October 2011
Intermediate to advanced
749 pages
23h 36m
English
Content preview from Optimal Estimation of Dynamic Systems, 2nd Edition
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Optimal Control and Estimation Theory 563
Exercises
8.1 Referring to Section 8.1, suppose that both x(t
f
) and t
f
are free, but related
by x(t
f
)=θ(t
f
). Derive the transversality condition to determine the final time
for this constraint.
8.2 Consider minimizing the loss function in Equation (8.22), with
φ
(x(t
f
), t
f
)=
0, equality constraint given by Equation (8.19), and final time fixed. The
continuous-time solution is given by the TPBVP shown in Equation (8.27),
with λ(t
f
)=0.Usingfirst-order finite difference approximations for the state
and costate derivatives, develop simple discrete-time approximations to the
TPBVP equations involving a constant sampling
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