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12.6 Solve the following Problem min 0 Sub Jet To (x² + u²) dr u₁ x (0) = 0 yx (1) ≥ 1. X = U, X

12.6 Solve the following Problem min 0 Sub Jet To (x² + u²) dr u₁ x (0) = 0 yx (1) ≥ 1. X = U, X

Advanced Engineering Mathematics
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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Below is a similar example of how it should be resolved. It is desired to find an extreme for the functional 1 √(x + (x+u²)dt Subject to Hamiltonian is: H = x+u² - Xu So the first order conditions are, Hu2uA = 0, X = -H₂ = -1, * = H₂=-u. x=-u; x(0) = 0 and From the second condition we have (t) Substituting into the first, we get the third condition we arrive at x(t) = ²4+B transversality condition condition Huu x(1) u(t) * = (t-A) B = = = , implying, 0. is free. In this case, the -t + A; (-t+A) .The values of A and B are obtained with the X(1) = 0, with which and finally from A = 1 implying, x (0) = 0, = 2 > 0, the extreme obtained is a minimum. and the initial We note that since
Transcribed Image Text:Below is a similar example of how it should be resolved. It is desired to find an extreme for the functional 1 √(x + (x+u²)dt Subject to Hamiltonian is: H = x+u² - Xu So the first order conditions are, Hu2uA = 0, X = -H₂ = -1, * = H₂=-u. x=-u; x(0) = 0 and From the second condition we have (t) Substituting into the first, we get the third condition we arrive at x(t) = ²4+B transversality condition condition Huu x(1) u(t) * = (t-A) B = = = , implying, 0. is free. In this case, the -t + A; (-t+A) .The values of A and B are obtained with the X(1) = 0, with which and finally from A = 1 implying, x (0) = 0, = 2 > 0, the extreme obtained is a minimum. and the initial We note that since
12.6 Solve the following Problem min flo 0 Sub Jet To (x² + ²) dr x = ₁ x (0) = 0 yx (1) ≥ 1.
Transcribed Image Text:12.6 Solve the following Problem min flo 0 Sub Jet To (x² + ²) dr x = ₁ x (0) = 0 yx (1) ≥ 1.
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