Robust Control
Code  Completion  Credits  Range 

XP35RRD  ZK  4  2P+2C 
 Lecturer:
 Tutor:
 Supervisor:
 Department of Control Engineering
 Synopsis:

Advanced course on selected topics in robust control.
 Requirements:

Students must be familiar with basic concepts of optimal and robust control. These could be obtained, for example, in an equally named graduate course (ORR) at FEE CTU. This advance course will not teach how to design a robust controller anymore. Instead, it will teach how to develop a computationally efficient and reliable algorithmic procedure for such design.
 Syllabus of lectures:

1. Parametric uncertainties: classification, Kharitonov's theorem for interval plants, Bialas' theorem for oneparameter uncertainties, zero exclusion principle, guardian maps, more complex parameter uncertainty structures.
2. Hankel, Toeplitz a mixed HankelToeplitz operator, Nehari's theorem.
3. Forumlation of a general problem of Hinf optimal control design: generalized plant, linear fractional transformation (LFT), 4 basic problems: full information (FI), disturbance feedforward (DF), full control (FC), output estimation (OE).
4. Solution to the Hinf problem leading to 2 coupled Riccati equations.
5. Robust stabilization of a system with coprime factor uncertainty.
6. Basic linear matric inequalities (LMI) in control: Bounded real lemma, KYP lemma. Solving the Hinf problem using LMIs.
7. Interpolation approach to control design: NevanlinnaPick problem
8. Design of robust controllers of a fixed order.
9. Linear parameter varying (LPV) control.
10. Passivity vs. robustness, dissipative systems.
11. Riccati equation: analysis, numerical solution, spectral factorization, positive real functions, inner functions, innerouter factorization, Jspectral factorization.
12. Reduction of order of a model and controller: truncation and residualization for balanced realization, diverse methods of balancing, minimization of Hankel norm of the approximation error. Lyapunov equation: properties and numerical solution.
 Syllabus of tutorials:

Exercises follow the lectures.
 Study Objective:

Motivation and goal for the course is to build a solid understanding of derivation of some classical methods for robust control design, namely Hinfoptimal control, in order to be able to modify the algorithms for systems with special structure. Several approaches for solving Hinf optimal control problem will be presented: statespace approach (based on solving two coupled Riccati equations), interpolation method (based on some fundamental results from complex analysis), polynomial approach (taking advantage of having the socalled „polynomial school of systems and controls“ started here in Prague) and LMIapproach (revolving around the optimizationintensive framework of linear matrix inequalities). Related issues such that positiveness and dissipativeness of systems will also be discussed.
 Study materials:

G. E. Dullerud, F. Paganini. A Course in Robust Control Theory. Springer; 1 edition, 2005.
K. Zhou, J. C. Doyle, K. Glover. Robust and Optimal Control.Prentice Hall, 1st edition, 1995.
B. A. Francis, A Course in H Control Theory, Springer, 1987.
M. Green and D. J. N. Limebeer. Linear Robust Control. Prentice Hall, London, 1994.
S. P. Bhattacharyya, H. Chapellat, L. H. Keel. Robust Control  The Parametric Approach. PrenticeHall, 1996.
 Note:
 Further information:
 https://moodle.fel.cvut.cz/courses/XP35RRD
 No timetable has been prepared for this course
 The course is a part of the following study plans:

 Doctoral studies, daily studies (compulsory elective course)
 Doctoral studies, combined studies (compulsory elective course)
 Doctoral studies, structured daily studies (compulsory elective course)
 Doctoral studies, structured combined studies (compulsory elective course)