Exact description of reachable sets and global optimality conditions for dynamic systems (Q1114921)

The set of points reachable from (controllable to) a set in a given interval of time T, by means of the solutions of a control process (possibly with state constraints) is considered. Under suitable assumptions it is proved that there is a locally Lipschitz function \(\phi\) : \(T\times R^ n\to R\) such that the reachable (controllable) set is equal to \(\{(t,x)\in T\times R^ n:\) \(\phi\) (t,x)\(\geq 0\}\). The function \(\phi\) is identified by suitable conditions.