A numerical method for determining monotonicity and convergence rate in iterative learning control

Abstract

In iterative learning control (ILC), a lifted system representation is often used for design and analysis to determine the convergence rate of the learning algorithm. Computation of the convergence rate in the lifted setting requires construction of large N×N matrices, where N is the number of data points in an iteration. The convergence rate computation is O(N²) and is typically limited to short iteration lengths because of computational memory constraints. As an alternative approach, the implicitly restarted Arnoldi/Lanczos method (IRLM) can be used to calculate the ILC convergence rate with calculations of O(N). In this article, we show that the convergence rate calculation using IRLM can be performed using dynamic simulations rather than matrices, thereby eliminating the need for large matrix construction. In addition to faster computation, IRLM enables the calculation of the ILC convergence rate for long iteration lengths. To illustrate generality, this method is presented for multi-input multi-output, linear time-varying discrete-time systems.

Keywords:

• iterative learning control
• monotonic convergence
• convergence rate
• implicitly restarting Lanczos method