Stability and Performance Analysis of Model Predictive Control of Uncertain Linear Systems
arxiv(2024)
Abstract
Model mismatch often poses challenges in model-based controller design. This
paper investigates model predictive control (MPC) of uncertain linear systems
with input constraints, focusing on stability and closed-loop infinite-horizon
performance. The uncertainty arises from a parametric mismatch between the true
and the estimated system under the matrix Frobenius norm. We examine a simple
MPC controller that exclusively uses the estimated system model and establishes
sufficient conditions under which the MPC controller can stabilize the true
system. Moreover, we derive a theoretical performance bound based on relaxed
dynamic programming, elucidating the impact of prediction horizon and modeling
errors on the suboptimality gap between the MPC controller and the Oracle
infinite-horizon optimal controller with knowledge of the true system.
Simulations of a numerical example validate the theoretical results. Our
theoretical analysis offers guidelines for obtaining the desired modeling
accuracy and choosing a proper prediction horizon to develop
certainty-equivalent MPC controllers for uncertain linear systems.
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