[x^*(t) = v_0t - \frac12gt^2 + \frac16u^*t^3]
| (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 | Dynamic Programming And Optimal Control Solution Manual
The optimal trajectory is:
Using Pontryagin's maximum principle, we can derive the optimal control: [x^*(t) = v_0t - \frac12gt^2 + \frac16u^*t^3] |
The optimal solution is to invest $10,000 in Option A at time 0, yielding a maximum return of $14,400 at time 1. 000 | 0 | 12