Reference
C. Liu, S. Shi, and B. De Schutter, "Stability and performance analysis of
model predictive control of uncertain linear systems,"
Proceedings of the 63rd IEEE Conference on Decision and
Control, Milan, Italy, pp. 7356-7362, Dec. 2024.
Abstract
Model mismatch often presents significant challenges in model-based controller
design. This paper investigates model predictive control (MPC) for uncertain
linear systems with input constraints, where the uncertainty is characterized
by a parametric mismatch between the true system and its estimated model. The
main contributions of this work are twofold. First, a theoretical performance
bound is derived using relaxed dynamic programming. This bound provides a novel
insight into how the prediction horizon and modeling errors affect the
suboptimality of the MPC controller to the oracle infinite-horizon optimal
controller, which has complete knowledge of the true system. Second, sufficient
conditions are established under which the nominal MPC controller, which relies
solely on the estimated system model, can stabilize the true system despite
model mismatch. Numerical simulations are presented to validate these
theoretical results, demonstrating the practical applicability of the derived
conditions and bounds. These findings offer practical guidelines for achieving
desired modeling accuracy and selecting an appropriate prediction horizon in
designing certainty-equivalence MPC controllers for uncertain linear systems.
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BibTeX
@inproceedings{LiuShi:24-024,
author = {Liu, Changrui and Shi, Shengling and De Schutter, Bart},
title = {Stability and Performance Analysis of Model Predictive Control
of Uncertain Linear Systems},
booktitle = {Proceedings of the 63rd IEEE Conference on Decision and
Control},
address = {Milan, Italy},
pages = {7356--7362},
month = dec,
year = {2024}
}