A Study Comparing Upadacitinib (ABT-494) to Placebo and to Adalimumab in Participants With Psoriatic Arthritis Who Have an Inadequate Response to at Least One Non-Biologic Disease Modifying Anti-Rheumatic Drug (DMARD)

* Clinical diagnosis of PsA with symptom onset at least 6 months prior to the Screening Visit and fulfillment of the Classification Criteria for PsA (CASPAR) criteria. * Participant has active disease at Baseline defined as \>= 3 tender joints (based on 68 joint counts) and \>= 3 swollen joints (based on 66 joint counts) at Screening and Baseline Visits. * Presence of either at Screening: 1. \>= 1 erosion on x-ray as determined by central imaging review or; 2. high-sensitivity C-reactive protein (hs-CRP) \> laboratory defined upper limit of normal (ULN). * Diagnosis of active plaque psoriasis or documented history of plaque psoriasis. * Participant has had an inadequate response (lack of efficacy after a minimum 12 week duration of therapy) to previous or current treatment with at least 1 non-biologic DMARD at maximally tolerated dose (methotrexate (MTX), sulfasalazine (SSZ), leflunomide (LEF), cyclosporine, apremilast, bucillamin or iguratimod), or participant has an intolerance to or contraindication for DMARDs as defined by the investigator. * Participant who is on current treatment with concomitant non-biologic DMARDs at study entry must be on \<= 2 non-biologic DMARDs (except the combination of MTX and leflunomide). The following non-biologic DMARDs are allowed: MTX, sulfasalazine, leflunomide, apremilast, hydroxychloroquine (HCQ) , bucillamine or iguratimod, and have been ongoing for \>= 12 weeks and at stable dose for \>= 4 weeks prior to the Baseline Visit. No other DMARDs are permitted during the study. i. Participants who need to discontinue DMARDs prior to the Baseline Visit to comply with this inclusion criterion must follow the procedure specified below or at least five times the mean terminal elimination half-life of a drug: 1. \>= 8 weeks for LEF if no elimination procedure was followed, or adhere to an elimination procedure (i.e., 11 days with cholestyramine, or 30 days washout with activated charcoal or as per local label); 2. \>= 4 weeks for all others.

* Prior exposure to any Janus Kinase (JAK) inhibitor (including but not limited to ruxolitinib, tofacitinib, baricitinib, and filgotinib). * Current treatment with \> 2 non-biologic DMARDs; or use of DMARDs other than methotrexate, sulfasalazine, leflunomide, apremilast, hydroxychloroquine, bucillamine, or iguratimod; or use of methotrexate in combination with leflunomide. * History of fibromyalgia, any arthritis with onset prior to age 17 years, or current diagnosis of inflammatory joint disease other than PsA (including, but not limited to rheumatoid arthritis, gout, overlap connective tissue diseases, scleroderma, polymyositis, dermatomyositis, systemic lupus erythematosus). Prior history of reactive arthritis or axial spondyloarthritis including ankylosing spondylitis and nonradiographic axial spondyloarthritis is permitted if documentation of change in diagnosis to PsA or additional diagnosis of PsA is made. Prior history of fibromyalgia is permitted if documentation of change in diagnosis to PsA or documentation that the diagnosis of fibromyalgia was made incorrectly.