I'm going to suggest Mayflies by Kevin O'Donnell Jr.
The protagonist of the story is a scientist who, through misadventure, ends up wired into the Earth's first interstellar ship as its central computer. The ship was conceived as a lifeboat, a way for at least some to escape a dying Earth, but the planned 15 year journey turned into a thousand year one when the scientist "wakes up" during launch and inadvertently shuts off the drive.
At first the scientist is restricted to observer status, as "The Program" that has been loaded into his brain to run the ship has control. Over time, he manages to take over the functions of The Program, one by one. Things also go from bad to worse with his passengers as subsequent generations forget their origins, and as aliens are encountered.
Towards the end of the story, he gains control over the drive - but realises his passengers aren't ready to survive without his oversight, and sets out to train the next generation to live independently.
Other things I remember ...
- The scientist was doing research into emergency resuscitation, and ended up having his life "saved" by his device.
- Overthrow of one on-ship society by the introduction of a labour based economy where a floor sweeper of average efficiency would earn 1 laitch (labour hour) per hour.
- A hive mind alien shows up, and takes over the mind of one baby. Realizing too late that he's "killed" an individual, he sticks around as a replacement as long as he can.
- Earth invents an FTL drive, but it can only be used for smaller vessels, but the ship works out how to synchronize multiple drives.
- An encounter with some violent aliens who do some nasty things as a part of psychological experiments on the passengers