Time optimal controls for semilinear distributed parameter systems. Existence theory and necessary conditions (Q1192243)

The paper discusses a time-optimal control problem concerning a dynamic object defined by \((*)\) \(\dot x(t)=Ax(t)+f(t,x(t),u(t))\), where \(A:{\mathcal D}(A)\subset X\to X\) generates a \(C_ 0\)-semigroup on the space \(X\), \(u(t)\) is a measurable control function with values in a metric space \(U\), \(x(t)\) is the system state, valued in \(X\), \(f:[0,\infty)\times X\times U\to X\) is a given mapping. The author discusses the problem concerning the existence of admissible trajectories and time-optimal controls for the case that the control domain is state-dependent. However, if a state-independent control domain is assumed and the target sets need not necessarily have non-empty interior then Pontryagin's maximum principle is used to prove a necessary condition for the existence of a time-optimal control.