Final answer:
Kublai Khan's control of the Yuan empire was contributed by adopting the Chinese name Yuan, conquering the Song dynasty, and establishing a capital city in China.
Step-by-step explanation:
Kublai Khan's control of the Yuan empire was contributed by several actions. Firstly, he adopted the Chinese name Yuan for his empire, which helped to reinforce the Mongols' connection to the Mandate of Heaven and their political legitimacy in China. Secondly, Kublai Khan successfully conquered the Song dynasty and became the first ruler over all of China who was not of Chinese origin. Lastly, he established a capital city in China and demanded recognition as the Son of Heaven, solidifying his authority and control over the Han Chinese people.