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A.L. Dontchev, I. Kolmanovsky, M. Krastanov, V.M. Veliov:
"Approximating open-loop and closed-loop optimal control by model predictive control";
Research Reports (Vienna University of Technology, Institute of Statistics and Mathematical Methods in Economics, Operations Research and Control Systems), 2019-09 (2019), 9; 14 pages.

This research report contains an extraction of some results from the report [6] and an additional material, as described in the next lines. We consider a nite-horizon continuous-time optimal control problem with nonlinear dynamics, an integral cost,control constraints and a time-varying parameter which represents perturbations or uncertainty. After time-discretization of the problem we employ a Model Predictive
Control (MPC) algorithm, which uses a \prediction"/forecast for the uncertain parameter and (possibly inexact) measurements of the state vector, and generates a piecewise constant control signal by solving auxiliary open-loop control problems. In our main result we derive an estimate of the di erence between the MPC-generated control and
the optimal feedback control, both obtained for the same value of the perturbation parameter, in terms of the step-size of the discretization and the measurement error. We also estimate the distance from the MPC-generated control to the the optimal open-loop
control in the problem with the \true" value of the uncertain parameter, depending on
the prediction error.

https://publik.tuwien.ac.at/files/publik_281825.pdf