An iterative learning control method for continuous-time systems based on 2-D system theory

Abstract

This letter presents a two-dimensional (2-D) system theory based iterative learning control (ILC) method for linear continuous-time multivariable systems. We demonstrate that a 2-D continuous-discrete model can be successfully applied to describe both the dynamics of the control system and the behavior of the learning process. We successfully exploited the 2-D continuous-discrete Roesser's linear model by extending the ILC technique from discrete control systems to continuous control systems. Three learning rules for ILC are derived. Necessary and sufficient conditions are given for convergence of the proposed learning rules. Compared to the learning rule suggested by Arimoto [2], our developed learning rules are less restrictive and have wider applications. The third learning rule proposed in this letter ensures the reference output trajectory can be accurately tracked after only one learning trial. Three numerical examples are used to illustrate the proposed control procedures.

Necessary and sufficient stability condition of LTV iterative learning control systems using a 2‐D approach

“…is a product of infinite series, which satisfies (27) Using the above equation repetitively and inserting (25), we obtain…”

Feedback iterative learning control for time-delay systems based on 2D analysis approach

“…3 ILC design transformation based on using 2D Roesser systems 3.1 2D system representation (6) is essentially a 2D process with evolution along two independent axes: time t and trial k. To clearly describe such a process, the type of continuous-discrete 2D linear system is popular, which is usually formulated in the form of Roesser's state-space models [7,13]. In this section, we will develop a new approach to achieving this 2D ILC dynamics formulation of TDS.…”

“…These approaches to feedback ILC are based on converting the two-dimensional (2D) problem into two separate one-dimensional (1D) problems. In references [7,8], the feedback ILC design has been successfully transformed into a control problem of 2D Roesser systems. The advantage of this transformation is that the entire 2D dynamics of ILC can be clearly described by a mathematical model, and the 2D system theory can be applied to the ILC stability analysis.…”

Trajectory‐keeping in satellite formation flying via robust periodic learning control

“…The paradigm of ILC was originally motivated in the context of what was called a 'multipass' system, where a process involved a movement along a path in space and was then returned to its starting location before repeating the movement (see [3][4][5]). While such multipass systems typically had a spatial-temporal nature, ILC was developed for lumped-parameter systems that were to be driven to have an output follow a desired trajectory in the time domain.…”