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G. Angelov, A. Corella, V.M. Veliov:
"On the accuracy of the model predictive control method";
Research Reports (Vienna University of Technology, Institute of Statistics and Mathematical Methods in Economics, Operations Research and Control Systems), 2021-05 (2021), 05; 20 pages.

The paper investigates the accuracy of the Model Predictive Control (MPC) method for finding online approximate optimal feedback control for Lagrange 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 er-
ror 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 in-
volves an extension of the notion of strong metric sub-regularity of set-valued maps and utilization of a specific new metric in the control space, which makes the proof non-standard. The result is specialized for two problem classes: coercive problems, and affine problems.

optimal control, Lagrange problem, model predictive control, metric sub-regularity

https://publik.tuwien.ac.at/files/publik_298642.pdf