Consider the optimal control problem min fu(t) ² dt Jo subject to the conditions a' (t) = x(t) + u(t), x(0) = xo, x(1) = 0. Show that the optimal control is u* (t) = 4x0 e-t/3 3(e-4/3-1)
Consider the optimal control problem min fu(t) ² dt Jo subject to the conditions a' (t) = x(t) + u(t), x(0) = xo, x(1) = 0. Show that the optimal control is u* (t) = 4x0 e-t/3 3(e-4/3-1)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:2. Consider the optimal control problem
min
S
u(t) 4 dt
26
subject to the conditions a' (t) = x(t) + u(t), x(0) = xo,
u* (t) =
410
3(e-4/31)
(1) = 0. Show that the optimal control is
-e-t/3
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