instantaneous frequency for a sum
Eventhough Laurent has given a broader sense of the answer, let me put here the communications theory sense ot it.

The concept of instantaneous freqency emerges when you consider Frequency Modulation or Phase Modulation systems, where the message is embedded into the change of the frequency or phase of a carrier signal. 

This carrier is typically a single cosine wave or a complex exponential equivalent which posses a single well defined angle, whose time derivative gives you the instantaneous frequeny; hence the message. That's why they are also called angle modulation or exponential modulation systems.

The understanding is that there must exist a single carrier to represent the modulated message. Your example includes a general sum of three complex exponentials (unless you speciy those $\alpha$ pars) whose simplification into a single carrier seems not possible on the surface. Then there won't be a unique single instantaneous frequency definition for $u(t)$. 

But you can consider three different instantaneous frequencies per complex exponential for your signal $u(t)$. Indeed this would be the case when multiple FM modulated signals (at different frequencies) were existing simultaneously as they are transmitted at different channels.