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09/12/12 5:22pm

I am trying to solve a simple optimal control problem, by using direct discretization with backward differences.

I was driven to try this out as FindMinimum did not work at all for more complex constrained optimization problems.

The problem is to minimize the travel time for a car starting at position x = 0, with velocity v=0 and arriving 300 distance units at rest, thus at tf we have x[tf]=300 and v[tf]=0.

The odes which are discretized are:
dv/dt = u
dx/dt = v

where u is the control (acceleration) bounded by:

-2 <= v <= +1.

The objective is to minimize tf which is the sum of the finite difference steps (the steps are fixed in number and are also optimization variables).

I attach the file I have written. I hope someone will be able to answer why FindMinimum does not work for this really trivial problem....


Attachment: car problem by hand implicit euler.nb, URL: ,
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