Delay effects on the discontinuous stabilization of the nonholonomic integrator and its generalizations

What the math gives to ML

The paper gives a concrete mechanism by which a delayed discontinuous controller becomes a hysteretic hybrid system rather than merely a destabilizing perturbation. Its transferable asset is the explicit reduced dynamics: delayed sign feedback produces a tunable energy contraction rate and an analytically characterized switching basin. This suggests a recurrent or state-space neural module with delayed binary mode selection, where hysteresis suppresses rapid gate chattering while retaining cheap hard switching. The result is not a general theorem for neural optimization, so the most credible transfer is a controlled architecture experiment rather than a claim of universal optimizer improvement.