Solution of finite time linear quadratic optimal control problem (time-invariant)

Can any body help me for solving finite time linear quadratic optimal control problem (time-invariant) both open loop and close loop in MATLAB? for open loop we must solve a linear system (TPBVP) are there any suggestion for the solution in MATLAB? I think "lqr" matlab doesnt solve finite time regulator.

subject to

for my problem matrices F,Q and R are positive diagonal matrices. for open loop case I must solve a linear system (TPBVP) for x and p (co-state) which x(0) is known and p(t_f) is known.