Angelov, G., Dominguez Corella, A., & Veliov, V. M. (2022). On the Accuracy of the Model Predictive Control Method. SIAM Journal on Control and Optimization, 60(4), 2469–2487. https://doi.org/10.1137/21M1460430
E105-04 - Forschungsbereich Variationsrechnung, Dynamische Systeme und Operations Research
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Journal:
SIAM Journal on Control and Optimization
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ISSN:
0363-0129
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Date (published):
16-Aug-2022
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Number of Pages:
19
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Publisher:
SIAM PUBLICATIONS
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Peer reviewed:
Yes
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Keywords:
Lagrange problem; metric subregularity; model predictive control; optimal control
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Abstract:
The paper investigates the accuracy of the model predictive control (MPC) method for finding on-line approximate optimal feedback control for Bolza-type problems on a fixed finite horizon. The predictions for the dynamics, the state measurements, and the solution of the auxiliary open-loop control problems that appear at every step of the MPC method may be inaccurate. The main result provides an error estimate of the MPC-generated solution compared with the optimal open-loop solution of the “ideal” problem, where all predictions and measurements are exact. The technique of proving the estimate involves an extension of the notion of strong metric subregularity of set-valued maps and utilization of a specific new metric in the control space, which makes the proof nonstandard. The result is specialized for two problem classes: coercive problems and affine problems.
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Project title:
Regularität von Abbildungen - Theorie und Anwendungen: I 4571-N (Fonds zur Förderung der wissenschaftlichen Forschung (FWF))
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Research Areas:
Mathematical and Algorithmic Foundations: 20% Fundamental Mathematics Research: 80%
