"determination to undertake" is correct and usable in written English.
You can use it when describing a person's strong commitment to do something. For example, "He has a strong determination to undertake the difficult task."
The team hopes Smith can come back, believing in his determination and willingness to undertake a grueling rehabilitation, and yet the evidence says his return might not be possible.
We must not allow the fates of reality-show contestants – often undertaking an unhealthily fast method of weight loss that doesn't tackle the fundamental cultural and behavioural aspects of the problem – to affect our determination to tackle the issue.
Results from behavioral economics suggest that the determination of whether and when to undertake job training, the selection of a field to be trained in as well as a provider, and the pursuit and completion of that training, represents an intrinsically challenging sequence of choices and actions for imperfectly rational individuals.
The faculty shall hear an appeal within ten working days of the date on which it decides to undertake appellate review, and make its determination as soon as may be thereafter.
A willingness to undertake a feat of epic stamina and determination to claim some notable piece of hostile geography for one's people, assuming they'd agreed to name it after you.
Determination letters, however, do not provide assurances about the complainant's ability to undertake future travel.
"The agency was required to undertake some type of consultation, informal or otherwise, prior to making a conclusive determination that there would be no effect," she wrote.
Not something to undertake lightly.
Some choose to undertake further studies abroad.
My job is to undertake research.
