Elements of Numerical Mathematical Economics with Excel

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11.2. Discrete dynamic systems: tabular method, Excel data table, and Solver

The dynamic programming recurrence algorithm can be also applied to typical OC problems expressed for example by the following:

\min_{u {t}} J (u) = y^{2} (2) + 2 \int_{t_{0}}^{T} u^{2} (t) d t

s . t . \frac{d y (t)}{d t} = a y (t) + b u (t),

and y (t) \in Y, u (t) \in U \forall t \in [t_{0}, T]

The goal, as usual, is to find the admissible optimal u ^∗(t) which causes the system

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