Control

Control Lyapunov Function (CLF)

A control Lyapunov function is a positive-definite, energy-like function of the state for which some admissible control input can always make its time derivative negative, certifying that the system can be driven toward an equilibrium or goal set. Introduced by Artstein and Sontag in the 1980s, CLFs turn stabilization into a pointwise constraint solvable by quadratic programming, and are frequently combined with control barrier functions to unify stability and safety.

Why it matters for physical AI

CLF certificates provide provable convergence for goal-reaching behaviors, and learning neural Lyapunov functions for complex dynamics is an active route to verified stability in learned robot controllers.