  With reference to an optimal control problem where the state has to approach
asymptotically a closed target while paying a non-negative integral cost, we
propose a generalization of the classical dissipative relation that defines a
Control Lyapunov Function to a weaker differential inequality. The latter
involves both the cost and the iterated Lie brackets of the vector fields in
the dynamics up to a certain degree k greater than or equal to 1, and we call
any of its (suitably defined) solutions a degree-k Minimum Restraint Function.
We prove that the existence of a degree-k Minimum Restraint Function allows us
to build a Lie-bracket-based feedback which sample stabilizes the system to the
target while regulating (i.e., uniformly bounding) the cost.
