August 2012
Intermediate to advanced
392 pages
10h 50m
English
Content preview from Nonlinear Optimal Control Theory
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The Maximum Principle and Some of Its Applications 189
Remark 6.7.10. For problems with t
0
and t
1
fixed, g automatically has
the form (6.7 .7) with g
2
≡ 0. If we assume that g is a convex function of
(t
0
, x
0
, t
1
, x
1
), then the assumption that g has the form (6.7.7) can be dropped.
Definition 6.7.11. The linear system (6.7.2) is said to be strongly normal
on an interval [t
0
, t
1
] with respect to a constraint set C if for every non-zero
vector µ in R
n
, max{L(t, µ, z): z ∈ C} is attained at a unique z
∗
(t) in C at all
but a finite set of points in [t
0
, t
1
].
Definition 6. 7.12. A control u is said to be piecewise constant on an interval
[t
0
, t
1
] if there exist
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