This monograph develops a framework for time-optimal control
problems, focusing on minimal and maximal time-optimal controls for
linear-controlled evolution equations. Its use in optimal control
provides a welcome update to Fattorini's work on time-optimal and
norm-optimal control problems. By discussing the best way of
representing various control problems and equivalence among them,
this systematic study gives readers the tools they need to solve
practical problems in control. After introducing preliminaries in
functional analysis, evolution equations, and controllability and
observability estimates, the authors present their time-optimal
control framework, which consists of four elements: a controlled
system, a control constraint set, a starting set, and an ending
set. From there, they use their framework to address areas of
recent development in time-optimal control, including the existence
of admissible controls and optimal controls, Pontryagin's maximum
principle for optimal controls, the equivalence of different
optimal control problems, and bang-bang properties. This monograph
will appeal to researchers and graduate students in time-optimal
control theory, as well as related areas of controllability and
dynamic programming. For ease of reference, the text itself is
self-contained on the topic of time-optimal control. Frequent
examples throughout clarify the applications of theorems and
definitions, although experience with functional analysis and
differential equations will be useful.
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