Method for solving optimal control

Hi All,
I am doing a mobile robot project that requires to solve an optimal control problem. I can solve the two-point boundary value problem directly. I just
don't know what is the advantage(s) of other methods such as Gradient method, quasilinearization or dynamic programming. Can someone help me out here? I also have a problem with costate boundary condition. The test books (such as Robert Stengel or Bryson and Ho) use lambda(tf) transpose[dphi/dx] at t = tf. It gives sub optimal performance for my problem. I know this because I varied the lambda(tf) from the formula and I can, sometimes, get better cost function. Any suggestions?
Thanks.
Everett
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