dynamic – AsymptoticOutputTracking for output with boundary condition

I want to try asymptotic output tracking, but with inequality.

There is a differential equation:


With output $y=frac{d}{dx}(-x^4)$,
The output should strive for $0$, i.e. $r_1=0$. Wherein $-1<x<1$.




f = -x(t)^4

asys = AffineStateSpaceModel({x'(t) - D(f, x(t)) == u(t)}, {{x(t), 
     1.25}}, {u(t)}, {D(f, x(t))}, t) // Simplify

pars1 = {Subscript(r, 1) -> 0, Subscript(p, 1) -> -10}

fb = AsymptoticOutputTracker(
   asys, {Subscript(r, 1)}, {Subscript(p, 1)}) // Simplify

I do not know whether it is possible to solve this task and how to set the required inequality.

I will be glad to any advice and help.