This advanced course will cover modern methods for optimal and robust control design. Emphasis will be put on practical computational design skills and realistic application problem formulations. Unifying concept of this course is that of minimizing a system norm. Depending on which norm is minimized, different properties of the resulting controller are guaranteed. Minimizing the H2 system norm leads to the celebrated LQ/LQG optimal control trading off the performance and the effort, while minimizing H∞ norm shifts the focus to robustness against uncertainties in the model. ?-synthesis is an extensions to the H∞ optimal control design methodology than takes the structure of the uncertainty into consideration. Methods for time-optimal and suboptimal control will be presented as well as they proved useful in applications with strict time constraints like positioning of a hard disk drive RW head. 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. Methods for reduction of model and controller order complete the course.
Basics of feedback control (frequency characteristics, feedback, stability, PID control, ...) ane matrix linear algebra (eigenvalues/eigenvectors, singular value decomposition, conditioning, ...). Passing some advanced course on linear systems (controllability/observability, minimal state-space realization, ...) is an advantage.
Design advanced feedback controllers for realistically complex systems, while using existing specialized software.
1. Static optimization (Lagrangian, Hamiltonian)
2. Discrete-time LQ control, steady-state discrete-time LQ optimal control, Ricatti equations
3. Continuous LQ control, Loop transfer recovery (LTR)
4. H2 optimal control
5. Time-optimal and suboptimal control (bang-bang control)
6. "Sliding mode" control
7. Analysis of robustness against unstructured and structured dynamic uncertainty (H∞-norm and structured singular value ?)
8. Design of robust controllers minimizing mixed sensitivity function, H∞-optimal control, ?-synthesis (DK iterations)
9. Design of robust controllers by loopshaping
10. Derivation of H∞-optimal control law: two coupled Riccati equations
11. LMI, semidefinite programming
12. Application of LMI in robust control: quadratic stability, H∞ optimal control
13. Linear parameter-varying control (LPV)
14. Model and controller order reduction
The exercises will consist of work on assigned projects.
[1.] S. Skogestad and I. Postlethwaite. Multivariable Feedback Control: Analysis and Design. John Wiley & Sons, 2.vydání, 2005.
[2.] M. Green and D. J. N. Limebeer. Linear Robust Control. Prentice Hall, 1994.
[3.] F. L. Lewis and V. L. Syrmos. Optimal Control. Wiley-Interscience, 2.vydání, 1995.