Optimal Control Theory by Suresh P. Sethi

Author:Suresh P. Sethi
Language: eng
Format: epub
ISBN: 9783319982373
Publisher: Springer International Publishing

(9.20)

where g is nondecreasing and concave in u. For this section, we will assume the sale date T to be fixed for simplicity and g to be strictly concave in u, i.e., g u ≥ 0 and g uu < 0 for all t. Also, g t ≤ 0,  g ut ≤ 0, and g(0, t) = 0; see Exercise 9.7 for an example of the function g(u, t).

The standard Hamiltonian is

(9.21)

where λ is given in (9.8). To maximize the Hamiltonian, we differentiate it with respect to u and equate the result to zero. Thus,

(9.22)

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