Can iControl 11.5 API work on BigIP 10.2

I think generally you need to ideally stick to at least the same major software version. Of course, from an iControl perspective, many of the calls will be the same and you could write code that checks for the TMOS version first and changes things as necessary to accommodate any differences in the call syntax/naming.

If you are using a specific SDK then things get somewhat trickier. If, for instance I was using Python I wouldn't really worry but I think things are more involved with Java and the like.