By the 17th century which european nation was most successful at exerting control over southeast asia?

The most successful nation from Europe that was exerting control over Southeast Asia was the Great Britain. This time was the period where the british were beginning what was later known as the british empire - the biggest nation on the planet.

Great Britain was most successful in Southeast Asia in the guise of the British East India Company, which rose to account for half of the world's trade, particularly in basic commodities including cotton, silk, indigo dye, salt,saltpetre, tea and opium. The company ruled the beginnings of the British Empire in India, the largest Empire to ever exist.