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

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Description/Abstract

Iterative Learning Control (ILC) is now well established in terms of both the underlying theory and experimental application. This approach is specifically tar- geted 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 indetermi- nates 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.