Numerical Optimization and Model Predictive Control (OPT)5 ECTS
(englische Bezeichnung: Numerical Optimization and Model Predictive Control)

Lectures:

• • Numerical Optimization and Model Predictive Control
    (Vorlesung, 3 SWS, Knut Graichen, Wed, 10:15 - 11:45, 04.023; The course is planned as a face-to-face event. Interested participants please register via StudOn, where you will also be informed about any date/mode changes.)
  • Exercises for Numerical Optimization and Model Predictive Control
    (Übung, 1 SWS, Paulina Spenger, Fri, 14:15 - 15:45, 04.023; The course is planned as a face-to-face event. Interested participants please register via StudOn, where you will also be informed about any date/mode changes.)

Empfohlene Voraussetzungen:

Basic knowledge of advanced mathematics (especially linear algebra)
Basic knowledge of dynamical systems in time domain description (e.g. Regelungstechnik B)

Inhalt:

Many problems in economy and industry require an optimal solution under consideration of specific criteria and constraints. From a mathematical point of view, this requires the numerical solution of a parametric optimization problem or a dynamic optimization problem. The latter formulation accounts for the dynamics of the underlying process and is particularly relevant in the context of optimal control and model predictive control (MPC).

In summary, the course covers the following topics:

• Introduction to and examples of static and dynamic optimization problems

• Unconstrained numerical optimization (optimality conditions, numerical methods)

• Constrained numerical optimization (linear/quadratic/nonlinear problems, optimality conditions, numerical methods)

• Dynamical optimization / optimal control problems (calculus of variations, optimality conditions, PMP, numerical methods)

• Nonlinear model predictive control (formulations, stability, real-time solution)
  

Lernziele und Kompetenzen:

After successful completion of the module, students will be able to

• differentiate the problem classes of parametric and dynamic optimization

• formulate and analyze practical optimization problems

• derive and solve the optimality conditions for unconstrained and constrained optimization problems using state-of-the-art software tools

• classify the different formulations and stability criteria for nonlinear model predictive control

• design a model predictive controller for a given control task and analyze the performance and stability properties in closed loop

• realize and implement a real-time MPC for highly dynamical nonlinear systems with sampling times in the (sub)millisecond range using modern state-of-the-art (N)MPC software

Literatur:

• S. Boyd, L. Vandenberghe. Convex Optimization. Cambridge University Press, 2004
• J. Nocedal, S.J. Wright. Numerical Optimization. New York: Springer, 2006
• M. Papageorgiou, M. Leibold, M. Buss. Optimierung. Berlin: Springer, 2012
• C.T. Kelley. Iterative Methods for Optimization. Society for Industrial und Applied Mathematics (SIAM), 1999
• D.P. Bertsekas. Nonlinear Programming. Belmont. Athena Scientific, 1999
• E. Camacho, C. Alba. Model Predictive Control. 2. Auflage, Springer, 2004
• L. Grüne, J. Pannek. Nonlinear Model Predictive Control: Theory and Algorithms, Springer, 2011

Studien-/Prüfungsleistungen:

Numerical Optimization and Model Predictive Control (Prüfungsnummer: 25281)

(englischer Titel: Numerical optimization and modelpredictive control)

Prüfungsleistung, Klausur, Dauer (in Minuten): 90, benotet, 5 ECTS

Anteil an der Berechnung der Modulnote: 100.0 %

Prüfungssprache: Englisch

Erstablegung: SS 2022, 1. Wdh.: WS 2022/2023

1. Prüfer:

Knut Graichen