Optimal and Robust Control

Assigned (compulsory) reading

Chapter 11 in Skogestad (2nd edition).

Recommended (not compulsory) further reading

The topic of model order reduction is typically discussed in general control systems textbooks at the level of ballanced truncation and Hankel norm minimization. There are a few dedicated monographs that go a bit further, namely [1] and [2]. The paper [3] seems like a short summary of [1] and is available online. When discussing the fundamental concepts such as reachability and controllability gramians and the related problems of reachability and observability, in the lecture we just waved hands while showing the result about minimum energy control. If this was not satisfactory, very nice tutorial [4] is available online, that unifies these problems with the more standard least squares problems in linear algebra. Warmly recommended paper.

1. A. C. Antoulas, Approximation of Large-Scale Dynamical Systems. Philadelphia: Society for Industrial and Applied Mathematic, 2005.
   
2. G. Obinata a B. D. O. Anderson, Model Reduction for Control System Design, 2001 edition. New York: Springer, 2000
3. A. C. Antoulas; Dan C. Sorensen. Approximation of large-scale dynamical systems: An overview. 2001. ONLINE at https://scholarship.rice.edu/bitstream/handle/1911/101964/TR01-01.pdf?sequence=1
4. R. W. Beard. Linear operator equations with applications in control and signal processing. IEEE Control Systems Magazine, 2002, 22.2: 69-79. DOI: 10.1109/37.993316