A new method to study ILC problem for time-delay linear systems

In this paper, we apply a new method, a delayed matrix exponential, to study P-type and D-type learning laws for time-delay controlled systems to track the varying reference accurately by using a few iterations in a finite time interval. We present open-loop P- and D-type asymptotic convergence results in the sense of λ-norm by virtue of spectral radius of matrix. Finally, four examples are given to illustrate our theoretical results.

[1]  James M. Ortega,et al.  Iterative solution of nonlinear equations in several variables , 2014, Computer science and applied mathematics.

[2]  Masaru Uchiyama,et al.  Formation of High-Speed Motion Pattern of a Mechanical Arm by Trial , 1978 .

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

[4]  Ji-Huan He,et al.  Variational iteration method for delay differential equations , 1997 .

[5]  Sun Mingxuan.  Robust Convergence Analysis of Iterative Learning Control Systems , 1998 .

[6]  Zeungnam Bien,et al.  Iterative learning control: analysis, design, integration and applications , 1998 .

[7]  AhnHyo-Sung,et al.  Iterative Learning Control , 1999 .

[8]  Zhengguo Li,et al.  Analysis and design of impulsive control systems , 2001, IEEE Trans. Autom. Control..

[9]  Z. Zenn Bien,et al.  Design Issues on Robustness and Convergence of Iterative Learning Controller , 2002, Intell. Autom. Soft Comput..

[10]  Jian-Xin Xu,et al.  On iterative learning from different tracking tasks in the presence of time-varying uncertainties , 2004, IEEE Trans. Syst. Man Cybern. Part B.

[11]  Xinzhi Liu,et al.  Exponential stability for impulsive delay differential equations by Razumikhin method , 2005 .

[12]  G. V. Shuklin,et al.  Relative Controllability in Systems with Pure Delay , 2005 .

[13]  Yangquan Chen,et al.  Fractional order [proportional derivative] controller for a class of fractional order systems , 2009, Autom..

[14]  Tamás Kalmár-Nagy,et al.  Delay differential equations : recent advances and new directions , 2009 .

[15]  D. Khusainov,et al.  Boundary Value Problems for Delay Differential Systems , 2010 .

[16]  Josef Diblík,et al.  Fredholm’s boundary-value problems for differential systems with a single delay , 2010 .

[17]  Hyo-Sung Ahn,et al.  On the PDα-type iterative learning control for the fractional-order nonlinear systems , 2011, Proceedings of the 2011 American Control Conference.

[18]  D. Khusainov,et al.  Boundary-Value Problems for Weakly Nonlinear Delay Differential Systems , 2011 .

[19]  Milan Medved,et al.  Stability and the nonexistence of blowing-up solutions of nonlinear delay systems with linear parts , 2011 .

[20]  Milan Medved,et al.  Sufficient conditions for the asymptotic stability of nonlinear multidelay differential equations with linear parts defined by pairwise permutable matrices , 2012 .

[21]  J. Diblík,et al.  Representation of a solution of the Cauchy problem for an oscillating system with two delays and permutable matrices , 2013 .

[22]  Margarita Rivero,et al.  Existence and stability results for nonlinear fractional order Riemann-Liouville Volterra-Stieltjes quadratic integral equations , 2014, Appl. Math. Comput..

[23]  Song Liu,et al.  Lyapunov method for nonlinear fractional differential systems with delay , 2015 .

[24]  M. Z. Liu,et al.  Exponential stability of the exact solutions and the numerical solutions for a class of linear impulsive delay differential equations , 2015, J. Comput. Appl. Math..

[25]  Guojun Li.  High-order iterative learning control for nonlinear systems , 2017, 2017 6th Data Driven Control and Learning Systems (DDCLS).