Similar to Chap. 2, this chapter also considers a class of discrete-time linear systems with randomly varying trial lengths. However, in contrast to Chap. 2, this chapter aims to avoid using the traditional \(\lambda \)-norm in convergence analysis which may lead to a non-monotonic convergence. Compared to Chap. 2, the main contributions of the chapter can be summarized as follows: (i) A new formulation is presented for ILC of discrete-time systems with randomly varying trial lengths by defining a stochastic matrix. Comparing with Chap. 2, the introduction of the stochastic matrix is more straightforward, and the calculation of its probability distribution is less complex. (ii) Different from Chap. 2, we investigate ILC for systems with nonuniform trial lengths under the framework of lifted system and the utilization of \(\lambda \)-norm is avoided.
This is a preview of subscription content, log in to check access.
Bien Z, Xu J-X (1998) Iterative learning control: analysis, design, integration and applications. Kluwer, BostonCrossRefGoogle Scholar
Park K-H (2005) An average operator-based PD-type iterative learning control for variable initial state error. IEEE Trans Autom Control 50(6):865–869MathSciNetCrossRefGoogle Scholar
Seel T, Schauer T, Raisch J (2011) Iterative learning control for variable pass length systems. In: Proceedings of 18th IFAC world congress, pp 4880-4885CrossRefGoogle Scholar
Longman RW, Mombaur KD (2006) Investigating the use of iterative learning control and repetitive control to implement periodic gaits. Lect Notes Control Inf Sci 340:189–218MathSciNetzbMATHGoogle Scholar
Moore KL (2000) A non-standard iterative learning control approach to tracking periodic signals in discrete-time non-linear systems. Int J Control 73(10):955–967MathSciNetCrossRefGoogle Scholar