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. $\frac{df}{dx}$.
Task: I want construct a continuous control $u$ that ensures the following condition:
$y(t)=y(0) e^{-\beta t}, \beta>0$
Which method to use for the solution: MRAC, asymptotic output tracking, feedback linearization, or something else?
I am not an expert, please do not pass by and give advice.