The phrase "undertook a program" is correct and can be used in written English.
It typically means that someone has accepted or taken on a program or project. Example: The company undertook a new training program for its employees to improve their skills and efficiency.
In the early 21st century the government undertook a program to encourage the development of theatre.
In 1939 the FBI undertook a program of surveying industrial plants engaged in the manufacture of strategic war material.
In eastern Finland the Russian church attempted to win converts, and in 1227 Duke Jaroslav undertook a program of forced baptisms, designed to tie Karelia closer to Novgorod.
As the United States prepared to withdraw from Indochina, particularly Vietnam, it undertook a program of, in President Nixon's words, "Vietnamization," in which American forces trained and equipped allied armies to take over the fighting.
As the other speakers undertook a program that amounted to a thundering response to the Republican convention last week in Tampa, Fla., they went after Mr. Romney on just about every conceivable issue.
In 1915 two small yeshivas, Etz Chaim and Rabbi Isaac Elhanan Theological Seminary, merged and undertook a program of further growth, adding Yeshiva College of secular studies in 1928 and becoming Yeshiva University in 1945.
The state is about to undertake a program that it has no capacity to implement and no track record for.
The Society has recently undertaken a program of guided tours of the city, called "Discover New York".
"There is wide speculation that China is going to undertake a program of monetary tightening," he said.
Only with the formation of the Reich ("empire") in 1871 was it possible to undertake a program of national codification.
It greatly influenced the Communist Party's decision to undertake a program of economic liberalization to relieve the hardships suffered by the Russian population during the Civil War.
