Differential inclusion

Summary

A differential inclusion is a relation $x'(t) \in F(t, x(t))$, where $F$ is a multivalued function that gives a set of allowed velocities at each time and state. It generalizes the ordinary differential equation $x' = f(t, x)$, which is the case where each set $F(t, x)$ has one element. Differential inclusions describe control systems, equations with discontinuous right side, and systems with uncertain data.