A sigmoid diffeomorphism lifts safe-set constraints for nonlinear systems into an unbounded domain, yielding an explicit asymptotically stabilizing controller with forward invariance guarantees via special Lyapunov functions.
In particular, we will require the sigmoid function to be strictly increasing in order to ensure the existence of its inverse
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A Constraint-Lifting Framework for Safe and Stable Nonlinear Control
A sigmoid diffeomorphism lifts safe-set constraints for nonlinear systems into an unbounded domain, yielding an explicit asymptotically stabilizing controller with forward invariance guarantees via special Lyapunov functions.