A first-order system is described by the following equation of motion in the state variable: y_ ¼  y þ u with initial condition y(0) ¼ 4 and y(T) free. Find in Excel the optimal control (unconstrained) that minimizes the following performance measure: JðuÞ ¼ Z 1 0 1 2 u2 dt þ y2 ð1Þ where the function outside the integral can be defined as a salvage value function h(y(T), T).

The costate equation is _ lðtÞ¼lðtÞ and the transversality condition to be met is as follows: vh vy ðy ðTÞÞ  l ðTÞ ¼ 0 namely, 2y ð1Þ ¼ l ð1Þ