Title: Explicit efficient constrained model predictive control

Authors: Darren Lamburn; Peter Gibbens; Steven Dumble

Addresses: School of Aerospace, Mechanical and Mechatronic Engineering, University of Sydney, New South Wales, Australia ' School of Aerospace, Mechanical and Mechatronic Engineering, University of Sydney, New South Wales, Australia ' School of Aerospace, Mechanical and Mechatronic Engineering, University of Sydney, New South Wales, Australia

Abstract: A more efficient model predictive control algorithm is algebraic model predictive control. The efficiency is improved by forming the prediction horizon with a non-uniform distribution of points. The most efficient case reduces the problem down to a single prediction point, defining the horizon length as well as removing any redundant control calculations. This paper shows that for this single prediction point case, the constrained control can be easily evaluated explicitly, thus making the control calculation deterministic and more efficient. We also show that because an explicit control can be determined for the system, the closed-loop constrained stability bounds can be evaluated a priori. Using the key constraint of the peak location of the response also allows the system to meet the constraints while still being explicit and deterministic. The proposed explicit algorithm is applied to two numerical simulation examples with the performance, computational efficiency and stability analysed.

Keywords: constraints; continuous linear systems; efficient predictive control; explicit MPC; model predictive control; constrained control; numerical simulation.

DOI: 10.1504/IJAAC.2016.079538

International Journal of Automation and Control, 2016 Vol.10 No.4, pp.329 - 355

Received: 26 Sep 2015
Accepted: 29 Jan 2016
Published online: 30 Sep 2016 *

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