Prajakta, you may wish to visit Prof van Willigenburg's website. I am sure you will find (perhaps, many) references to what you are looking for (and some good ones in the publications ref list).

http://gvw007.yolasite.com/

Hope it helps. Best Wishes.

Here is a reference to a Berkley course of optimal control (I think, it might help)

https://math.berkeley.edu/~evans/control.course.pdf

as for the examples, I can refer you to a paper, whith a detailed explanation of a time optimal control  algorithm for a nonlinear system (sorry for self promotion here)

https://www.researchgate.net/publication/227104041_Numerical_methods_of_optimal_control_of_the_HIV-infection_dynamics

Article Numerical methods of optimal control of the HIV-infection dynamics

thank you!

Prajakta,

You may want to take a look at H. Hermes and J. P. La Salle, Functional Analysis and Time Optimal Control. (Mathematics in Science and Engineering, Volume 56). VIII + 136 S. m. Abb. New York/London 1969. Academic Press.

http://onlinelibrary.wiley.com/doi/10.1002/zamm.19720520711/abstract

Best, Soledad

Another useful book:

"Foundations of Optimal Control" by E. B. Lee and Lawrence Markus