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Processes 2015, 3(1), 161-177;

Fast Wavelet-Based Model Predictive Control of Differentially Flat Systems

School of Chemical Engineering, University of New South Wales, Sydney, New South Wales 2052, Australia
This paper is an extended version of paper presented at Australian Control Conference, Canberra, Australia, 17–18 November 2014.
Author to whom correspondence should be addressed.
Academic Editor: Gabriele Pannocchia
Received: 19 December 2014 / Revised: 18 February 2015 / Accepted: 26 February 2015 / Published: 11 March 2015
(This article belongs to the Special Issue Process Control: Current Trends and Future Challenges)
Full-Text   |   PDF [415 KB, uploaded 11 March 2015]


A system is differentially flat if it is Lie–Bäcklund (L-B) equivalent to a free dynamical system that has dimensions equal to that of the input of the original system. Utilizing this equivalence, the problem of nonlinear model predictive control of a flat system can be reduced to a lower dimensional nonlinear programming problem with respect to the flat outputs. In this work, a novel computational method based on Haar wavelets in the time-domain for solving the resulting nonlinear programming problem is developed to obtain an approximation of the optimal flat output trajectory. The Haar wavelet integral operational matrix is utilized to transform the nonlinear programming problem to a finite dimensional nonlinear optimization problem. The proposed approach makes use of flatness as a structural property of nonlinear systems and the convenient mathematical properties of Haar wavelets to develop an efficient computational algorithm for nonlinear model predictive control of differentially flat systems. Further improvement on computational efficiency is achieved by providing solutions with multiple resolutions (e.g., obtaining high resolution solutions only for the near future, but allowing coarse approximation for the later stage in the prediction horizon). View Full-Text
Keywords: nonlinear model predictive control; differential flatness; Haar wavelets nonlinear model predictive control; differential flatness; Haar wavelets
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Wang, R.; Tippett, M.J.; Bao, J. Fast Wavelet-Based Model Predictive Control of Differentially Flat Systems. Processes 2015, 3, 161-177.

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