Time Optimization problem from Optimal control: Using bvp4c command, Is it possible to obtain a solution that start on my initial guess (states and adjoint variables)?

Hello!

I'm trying to simulate the time optimization problem with fixed initial and final conditions(boundary). And I want to x(0) = [1;-1], and adjoint variables psi(0) = [-1;3]. The problem is, when Matlab finds a solution, only satisfies x(0) = [1;-1] condition but psi(0) = another values. I need to start on this specific vales because it values satisfies my Hamiltonian valued in zero is equeal to zero H(0) = 0. Maybe with this parameters I can show Hamiltonian is constat for all time (H(t) = 0).

Is it exist any way to do that with bvp4c? or another command? maybe fmincon (i never used before but meaybe it's posible to solve)?

I'm using Matlab R2011a. I'll attach my full code and pdf with equations.

Note: I'm using command try because from some values of PSI the Jacobian is singular and I compare if t > 0 becasue sometimes the resulting time is negative. The time to computes this is high(some hours) but you can make less time if you change the step in PSI1.

Thank you in advance, blessings!