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##

4.3.1 Changes of variables

Some
control problems that we are interested in do not fit into the
setting of the Basic Fixed-Endpoint or Variable-Endpoint Control
Problem. We now want to discuss several such scenarios and, for
each one, to arrive at the correct statement of the maximum
principle. One way to do this is to formally reduce a problem at
hand to one of the two basic problems considered above by changing
variables; the changes of variables that we will use were
already discussed in Section 3.3. Another approach is
to adapt the proof of the maximum principle to these new
situations; this task can be somewhat more challenging but also
more insightful as it helps us better understand the proof. These
various cases also help clarify why we say
``maximum *principle*" (rather than calling it a theorem): this terminology reflects the fact that specific versions of the result for different problems are different, but share the same basic features.

**Subsections**

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Daniel
2010-12-20