3 problems

Optimality conjecture. For $\Theta=\Theta_{M,\,\lambda}$, an optimal proxy function minimizing the ratio $\overline{V}/\alpha$ is the entropy-type function defined in equation (2).

Let $M$ be a smooth submanifold of $\mathbb{R}^D$, let $G:M\to\mathbb{R}^d$ be a smooth parametrization, and let $\mathrm{Lie}^{\geq 2}(\partial G)$ denote the span of Lie brackets…

The analysis considers PID controllers whose transfer function has real roots, corresponding to an overdamped linear filter; imaginary roots instead correspond to an underdamped os…