Apologies for following up myself, but I just now remembered one very well-known (at least in Europe) case: The Docklands Light Railway in London.
Accoring to the info on this page: http://www.tfl.gov.uk/dlr/about/infopack.shtml, (follow the DOWNLOAD FREE INFORMATION PACK (PDF) link), construction started in 1984 and it was opened to the public in 1987. It was computer-controlled right from the start.
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