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Optimal and robust control design

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Code Completion Credits Range Language
BE3M35ORC Z,ZK 8 2P+2C English
Garant předmětu:
Zdeněk Hurák
Zdeněk Hurák
Zdeněk Hurák
Department of Control Engineering

This advanced course on control design will cover modern methods for optimal and robust control design. Emphasis will be put on practical computational design skills. Unifying idea of the course is that of minimization of a system norm. Depending on which norm is minimized, different properties of the resulting controller are guaranteed. Minimizing H2 norm leads to the celebrated LQ/LQG optimal control trading off the performance and the effort, while minimizing Hinf norm shifts the focus to robustness against uncertainties in the model. Mu-synthesis as an extensions to Hinf optimal control design that take the structure of the uncertainty into consideration represents a very powerfull tool for robust control design. Standing a little bit aside yet being useful in space missions are the methods for time-optimal and suboptimal control. As a self-contained add-on to the course, introduction to the topic of semidefinite programming and linear matrix inequalities (LMI) will be made, as these constitute a very elegant theoretial and a powerful computational tool for solving all the previously introduced tasks in optimal and robust control.


Basic course on feedback control: dynamic system, transfer function, state-space model, stability, frequency response, Bode plot, feedback. These topics will also be covered by the SpaceMaster course Space systems, modeling and identification (SSMI).

Basic couse on linear algebra: solving linear systems, basic matrix decompositions (LU, Cholesky, QR, SVD), eigenvectors/eigenvalues, singular values, conditioning.

Syllabus of lectures:

1.Static optimization

2.Discrete-time LQ control

3.Steady-state discrete-time LQ optimal control

4.Continuous LQ control

5.H2 optimal control

6.Time-optimal and suboptimal control (bang-bang control)

7.Analysis of robustness against unstructured dynamic uncertainty

8.Analysis of robustness against structured dynamic uncertainty (structured singular values)

9.Design of robust controllers minimizing mixed sensitivity function, H?-optimal control, Mu- synthesis (DK iterations)

10.Design of robust controllers by loopshaping (Glover-McFarlane)

11.LMI, semidefinite programming

12.Application of LMI in robust control: quadratic stability, Hinf

13.Model and controller order reduction

Syllabus of tutorials:

Following the topics of the lectures.

Study Objective:
Study materials:

1.Frank L. Lewis and Vassilis Syrmos: Optimal Control, 2nd ed., Wiley, 1995. [amazon link]

2.Sigurd Skogestad and Ian Postlethwaite: Multivariable Feedback Control: Analysis and Design, 2nd ed., Wiley, 2005. [amazon link]. This book can be borrowed at the faculty library.

Further information:
Time-table for winter semester 2023/2024:
Time-table is not available yet
Time-table for summer semester 2023/2024:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2024-05-16
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