### COURSE ORGANIZATION

#### PERSONNEL

Lecturers: | Roy Smith | |||

Paul Goulart | ||||

Office | Phone | |||

Alberto Giovanni Busetto | ETL K 14.1 | 044 632 46 88 | alberto.busetto(at)inf.ethz.ch | |

Angelos Georghiou | ETL K 12 | 044 632 85 31 | angelosg(at)control.ee.ethz.ch | |

Marius Schmitt | ETL K 12 | 044 632 4274 | schmittm(at)student.ethz.ch |

#### LECTURE LOCATION AND SCHEDULE

Lecture: | Tuesdays | 16:15 to 18:00 | CAB G 61 |

Exercises: | Fridays | 10:15 to 12:00 | ETZ D 61.1 |

#### PREREQUISITES

Control systems (227-0216-00L), Linear system theory (227-0225-00L), or equivalents, as well as sufficient mathematical maturity.#### CONTENT

An optimization based approach to robust control theory and applications. Topics will include: H-infinity and H-2 control design; structured-singular value analysis and synthesis; model reduction; convex optimization; semi-definite programming; and interior point methods.#### GRADING

The majority of the course grade will depend on a written project report. Details of the project will be made available during the course. The idea is that students will choose a robust control design and analysis application; design robust controllers; assess their performance; simulate their behaviour; and write up the results. The relative weighting of the course components in the assessment of the final grade will be:Exercises: | 30 % |

Final project proposal: | 10 % |

Final project report: | 60 % |

### LECTURE MATERIALS

Lecture | Date | Topic | MATLAB code | Last revised |
---|---|---|---|---|

01 | 19.02.2014 | Introduction and overview | 17.02.2014 | |

02 | 25.02.2014 | SISO robustness analysis | 04.03.2014 | |

03 | 04.03.2014 | MIMO robustness analysis | 04.03.2014 | |

04 | 11.03.2014 | Stability and Performance | 11.03.2014 | |

05 | 18.03.2014 | Convex Optimization | 18.03.2014 | |

06 | 25.03.2014 | Duality at KKT Conditions | 25.03.2014 | |

07 | 01.04.2014 | Structured singular value I | 01.04.2014 | |

08 | 08.04.2014 | Structured singular value II | 08.04.2014 | |

09 | 15.04.2014 | Robust synthesis | D-K iteration example | 15.04.2014 |

10 | 29.04.2014 |
H_{2} synthesis |
29.04.2014 | |

11 | 06.05.2014 | IQCs and Multiobjective Design | 06.05.2014 | |

12 | 13.05.2014 | µ-Synthesis and other problems | Aeroelasticity design example | 13.05.2014 |

13 | 20.05.2014 | Model Reduction | 20.05.2014 | |

14 | 27.05.2014 | Modeling and validation | 27.05.2014 |

Podcasts of the lectures can be downloaded or viewed online. (2014 lectures, 2012 lectures).

### EXERCISES

Exercise | Date | Questions | Hints | Solutions | Last revised |
---|---|---|---|---|---|

1 | 21.02.2014 | Exercise 1 | Solutions 1 | 21.02.2014 | |

2 | 28.02.2014 | Exercise 2 | Solutions 2 | 27.02.2014 | |

3 | 07.03.2014 | Exercise 3 | Solutions 3 | 07.03.2014 | |

4 | 14.03.2014 | Exercise 4 | Hints 4 | Solutions 4 | 14.03.2014 |

5 | 21.03.2014 | Exercise 5 | Solutions 5 | 21.03.2014 | |

6 | 27.03.2014 | Exercise 6 | Solutions 6 | 27.03.2014 | |

7 | 04.04.2014 | Exercise 7 | Solutions 7 | 04.04.2014 | |

8 | 11.04.2014 | Exercise 8 | Solutions 8 | 08.05.2014 | |

9 | 2.05.2014 | Exercise 9 | 2.05.2014 | ||

10 | 8.05.2014 | Exercise 10 | 8.05.2014 | ||

11 | 15.05.2014 | Exercise 11 | 15.05.2014 |

Grades for each exercise can be found here.

