This　note　studies　robust　output　regulation　problem　for　discrete-time　linear　systems　with　unknown　system　dynamics.　Combining　standard　internal　model　and　approximate/adaptive　dynamic　programming　(ADP),　an　adaptive　optimal　output　feedback　controller　is　developed　in　the　case　that　the　state　and　disturbance　of　the　system　are　unmeasurable.　It　is　shown　that　the　proposed　controller　can　achieve　asymptotic　tracking　while　making　the　system　exponentially　stable.　Quarter　passive　suspension　vehicle　model　is　given　to　illustrated　the　effectiveness　of　the　algorithm.　©　2022,　The　Author(s),　under　exclusive　license　to　Springer　Nature　Singapore　Pte　Ltd.