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MCRF

Traditionally, the time domains that are widely used in mathematical
descriptions are limited to real numbers for the case of
continuous-time optimal control problems or to integers for the case
of discrete-time optimal control problems. In this paper, based on a
family of "needle variations", we derive maximum principle for
optimal control problem on time scales. The results not only unify
the theory of continuous and discrete optimal control problems but
also conclude problems involving time domains in partly continuous
and partly discrete ingredients. A simple optimal control problem on
time scales is discussed in detail. Meanwhile, the results also
unify the theory of some hybrid systems, for example, impulsive
systems.

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