8) Consider the following scalar optimal control problem,

x(t) = 2z(t) +u(t),

Minimize J defined as

- 125

√5

=

x(0) = 5,

(2x(t)² + u(t)²) dt.

Compute the optimal control u(-), the associated state trajectory (), and the corresponding

optimal cost Jopt. Plot z(t) and u(t).