Robert Downey Jr., who earlier this year won an Academy Award, will make his Broadway debut this fall in “McNeal,” a new drama by the Pulitzer-winning playwright Ayad Akhtar.

The play is about a gifted novelist with a difficult family life and a potentially problematic interest in artificial intelligence. Downey will play the writer.

The production is being staged by Lincoln Center Theater, one of four nonprofits with Broadway houses, at its Vivian Beaumont Theater. Previews are to begin Sept. 5, and the opening is scheduled for Sept. 30.

“McNeal” will be directed by Bartlett Sher, a resident director at Lincoln Center Theater and a Tony winner for “South Pacific.”

Downey, 59, has been a prolific and enormously successful film actor, overcoming significant challenges (he had a long battle with substance abuse and served time in prison on drug charges). He has built a career that has been lucrative (he starred as Iron Man in multiple Marvel movies) and acclaimed (he won the Oscar for best supporting actor for a widely praised performance as Lewis Strauss, a government official, in “Oppenheimer”).

His stage experience is limited — his one Off Broadway credit, “American Passion,” opened and closed on the same date in 1983 — and he said in a statement, “It’s been 40 years since I was last on ‘the boards,’ but hopefully I’ll knock the dust off quick.”

Akhtar is a playwright and a novelist with an appetite for complex and thorny subjects whose previous plays have explored finance and Islam. He has had a long relationship with Lincoln Center Theater, which first produced his Pulitzer-winning play, “Disgraced,” on its Off Off Broadway stage, and also presented his plays “The Who & The What” Off Off Broadway and “Junk” on Broadway.

Akhtar is also working on a musical: He is one of the book writers for a stage adaptation of the film “La La Land” that is now in development.