🚀 go-pugleaf

In article <1h08q1INNl15@flop.ENGR.ORST.EDU> saleh@ece.orst.edu (Hassan Saleh) writes:
>
>   Is there any public domain program available for the solution
>   of nonlinear optimal control problems ? I tried using colnew
>   to solve the resulting two-point boundary value problems but
>   I always get "singular elimination matrix" some where.
>
>   H. I. SALEH

I'm working on a nonlinear optimal control package now, but it will be
some time before I'm finished.  If you want to solve your problem by
solving the BVP which arises out of the Euler-Lagrange equations, you
must make sure that the sum of the Jacobian matrices of the initial
and final conditions for the BVP is non-singular.  If it isn't, you
must use a smooth, time-dependent (non-singular, for all time of interest)
state-transformation which results in the sum of the Jacobians being
non-singular.  This is usually not hard to do.

However, even if you accomplish this, if you don't have a good initial guess
for the initial conditions (and for most BVP software, a good initial guess
for the state and adjoint trajectories), the software will not be able to
find a solution.