Differential models, such as any of those from Chapter 13,
are usually referred to as *control systems*
or just *systems*, a term that we have used already.
These are divided into *linear* and *nonlinear* systems, as
described in Sections 13.2.2 and 13.2.3,
respectively. Formulation 14.1 can be considered in control
terminology as the design of an *open-loop control law* for the
system (subjected to nonconvex constraints on the state space). The
*open-loop* part indicates that no
feedback is used. Only the action trajectory needs to be specified
over time (the feedback case is called *closed-loop*; recall Section
8.1). Once the initial state is given, the state
trajectory can be inferred from the action trajectory. It may also be
qualified as a *feasible* open-loop control law, to indicate that
it satisfies all constraints but is not necessarily optimal. It is
then interesting to consider designing an *optimal* open-loop
control law. This is extremely challenging, even for problems that
appear to be very simple. Elegant solutions exist for some restricted
cases, including linear systems and some wheeled vehicle models, but
in the absence of obstacles. These are covered in Chapter
15.

Steven M LaValle 2012-04-20