August 2012
Intermediate to advanced
392 pages
10h 50m
English
Content preview from Nonlinear Optimal Control Theory
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70 Nonlinear Optimal Control Theory
The collection of intervals {E
ki
} where k ranges over the s ame index set as do
the intervals I
k
and i ranges over the set 1, . . . , q, constitutes a subdivision of
I into a finite number of non-overlapping subintervals. This subdivision, rela-
beled as {E
j
}, is the subdivision whose exis tence is asse rted in the theorem. If
an interval E
j
was originally the interval E
ki
, then the function f
E
j
assigned
to E
j
is f
i
. If we now compare the definition of λ in (3.6.14) with (3.6.3) and
we see that to prove the theorem we must show that for arbitrary t
′
and t
′′
in
I and a ll x in X
Z
t
′′
t
′
λ(t, x)dt
< ¯ǫ. (3.6.15)
There ...
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