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.
Note that the sigmoid integral functions V(ζ) exhibit quadratic behavior near ζ = 0 and approach linear behavior for |ζ| ≫ 0
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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.