Example 11.14 generalizes nicely to the case of states.
In operations research and artificial intelligence literature, these
are generally referred to as *partially observable Markov decision
processes* or *POMDPs* (pronounced ``pom dee peez'').
For the case of three states, the probabilistic I-space,
,
is a -simplex embedded in
. In general, if , then
is an -simplex embedded in
. The coordinates
of a point are expressed as
. By
the axioms of probability,
, which implies
that
is an -dimensional subspace of
. The
vertices of the simplex correspond to the cases in which the state
is known; hence, their coordinates are
,
, ,
. For convenience,
the simplex can be projected into
by specifying a point in
for which
and then
choosing the final coordinate as
. Section 12.1.3 presents algorithms for planning
for POMDPs.

Steven M LaValle 2020-08-14