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# Nonlinear Model Predictive Control

## Module MA5321

This Module is offered by TUM Department of Mathematics.

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

### Module version of WS 2013/4

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
SS 2014WS 2013/4

### Basic Information

MA5321 is a semester module in English language at Master’s level which is offered irregular.

This module description is valid from WS 2013/4 to SS 2017.

180 h 60 h 6 CP

### Content, Learning Outcome and Preconditions

#### Content

Nonlinear mathematical control theory:
Stability of nonlinear differential equations, Ljapunov functions, asymptotic controllability, different methods of feedback stabilization, stability and stabilization of perturbed systems
Nonlinear Model predictive control (NMPC):
Fundamentals of NMPC, finite and infinite horizon NMPC, stability and suboptimality with/without constraints, feasibility and robustness

#### Learning Outcome

After successful completion of the module, students are familiar with the fundamentals of nonlinear mathematical control theory and have a detailed knowledge of nonlinear model predictive control as an important field of nonlinear control theory. They are able to apply this knowledge to the solution of typical control problems from science and engineering.

#### Preconditions

MA5334 - Model Predictive Control
MA2304 - Numerical Methods for Ordinary Differential Equations
MA2005 - Ordinary Differential Equations
MA2503 - Nichtlineare Optimierung

### Courses, Learning and Teaching Methods and Literature

#### Courses and Schedule

VO 4 Nonlinear Model Predictive Control Callies, R. Tue, 14:15–15:45, MI 02.10.011
Thu, 12:15–13:45, MI 02.08.020

#### Learning and Teaching Methods

Lecture with integrated exercise
In the lectures, the contents will be presented in a talk with demonstrative examples, as well as through discussion with the students. The lectures should motivate the students to carry out their own analysis of the themes presented and to independently study the relevant literature. Corresponding to each lecture, practice sessions will be offered, in which exercise sheets and solutions will be available. In this way, students can deepen their understanding of the methods and concepts taught in the lectures and independently check their progress.

#### Media

Blackboard and beamer

#### Literature

L. Grüne, J. Pannel: Nonlinear Model Predictive Control, Springer 2011
E. Camacho, C. Bordons: Model predictive control, Springer 2008
J. Rawlings: Model predictive control, Nob Hill Pub 2009

### Module Exam

#### Description of exams and course work

The exam will be in written form (60 minutes). Students demonstrate that they have gained deeper knowledge of definitions, theorems and main mathematical tools of nonlinear mathematical control theory - and especially nonlinear model predictive control - presented in the course and their applicability to problems in science and engineering. The students are in particular expected to have profound knowledge of stability and controllability of nonlinear systems and how to stabilize systems in presence of perturbations and constraints. The students are expected to be able to derive the different methods, to explain their special properties, and to transform them into formulations properly suited for realtime applications.

#### Exam Repetition

The exam may be repeated at the end of the semester.

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