[\dotx(t) = (A - BR^-1B'P)x(t)]
The optimal solution is to invest $10,000 in Option A at time 0, yielding a maximum return of $14,400 at time 1. Dynamic Programming And Optimal Control Solution Manual
Using Pontryagin's maximum principle, we can derive the optimal control: [\dotx(t) = (A - BR^-1B'P)x(t)] The optimal solution
| (t) | (x) | (y) | (V(t, x, y)) | | --- | --- | --- | --- | | 0 | 10,000 | 0 | 12,000 | | 0 | 0 | 10,000 | 11,500 | | 1 | 10,000 | 0 | 14,400 | | 1 | 0 | 10,000 | 13,225 | yielding a maximum return of $14
Using dynamic programming, we can break down the problem into smaller sub-problems and solve them recursively.