Time-optimal control for infinite dimensional linear systems (Q1209006)

The paper extends previous work by \textit{A. Friedman} [J. Math. Anal. Appl. 19, 35-55 (1967; Zbl 0155.159)], \textit{H. Fattorini} [J. Math. Anal. Appl. 22, 382-384 (1968; Zbl 0162.145)] and \textit{N. Ahmed} [J. Optimization Theory Appl. 47, 129-158 (1985; Zbl 0564.49021)], by removing some of their restrictive hypotheses. A class of time-varying infinite-dimensional linear systems is considered which generate a strongly continuous evolution operator which is not necessarily invertible. The paper studies the time optimal control problem under time dependent control constraints and a moving target set. Existence of a bang-bang type time optimal control is proven, and it is shown that this control satisfies a maximum principle. An example of a parabolic control system is formulated.