Optimal and Robust Control

Assigned (compulsory) reading

Lecture notes for this week.

Recommended (not compulsory) further reading

Calculus of variations is a well-established discipline in mathematical analysis and many dozens books and hundreds if not thousands of online texts are available. The slender monograph [1] is a true classic. The recently published [2] is a bit more approachable, though. By the way, it's author has regular columns in SIAM News on the topics related to calculus of variations and dynamical systems (see https://sinews.siam.org/About-the-Author/mark-levi); you may find some of the very interesting.

Nontheless, within our course the calculus of variations is just a framework within which continuous-time optimal control problems are systematically formulated. The ambitions to solve general optimal control problems in the same way as one can solve the catenary problem or the brachistochrone problem mostly come in vain and one either has to resort to numerical solution or needs to consider a restricted class of problems for which the solution procedure is available such as LQ-optimal control. Furthermore, in some sense the classical calculus of variations has been superseeded by the powerful result of Pontryagin (Pontryagin's Principle of Maximum) about which we will learn next week. Hence we do not want to dwell in the calculus of variations realm too long. Anyway, among the numerous control theory textbooks that do build on top of calculus of variations, we can recommend [3]. Partly because it's preprint is available online for free.

[1] I. M. Gelfand and S. V. Fromin. Calculus of Variations. Dover, 2000.

[2] M. Levi. Classical Mechanics with Calculus of Variations and Optimal Control - An Intuitive Introduction. AMS, 2014.

[3] D. Liberzon. Calculus of Variations and Optimal Control Theory - A Concise Introduction. Princeton University Press, 2012. Preprint available freely ONLINE at http://liberzon.csl.illinois.edu/teaching/cvoc/cvoc.html.