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Department of Mathematics

Chair of Applied Mathematics Prof. Dr. L. Grüne / Prof. Dr. A. Schiela

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Model Predictive Control
Course at the Winter School of the
International Doctorate Program
"Identification, Optimization and Control with Applications in Modern Technologies"
4th - 6th March 2009, Schloss Thurnau
Prof. Dr. Lars Grüne, Universität Bayreuth

Summary: This course gives an introduction into the theoretical foundations of model predictive control (MPC), focusing on nonlinear MPC and systems theoretic properties like stability, inverse optimality and suboptimality.

  Slides (PDF format, including "click-through" animations)
  Handout (PDF format, static version of the slides suitable for printing)

 Matlab examples from the course
  Purpose: The examples illustrate different NMPC variants for the car-on-the-road problem from p.11 of the slides.

Usage: After starting the respective M-File in Matlab, each left-click into the graphics window will make the MPC closed loop trajectory advance for one time step. A right-click will stop the program. Feel free to modify the parameters in the files (in particular the optimization horizon N) in order to see different effects.

Note: The M-Files need Matlab's Optimization Toolbox.

  mpc_1.m (no stabilizing constraints, norm^2 distance as running cost)
  mpc_2.m (equilibrium endpoint constraints, norm^2 distance as running cost)
  mpc_3.m (regional endpoint constraints + terminal cost, norm^2 distance as running cost)
  mpc_4.m (no stabilizing constraints, weighted norm^2 distance as running cost)

 Further reading
  The material from this course is now available in a book. See   www.nmpc-book.com   for details.

For MPC with stabilizing constraints (Part I of the course) I recommend the survey article Constrained model predictive control: Stability and optimality by D. Mayne et al. as a starting point for further reading.

Part II of the course is mainly based on my article Analysis and design of unconstrained nonlinear MPC schemes for finite and infinite dimensional systems. In the list of references of this article you also find most of the literature cited in the slides.

The last section of Part II is based on A networked unconstrained nonlinear MPC scheme by J. Pannek, K. Worthmann and myself. The full proof of Theorem 5.2 can be found here.
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