This is actually a part of a time optimal control problem(more specifically, a bang bang control), I am trying to solve the relevant canonical equations but I just don’t know how to determine the boundary conditions of the 4 Lagrangian multipliers “p” and the solve range 𝑇.

So the question is how to determine the boundary conditions of the 4 Lagrangian multipliers “p and once I have the boundary conditions, how to solve the ODEs numerically and find the optimal time 𝑇?

And the equations are in the file

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