You raise a fascinating question: Do mitzva obligations apply to a person while he is sleeping? Considering that while one is sleeping, he is not going to be making decisions, much halachic discussion focuses on what others should do when observing a sleeping person in a situation in which he is normally required to do something or to refrain from being in a forbidden state. However, we will also deal with one’s obligation to plan ahead before going to sleep.
Certain sources indicate that when a person is sleeping, the laws of the Torah fundamentally do not apply to him. Nevertheless, there are several and stronger sources that prove that mitzvot do apply, at least on some level.
If rain forces one to sleep inside his house on Sukkot and the rain stops during the night, he does not have to return to the sukka at that point.[1] The Beit Yosef[2] writes that a major part of this discussion pertains to the people of the household not being required to wake the sleeping person. The simple implication of the sources, however, is that this exemption is unique to sukka, since that mitzva does not apply to one who will be unusually bothered to be in the sukka under those uncomfortable circumstances.[3] The classical commentaries do not speak of a sweeping rule that mitzvot do not apply to those who are sleeping, implying that there is no such rule.
On the other hand, Rav S.Z. Auerbach ruled that one is not obligated in sukka, or other mitzvot for that matter, when he is sleeping, and it is therefore (theoretically) permitted to remove a sleeping person from the sukka.[4] In regard to what the friend of someone who is sleeping should do as the end time for reciting Kri’at Shema draws near, those who follow Rav Auerbach would not require waking him, though others would.[5] Another important source involves a kohen sleeping in a room where someone had died. The Rama[6] rules that people should wake the kohen so he can leave the premises.
In addition to the existence of distinctly different viewpoints as to the applicability of mitzvot to one who is sleeping, there is also logic to distinguish between fulfilling positive mitzvot and avoiding aveirot, in two directions. In some ways, being physically involved in a situation of aveira while sleeping may be more problematic than simply not doing a mitzva at that point.‎{&‎7&} Conversely, even if one is exempt from a mitzva when sleeping, if he does not perform it, he will not be credited for what he did not do, such that there is certainly something to be gained by waking him. We may make other distinctions as well: whether a Torah-level mitzva (e.g., Kri’at Shema) or a Rabbinic one (e.g., Shacharit) is at stake;‎{&‎8&} whether the specific person would want to be woken;‎{&‎9&} and whether when the person went to sleep he realized that the problem would likely arise while he would be sleeping.‎{&‎10&}
This last distinction brings us to the crucial practical point regarding your question. It is forbidden for one to go to sleep in a manner that will likely cause him to miss a mitzva. In several cases, there are Rabbinical prohibitions regarding eating or sleeping before performing a particular mitzva, even when one plans to perform the mitzva within its proper time.[11] This prohibition sometimes begins even before the mitzva applies.‎{&‎12&} Although Chazal obviously do not forbid going to sleep at night out of fear that one will wake up too late for Kri’at Shema and Shacharit, they had harsh things to say about those who are not careful to wake up in time.[13] Therefore, irrespective of one’s fundamental approach to obligations while a person sleeps, one should have a good plan before going to sleep to enable him to perform the mitzva when it becomes incumbent upon him.[14]
Although this may be more difficult to accomplish on a plane than at home, the difficulty does not reach the level that one can legitimately ignore the need to make a sincere effort (including asking people to wake him). If, as might happen, the plans do not succeed, then one’s lack of fulfillment will be considered an oness,[15] and he will not be deemed culpable for his failure.