Course Outline  
Lecture (AJC 2121):  MW 2:00pm  3:15pm. P. S. Krishnaprasad 
Office Hours (AVW 2233):  M 5:00 pm  7:00 pm; Tu 5:15 pm  7:15 pm (discussion period in CSI 2107). 
Office Hours for Teaching Assistant  Mr. Semih Kara in AVW 1301:  W 4:00 pm  5:00 pm; Th 4:00 pm  5:00 pm. 
Special Announcements in reverse chronological order
Keeping track of weekly progress in spring 2019(12) Homework 8 posted and emailed along with paper by Lax. Due date for HW 8 is Wednesday April 17 in class (before Midterm 2 starts). (11) Homework Set 7 posted and emailed (on calculus of variations  due back April 8, Monday). Midterm Examination II is moved to WEDNESDAY, APRIL 17. Material covered up to and during the week of April 10 will be relevant to the exam. (10) I have provided a link below to the announcement of the award of the 2019 Abel Prize to Professor Karen K. Uhlenbeck. This was in recognition “for her pioneering achievements in geometric partial differential equations, gauge theory and integrable systems, and for the fundamental impact of her work on analysis, geometry and mathematical physics.” All this is an outgrowth of the subject of calculus of variations, as explained in both informal as well as technical terms at the Abel Prize website. Read for inspiration and more. (9) Homework Set 6 (focusing on Frechet derivatives, Lagrange multiplier theorem etc. based on Lecture Notes 5)  to be completed and returned to the GTA in his office by Friday, March 15, 2019. (8) Homework set 5 (focusing on Gateaux and Frechet derivatives) posted  to be completed by Monday, March 4. NOTE  first Midterm on March 4 is in class closed book variety, based on material covered until today  February 25. (7) Fix to legibility issue in page 12 of Lecture 4 notes included. (6) Homework set 4 due back in class on Monday, February 25. Lecture Notes 4 posted  same as from 2019. Work through the chapters of Cinlar and Vanderbei on Sets and Metric Spaces (upto and including page 44) as a background resource  as needed when you read my lecture notes. Also work through the first chapter of Liberzon's book (to get the notion of local extrema, necessary conditions etc.). If you complete these readings by the end of this month you would be prepared for advanced material. (5) Homework set 3 due back in class on Monday, February 18. Lecture Notes 3 posted  same as from 2016. (4) Homework set 2 due back in class on Monday, February 11. Lecture Notes 2 posted  same as from 2016. (3) Weekly discussion sessions 5:157:15 pm on TUESDAYS in room CSI 2107. (2) Lecture Notes 0 and 1 are posted (same as from 2016). Homwework Set 1 (both parts (a) and (b))  to be returned Monday February 4 in class. (1) Textbook for the course is Daniel Liberzon's Calculus of Variations and Optimal Control Theory

The Brachystochrone problem was originally set by Johann Bernoulli in June 1696. The paper of Hector J. Sussmann and Jan C. Willems in the IEEE Control Systems Magazine, June 1997, pp 3244, celebrates this event as a beginning of optimal control theory.
Solution (based on calculus) of Queen Dido's problem by P. D. Lax from American Mathematical Monthly, vol. 102, No. 2, February 1995, pp. 158159
Book by John T. Betts Practical Methods for Optimal Control and Estimation using Nonlinear Programming
Link to book by Daniel Liberzon on Calculus of Variations and Optimal Control
Real Analysis Book by Cinlar and Vanderbei  material useful in Systems courses
Published version of Cinlar Vanderbei book in Springer Undergraduate Texts series
About C. Caratheodory
Impact of Control Technology vignettes, and, full report (warning 35 MB)
