Optimal and Robust Control

Assigned (compulsory) reading

Read Chapter 3 in [1]. Skim through Chapter 4 on algorithmic differentiation. Alternatively, Chapter 6 (or at least 6.6) in [2].

1. M. Diehl. Numerical Optimal Control. Lecture notes (draft). October 1, 2011. [ONLINE] downloadable at https://www.vehicular.isy.liu.se/Edu/Courses/NumericalOptimalControl/Diehl_NumOptiCon.pdf.
2. J. R. R. A. Martins and A. Ning. Engineering Design Optimization. Draft. [ONLINE] downloadable at http://flowlab.groups.et.byu.net/mdobook.pdf.
   

Recommended (not compulsory) further reading

The material covered (or actually just overviewed) in this lecture is very standard and described in gazillions of resources, both printed and online.

Here we give our personal tips: the recently published [1] serves a good job of providing an overview and insight (furthermore, a short version is available online); [2] is a classic and very readable; if you only want to own a single comprehensive and up-to-date book on optimization, [3] might be your choice. The recently published [4] is particularly enjoyable in that it also contains Matlab codes; in fact, we used it to prepare part of this lecture. Yet another recent and equally accessible book is [5]. It is particularly beautifully typeset with a wealth of Julia code; both the book and Jupyter notebooks are available online. Yet another resource is [6], which has also been made available online by its authors (on their webpage). It is perhaps worth mentioning that its authors are leaders in the area of model predictive control (MPC) and their selection composition of the introductory chapter reflect their preference for those concepts and methods in numerical optimization that are relevant for MPC.

1. L. E. Ghaoui, Optimization Models. Cambridge University Press, 2014. A shorter version of the books is available [ONLINE] at https://inst.eecs.berkeley.edu/~ee127/sp21/livebook/.
2. D. G. Luenberger and Y. Ye, Linear and Nonlinear Programming, 4th edition. New York, NY: Springer, 2016.
3. J. Nocedal and S. Wright, Numerical Optimization, 2nd edition. New York: Springer, 2006.
4. A. Beck. Introduction to Nonlinear Optimization: Theory, Algorithms and Applications with Matlab, SIAM, 2014.
5. M. J. Kochenderfer and T. A. Wheeler. Algorithms for Optimization. MIT Press, 2019. [Online]. Available at https://algorithmsbook.com/optimization/.
6. F. Borrelli, A. Bemporad, and M. Morari, Predictive Control for Linear and Hybrid Systems. Cambridge, New York: Cambridge University Press, 2017. [Online]. Available: http://cse.lab.imtlucca.it/~bemporad/publications/papers/BBMbook.pdf.

• Cleve’s Corner: Cleve Moler on Mathematics and Computing. “Complex Step Differentiation.” Blog, October 14, 2013. https://blogs.mathworks.com/cleve/2013/10/14/complex-step-differentiation/.