Exercises will be distributed each week in the exercise session, and made available here for download. The assistants will present background material for the exercise in the exercise session and be available to answer questions.

We expect to assign 10 exercises for the class. The grading will be on a quantized scale: 0, 1 or 2. However only your best 8 exercise scores will count towards your course grade.

Exercises must be done individually. You are encouraged to discuss the exercises amongst yourselves but are not allowed to share your solutions or other written material.

The email address for submissions is
*ifaatic@ee.ethz.ch*. Exercises should be handed in as PDF attachments to an email
to this address, with filename **ATICXX-Surname-StudentNumber.pdf**, where XX is the
exercise number. For example ATIC01-Jones-01-234-567.pdf. The exercises must be
submitted no later than 09.59 on the next Friday.
The assistants will discuss the solution during the exercise session immediately following the deadline.

### OFFICE HOUR

The office will be on Wednesdays at 4-5pm in ETL I10. During the office hours you can ask questions about the homework and your individual projects.

### DESIGN PROJECT

The details of the design project are given in the
attached description
**(updated: 16 April 2014)**.

For examples of prior student projects, please see here. You may use any of the models given in these earlier projects as the starting point for your own project.

Date | Project submission | Filename for submission |
---|---|---|

18.04.2014 | 1 page preliminary proposal | ATICprop-Surname-StudentNumber.pdf |

01.06.2014 | 5 page project report | ATICreport-Surname-StudentNumber.pdf |

The email address for the submission of these items is
*ifaatic@ee.ethz.ch*. The proposal and report must be handed in as PDF attachments to an email
to this address, with filename given in the above table.

The preferred software for creating both the proposal and the report is LaTeX or one of its variants (MikTeX, Texshop, etc.). The following .cls and example files can be used to format your report. They are actually those required by almost all IEEE conferences for the submission of papers. Also attached here is an example layout and extensive documentation of paper formatting.

File | Description |
---|---|

IEEEtran.cls | Class file for IEEEtran style |

bare_conf.tex | Simple example of a conference paper submission |

IEEEtran_HOWTO.pdf | Detailed description for using the class file (read only the first parts) |

Microsoft Word is not a high quality typesetting program and for most conferences is not acceptable. If you don't know how to use LaTeX and would like to use Microsoft Word instead please make sure all of the following conditions are satisfied:

- You can make Word generate the correct two-column format with the appropriate font size.
- The resulting PDF has all fonts embedded and no bitmapped fonts.
- You are unlikely to want to write another technical paper or report in your career.

### REFERENCES

The following papers contain details about the material presented in the course.

Authors | Year | Title and source |
---|---|---|

Desoer and Wang | 1980 |
"On the Generalized Nyquist Stability Criterion,"
IEEE Trans. Automatic Control., Vol. 25, No. 2, pp. 187-196. |

Doyle | 1982 |
"Analysis of feedback systems with structured uncertainties"
IEE Proceedings, Vol. 129, Pt. D, pp. 242-250. |

Packard and Doyle | 1993 |
"The Complex Structured Singular Value"
Automatica, Vol. 29, No. 1, pp. 71-109. |

Scherer, Gahinet and Chilali | 1997 |
"Multiobjective Output-Feedback Control via LMI Optimization"
IEEE Trans. Automatic Control, Vol. 42, No. 7, pp. 896-911. |

de Oliveira, Geromel and Bernussou | 2002 |
"Extended H_2 and H_infinity norm characterizations and
controller parametrizations for discrete-time systems,"
Int. J. Control, Vol. 75, No. 9, pp. 666-679. |

Laughlin, Jordan and Morari | 1986 |
"Internal model control and process uncertainty; mapping
uncertainty regions for SISO controller design,"
Int. J. Control, Vol. 44, No. 6, pp. 1675-1698. |