On the Accuracy of the Model Predictive Control Method
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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Information & Authors
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Published In
SIAM Journal on Control and Optimization
Pages: 2469 - 2487
DOI: 10.1137/21M1460430
ISSN (online): 1095-7138
Copyright
© 2022, Society for Industrial and Applied Mathematics.
History
Submitted: 18 November 2021
Accepted: 19 May 2022
Published online: 16 August 2022
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Funding Information
Austrian Science Fund https://doi.org/10.13039/501100002428 : I4571
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