By Suresh P. Sethi

ISBN-10: 089838074X

ISBN-13: 9780898380743

ISBN-10: 9401730288

ISBN-13: 9789401730280

Booklet via Sethi, Suresh P., Thompson, Gerald L.

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E-book via Sethi, Suresh P. , Thompson, Gerald L.

**Extra resources for Solutions Manual for Optimal Control Theory: Applications to Management Science**

**Example text**

S;1:. 69). r' doesn't exist and we need to define as follows: 1 Since B For for the no-bequest case, rc 1 rc => T Z = 1 < B< 0. 10. (a) < B <-.!. rc \~en => { u' u* g/r-l , c 0, v* 1, t € 1, Vt [O,T-T Z] t € [T-T Z ' T] lower and upper bounds on the selling rate are imposed, then it is no longer possible to switch from a security position to cash position instantaneously at t = 5. ly, = =3 YO * * [t ,f(t ) l, y = Sand = S. 3e· lt ) We remark that f (t *) > t * (c) * f(t) for is well defined and that O:S; t * < S.

This isa boundary control rather than an interior control. 22. The problem is Maximize{J = {T,u} Subject to lui :s; 1 T 2f x = u, 0 2 -u dt} x(O) x(T) 5, 0, 2. H= H - 102 u 2 + const. ' =-u+A=O~ u - 10 u 2 H(T) ~ AU 2 A(T) = 0 control. ~ + Aul A= 0 u A ~ ~ u(T) 0 T u = 0 o which is an interior This solution does not satisfy the maximum principle necessary conditions. We show how to construct feasible trajectories with negative (non-zero) values of J which are arbitrarily close to zero. 2 f 5£ £ £2 dt -"2 o not feasible.

33. j 1,Z, ... ,k. H const. o To guess the solution, note that in the objective function is large when the coefficient of coefficient of initially that u1 = 0 =1 1, u1 run through uz(t) is small when from xz for t both resevoirs. page. U z = O. When t = 4 to 10. t t t is small, and the is small. Hence = 4, x 1 (4) = 0, so Since all the water must and there are 8 units, we must make =Z to 10 in order to completely empty Our solution guess is plotted on the next -39- 1 o 1 o 6 4 o 2 4 To complete the maximum principle verification we find one possible solution for the quantities in the Lagrangian.

### Solutions Manual for Optimal Control Theory: Applications to Management Science by Suresh P. Sethi

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