I've been researching the Lake Providence Cadets for several years. My latest find is a xeroxed photo from the North Louisiana Historical Journal of some of the Cadets at their training camp about a mile from Lake Providence.
Your great grandfather A.W. Roberts and my great grandfather served together in the Cadets and were captured at Port Hudson. I believe they shared the same block house at Johnson's Island and were eventually transferred together to Fort Delaware. They were released from Fort Delaware on the same day.
I know quite a bit about A. W. Roberts and would be glad to share my research with you. Please email me at: firstname.lastname@example.org.