That would depend of course on how deep and broad your knowledge is, and in which sub-discipline you want to contribute. Here are some links to basic but modern books on the topic.

1.http://www.adlibris.com/se/bok/control-and-optimization-with-pde-constraints-9783034806305

2. http://www.amazon.com/Optimal-Differential-Equations-Graduate-Mathematics/dp/0821849042

3. http://books.google.se/books?id=PFbqxa2uDS8C&hl=sv&source=gbs_similarbooks

Again, precisely the type of PDE that you wish to control will influence the book(s) you may wish to buy.

The last one is a page with several similar books, with links to descriptions. Good luck!

@ Micheal

Thanks for your response and wishes.

Precisely I am working on model based control of underground coal gasification (UCG) process. The process model I am considering contains a non-homogeneous 1-D parabolic PDE (heat equation with diffusion term along with extra convective term and heat source from the chemical reactions ).

As my background is of Electrical engineering with emphasis on control systems, so I want to start from the very basic

regards

"An Introduction to Infinite-Dimensional Linear Systems Theory" Ruth F. Curtain & Hans Zwart