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@unpublished{faucris.276378997,
abstract = {The local stability and convergence for Model Predictive Control (MPC) of unconstrained nonlinear dynamics based on a linear time-invariant plant model is studied. Based on the long-time behavior of the solution of the Riccati Differential Equation (RDE), explicit error estimates are derived that clearly demonstrate the influence of the two critical parameters in MPC: the prediction horizon $T$ and the control horizon $\tau$. In particular, if the MPC-controller has access to an exact (linear) plant model, the MPC-controls and the corresponding optimal state trajectories converge exponentially to the solution of an infinite-horizon optimal control problem when $T-\tau \rightarrow \infty$. When the difference between the linear model and the nonlinear plant is sufficiently small in a neighborhood of the origin, the MPC strategy is locally stabilizing and the influence of modeling errors can be reduced by choosing the control horizon $\tau$ smaller. The obtained convergence rates are validated in numerical simulations.},
author = {Veldman, Daniel and Zuazua Iriondo, Enrique},
faupublication = {yes},
keywords = {Convergence; Model Predictive Control; Receding Horizon Control; Stability},
note = {https://cris.fau.de/converis/publicweb/Publication/276378997},
peerreviewed = {automatic},
title = {{Local} {Stability} and {Convergence} of {Unconstrained} {Model} {Predictive} {Control}},
url = {http://arxiv.org/abs/2206.01097},
year = {2024}
}