An approach to iterative learning control for spatio-temporal dynamics using nD discrete linear systems models

Iterative Learning Control (ILC) is now well established in terms of both the underlying theory and experimental application. This approach is specifically targeted at cases where the same operation is repeated over a finite duration with resetting between successive trials or executions. Each pass or execution is known as a trial and the key idea is to use information from previous trials to update the control input used on the current one with the aim of improving performance from trial-to-trial. In this paper, the subject area is the application of ILC to spatio-temporal systems described by a linear partial differential equation (PDE) using a discrete approximation of the dynamics, where there are a number of construction methods that could be applied. Here explicit discretization is used, resulting in a multidimensional, or nD, discrete linear system on which to base control law design, where n denotes the number of directions of information propagation and is equal to the total number of indeterminates in the PDE. The resulting control laws can be computed using Linear Matrix Inequalities (LMIs) and a numerical example is given to illustrate the complete design approach. Finally, a natural extension to robust control is noted and areas for further research briefly discussed