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.
Some extensions of liapunov’s second method
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Generalizes Olfati-Saber model to nonlinear navigational feedback, proves exponential velocity alignment to center-of-mass velocity and bounded leader distance under mild conditions, shows no periodic orbits in dissipative cases, and computationally optimizes for reduced propulsion energy.
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Energy-efficient flocking with nonlinear navigational feedback
Generalizes Olfati-Saber model to nonlinear navigational feedback, proves exponential velocity alignment to center-of-mass velocity and bounded leader distance under mild conditions, shows no periodic orbits in dissipative cases, and computationally optimizes for reduced propulsion energy.