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A new procedure for the design of iterative learning controllers using a 2D systems formulation of processes with uncertain spatio-temporal dynamics

Cichy B., Gałkowski K., Dąbkowski K., Aschemann H., Rauh A.

Control and Cybernetics

2013

Vol. 42, no. 1

9--26

Iterative Learning Control (ILC) is well established in control of linear and nonlinear dynamic systems, both as to underlying theory and experimental validation. This approach specifically aims at applications with the same operation repeated over finite time intervals and reset taking place between subsequent executions (the trials). The main principle behind ILC is to suitably use information from previous trials in selection of the input signal in the current trial with the objective of performance improvement from trial to trial. In this paper, new computationally efficient results are presented for an extension of the ILC approach to the uncertain 2D systems that arise from time and space discretization of partial differential equations. This type of application implies the need to use a spatio–temporal setting for the analysis of the control procedure. The resulting control laws can be computed using Linear Matrix Inequalities (LMIs). An illustrative example is provided.