Optimal and robust control
- Zdeněk Hurák (guarantor)
- Zdeněk Hurák (guarantor)
- Department of Control Engineering
This is an advanced course about modern control design methods that formulate the design as a mathematical optimization. Besides teaching practical design skills, the course will also help develop deeper understanding of fundamental concepts as well as build awareness of the latest results. Thanks to its background in mathematical optimization, the benefits of the course can certainly be seen beyond the borders of automatic control domain.
The course can be viewed as an extension of the equal-named course in the master program (B3M35ORR). However, numerous topics are new and those few topics that already appeared in the master version will be discussed at a significantly deeper level. This time the motivation is not just to give practical tool but also to go through the proofs, discuss various interpretations, and survey the results from the latest literature.
From the student perspective, the goal of this course is to acquire advanced competences (knowledge and skills)
in the area of computational design of control systems (or rather control algorithms). The methods will almost exclusively assume availability of a mathematical model of the system to be controlled (hence model-based control design). We will consider dynamical systems in continuous as well as discrete time, linear and nonlinear, single and multiple inputs and outputs. Since all the design methods introduced in this course formulate the design task as an optimization, the crucial competences will come from the areas of optimization, both finite-dimensional (linear, quadratic, nonlinear and semidefinite programming) and infinite-dimensional (calculus of variations, operator theory, differential games).
- Syllabus of lectures:
1. Numerical methods for open-loop control / trajectory optimization: indirect methods
2. Numerical methods for open-loop control / trajectory optimization: direct methods
3. Trajectory tracking - LQ optimal control for time-varying linear systems
4. Optimal feedback control of nonlinear systems - state-dependent Riccati equations (SDRE)
5. Model predictive control (MPC) - online approaches
6. Model predictive control (MPC) - explicit approaches
7. Optimal control based on dynamic programming: reinforcement learning
8. Pasivity-based control (PBC)
9. l1 and L1 optimal control
10. H∞ optimal control - by solving Riccati equations
11. H∞ optimal control - by solving linear matrix inequalities (LMI)
12. Linear-parameter-varying (LPV) control
13. Data-driven control design: quantitative feedback theory (QFT)
14. Iterative learning control (ILC)
- Syllabus of tutorials:
- Study Objective:
- Study materials:
No single (text)book is selected as the compulsory text for this course. Literature will always be specified for invididual lectures with a special preference for online resources (journal papers and lecture notes).
Below we give a list of recommended books that cover the course topics and which could be used to get additional information. These available in a few copies in the university (or department) library; some of them are even freely available online.
D. E. Kirk. Optimal control theory. Dover Publishing, 1st ed., 1998. ISBN 048632432X
J. T. Betts. Practical methods for optimal control and estimation using nonlinear programming. SIAM, 2nd ed., 2010. ISBN 0898716888
M. Diehl. Numerical optimal control. Lecture notes (draft), 2011. Available online.
F. Borrelli, A. Bemporad, M. Morari. Predictive control for linear and hybrid systems. Cambridge University Press, 1st ed., 2017. ISBN-10: 1107652871
K. Zhou, J. C. Doyle, K. Glover. Robust and optimal Control. Prentice Hall, 1st ed., 1996. ISBN 0134565673
M. A. Dahleh, I. J. Diaz-Bobillo. Control of uncertain systems - a linear programming approach. Prentice Hall, 1st ed., 1995. ISBN 0132806452
B. A. Francis, A Course in H control theory, Springer, 1st ed., 1987. ISBN 978-3-540-17069-3
- Further information:
- No time-table has been prepared for this course
- The course is a part of the following study plans: