Abstract
Iterative learning control is now well established for linear and nonlinear dynamics 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 repetitions. Each repetition or pass 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, new results on ILC applied to systems that arise from discretization of bi-variate partial differential equations describing spatio-temporal systems or processes are developed. Theses are based on Crank-Nicholson discretization of the governing partial differential equation, resulting in an unconditionally numerically stable approximation of the dynamics. It is also shown that this setting allows the selection of a finite number of points for sensing and actuation. The resulting control laws can be computed using Linear Matrix Inequalities (LMIs). Finally, an illustrative example is given and areas for further research are discussed.
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This work has been partially supported by the Ministry of Science and Higher Education in Poland under the project N N514 293235.
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Cichy, B., Gałkowski, K. & Rogers, E. Iterative learning control for spatio-temporal dynamics using Crank-Nicholson discretization. Multidim Syst Sign Process 23, 185–208 (2012). https://doi.org/10.1007/s11045-010-0132-1
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DOI: https://doi.org/10.1007/s11045-010-0132-1