Which way of solving from nonlinear control to choose?

I have a nonlinear system:

begin{cases} x’=f(x)+u y=f(x) end{cases}

where $f(x)$ – gradient of some one-extremal function (for example $f=e^{-(x)^2}$), i.e. $frac{df}{dx}$.

I want to construct a continuous control $u$ that ensures the following condition:

$y(t)=y(0) e^{-beta t}, beta>0$

Which method (available in Mathematica) should I use for the solution: Asymptotic Output Tracking, Feedback Linearization, Asymptotic Output Tracking with Estimator, or something else?

I would appreciate your help in choosing the most appropriate method.