I'm looking for a comprehensive introduction to the theoretical side of optimal control, existence of solutions and so on, including theory behind numerical solution methods. Regarding the latter I'm specifically interested in direct solution methods (the practical side of which are nicely described in Practical Methods for Optimal Control and Estimation Using Nonlinear Programming by JT Betts). What would you recommend?
Sincerely, Olav
Check out "Numerical Methods for Unconstrained Optimization and Nonlinear Equations", by Dennis and Schnabel.
What I found excellent about this book is that it develops an optimization library and routines as you go through it and contains a beautifully written set of algorithms to code the solutions.
it also contains a set of very nice pathological problems to teach you the pitfalls of building any methods of solution.
There are two other books that I need to mention and that you should explore if you get a chance.
Optimization in Operations Research by Rardin
Engineering Optimization, Theory and Practice, Rao
There are some other books as there are a a lot of great books in this area, but the titles are escaping me as I am not home.
Lastly, you might check out the Open Courseware at place like MIT and of course, peruse your college library and see if anything there fits your requirements and likes.