What you are looking for is a cross-compiling toolchain.
A toolchain includes a cross-compiler (a compiler that runs on the current platform but builds the binary code to run on another, on your case, AIX), the C or C++ library, and some other interesting tools.
I have successfully used buildroot in the past, which is a tool that automates the process of creating a cross-compiling toolchain. I know they support several target platforms, maybe AIX is among them.
If you want to compile your toolchain by hand, take a look at the Roll-your-own section on this page.
Another approach, probably easier on your case, would be to install a AIX system inside a virtual machine on Ubuntu. This way you would have access to a complete AIX system running inside your machine, giving the opportunity to develop and test your application under real conditions (or whatever reasons you may find interesting for doing such a thing).