Iterative Learning Control Design for Discrete Stochastic Linear Systems

This paper develops a new iterative learning control law for stochastic linear systems. The design is based on recently developed passivity based control of repetitive process, which are a class 2D nonlinear systems. In particular, this theory is used to design a nonlinear control law for linear dynamics, which allows tuning of the control law to achieve better performance. A supporting example is given, including a comparison with a previously reported design.

[1]  A. Isidori,et al.  Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems , 1991 .

[2]  Samer S. Saab.  Optimality of first-order ILC among higher order ILC , 2006, IEEE Transactions on Automatic Control.

[3]  Dong Shen,et al.  Survey on stochastic iterative learning control , 2014 .

[4]  Christopher I. Byrnes,et al.  Passivity and absolute stabilization of a class of discrete-time nonlinear systems, , 1995, Autom..

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

[6]  Krzysztof Galkowski,et al.  Stochastic Stability of Some Classes of Nonlinear 2D Systems , 2018, Autom. Remote. Control..

[7]  Samer S. Saab.  Optimal selection of the forgetting matrix into an iterative learning control algorithm , 2005, IEEE Transactions on Automatic Control.

[8]  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).

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

[10]  Krzysztof Galkowski,et al.  Experimentally supported 2D systems based iterative learning control law design for error convergence and performance , 2010 .

[11]  Krzysztof Galkowski,et al.  Dissipativity and stabilization of nonlinear repetitive processes , 2016, Syst. Control. Lett..

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

[13]  Dong Shen,et al.  A Technical Overview of Recent Progresses on Stochastic Iterative Learning Control , 2018, Unmanned Syst..

[14]  Se-Kyu Oh,et al.  Stochastic iterative learning control for discrete linear time-invariant system with batch-varying reference trajectories , 2015 .

[15]  J. Willems.  Dissipative dynamical systems part I: General theory , 1972 .

[16]  A.G. Alleyne,et al.  A survey of iterative learning control , 2006, IEEE Control Systems.