 2008 .

[14]  Yangquan Chen,et al.  A generalized fractional-order iterative learning control , 2011, IEEE Conference on Decision and Control and European Control Conference.

[15]  O. Agrawal,et al.  Advances in Fractional Calculus , 2007 .

[16]  Kok Kiong Tan,et al.  Iterative learning feedback control of human limbs via functional electrical stimulation , 1999 .

[17]  Sandipan Mishra,et al.  Fundamental issues in iterative learning controller design: Convergence, robustness, and steady state performance , 2008 .

[18]  Hyo-Sung Ahn,et al.  Fractional‐order iterative learning control for fractional‐order linear systems , 2011 .

[19]  Saburou Saitoh.  Weighted L p -Norm Inequalities in Convolutions , 2000 .

[20]  Kevin L. Moore,et al.  Iterative Learning Control: Brief Survey and Categorization , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[21]  Masayoshi Tomizuka,et al.  Model inverse based Iterative Learning Control using finite impulse response approximations , 2009, 2009 American Control Conference.

[22]  Wenchang Tan,et al.  Intermediate processes and critical phenomena: Theory, method and progress of fractional operators and their applications to modern mechanics , 2006 .

[23]  Peter Xiaoping Liu,et al.  All-pass filtering in iterative learning control , 2009, Autom..

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

[25]  J. Machado.  Analysis and design of fractional-order digital control systems , 1997 .

[26]  K. Moore,et al.  Iterative Learning Control: Robustness and Monotonic Convergence for Interval Systems , 2010 .

[27]  Krzysztof Galkowski,et al.  PI control of discrete linear repetitive processes , 2006, Autom..

[28]  Kevin L. Moore,et al.  On D"-type Iterative Learning Control , 2001 .

[29]  Y. Chen,et al.  Fractional order iterative learning control , 2009, 2009 ICCAS-SICE.

[30]  YangQuan Chen,et al.  UBIQUITOUS FRACTIONAL ORDER CONTROLS , 2006 .

[31]  Krzysztof Galkowski,et al.  Modelling and Control of Bi-Directional Discrete Linear Repetitive Processes , 2010, IEEE Transactions on Automatic Control.

[32]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[33]  Eric Rogers.  Iterative learning control --- from Hilbert spaces to robotics to healthcare engineering , 2007 .

[34]  K L Moore,et al.  Iteration-domain closed-loop frequency response shaping for discrete-repetitive processes , 2010, Proceedings of the 2010 American Control Conference.