[Dev] Augmented adjoints for variable times

[jbcaillau]

@ocots update formulas for adjoint to variable initial and final times (only one variable, or both)

See also#183

[ocots]

Could be great to haves different cases solved by hand for testing.

[jbcaillau]

Could be great to haves different cases solved by hand for testing.

• yes, or solved by direct approach and compared
• note that a safe way is to check PMP (transversality conditions, etc.) on the transformed problem on $[0,1]$

[jbcaillau]

@ocots alternative (and preferred) approach to keep everything hamiltonian (including $t_0 / t_f$ adjoints):

• naive def of $t_0 / t_f$ adjoints
• mitigated transversality
• conditions allowing init with $p_{t0} = p_{tf} = 0$ (no need to pass them explicitly, then), see joint detailed computation:

$$ p_{t0}(t_f) = -H(t_0),\quad p_{tf}(t_f) = H(t_f). $$