Viability kernel
Graduate
Consider a control system $\dot x = f(x, u)$ and a set of state constraints $K$. The viability kernel of $K$ is a subset of $V \subset K$ such that for every initial state $x_0 \in V$, there exists at least one choice of admissible inputs $u(t)$ such that a solution starting from $x_0$ and controlled by $u(t)$ stays in $K$ forever.
Properties
- The viability kernel is the largest controlled invariant (or weakly forward invariant) subset of $K$.