Robust Control

Robust Control - XP35RRD

 Credits 4 Semesters Winter Completion Exam Language of teaching undefined Extent of teaching 2P+2C
Annotation
Advanced course on selected topics in robust control.
Study targets
Motivation and goal for the course is to build a solid understanding of derivation of some classical methods for robust control design, namely Hinf-optimal 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: state-space 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 so-called "polynomial school of systems and controls" started here in Prague) and LMI-approach (revolving around the optimization-intensive framework of linear matrix inequalities). Related issues such that positiveness and dissipativeness of systems will also be discussed.
Course outlines
1. Parametric uncertainties: classification, Kharitonov's theorem for interval plants, Bialas' theorem for one-parameter uncertainties, zero exclusion principle, guardian maps, more complex parameter uncertainty structures.

2. Hankel, Toeplitz a mixed Hankel-Toeplitz 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: Nevanlinna-Pick 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, inner-outer factorization, J-spectral 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.
Exercises outlines