Iterative learning control for discrete-time systems with exponential rate of convergence

Abstract

An algorithm for Iterative Learning Control is proposed based on an optimization principle used by other authors to derive gradient type algorithms. The new algorithm is a descent algorithm and has potential benefits which include realization in terms of Riccati feedback and feedforward components. This realization also has the advantage of implicitly ensuring automatic step size selection and hence guaranteeing convergence without the need for empirical choice of parameters. The algorithm achieves a geometric rate of convergence for invertible plants. One important feature of the proposed algorithm is the dependence of the speed of convergence on weight parameters appearing in the norms of the signals chosen for the optimization problem.

Iterative nonlinear model predictive control. Stability, robustness and applications

“…Originally, it has been devised for dealing with linear batch processes, specially chemical processes (Lee et al, 1999), and it belongs to the class of model-based iterative controllers. Other example of model-based iterative controller is the qilc, presented by Amann et al (1996). In this work, we have tested the bmpc controller on the simulated pH plant.…”

One-Learning-Epoch Optimal LQDT with Input Constraint for the Repetitive Proper System with Unknown Disturbances

“…It is an error collection concept that accumulates the errors between output and reference during every iteration, and then uses it to improve the output tracking performance. Basically, our proposed ILC is identical to the optimal ILC [5] for this special case, although both formulations are quite different. However, due to the initialization of the methodology itself, it significantly reduces the learning epochs for the pre-specified tracking performance than that in [5].…”

“…The specified task is regarded as improving the tracking performance of systems. The objective of iterative learning control (ILC) [1][2][3][4][5][6] is to use the information from previous executions of the task and do repetitive work by tracking error in attempt to achieve the desired trajectory to minimal error, which has been successfully applied to the real systems, such as industrial robots, wafer scanner, chemical processes and many production machines.…”

Combined On-Line and Run-to-Run Optimization of Batch Processes with Terminal Constraints

“…Consequently, a high gain can be used to obtain fast convergence. Also, Amann et al (1996) propose a norm-optimal ILC scheme.…”

“…For discrete-time systems, Amann et al (1996) proposed to shift the error trajectories of the previous run backwards in time by rT s (anticipation), where r is the system relative degree and T s the sampling time. The same idea is also used to cope with varying initial conditions (Sun and Wang, 2003) or in the context of time-delay systems (Hideg, 1996;Park et al, 1998).…”