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Iterative learning control for spatio-temporal dynamics using Crank-Nicholson discretization

Iterative learning control for spatio-temporal dynamics using Crank-Nicholson discretization
Iterative learning control for spatio-temporal dynamics using Crank-Nicholson discretization
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.
185-208
Cichy, B
7f9e82ee-ff3f-40d7-839e-0e54d878538e
Galkowski, K
65b638be-b5a5-4e25-b1b8-e152c08a1cbb
Rogers, E
611b1de0-c505-472e-a03f-c5294c63bb72
Cichy, B
7f9e82ee-ff3f-40d7-839e-0e54d878538e
Galkowski, K
65b638be-b5a5-4e25-b1b8-e152c08a1cbb
Rogers, E
611b1de0-c505-472e-a03f-c5294c63bb72

Cichy, B, Galkowski, K and Rogers, E (2012) Iterative learning control for spatio-temporal dynamics using Crank-Nicholson discretization. Multidimensional Systems and Signal Processing, 23 (1-2), 185-208.

Record type: Article

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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Published date: 2012
Organisations: Southampton Wireless Group

Identifiers

Local EPrints ID: 272473
URI: https://eprints.soton.ac.uk/id/eprint/272473
PURE UUID: 840168e5-45cc-452e-af5b-8f24f3f7913f
ORCID for E Rogers: ORCID iD orcid.org/0000-0003-0179-9398

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Date deposited: 15 Jun 2011 11:35
Last modified: 29 Oct 2019 02:08

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