K. Kraft and S. Larsson, 

The dual weighted residuals approach to optimal control of ordinary
differential equations,

preprint 2008:2, Department of Mathematical Sciences, 
Chalmers University of Technology

Abstract.

  The methodology of dual weighted residuals is applied to an optimal
  control problem for ordinary differential equations.  The
  differential equations are discretised by finite element methods.
  An {\apost} error estimate is derived and an adaptive algorithm
  is formulated.  The algorithm is implemented in Matlab and tested on
  a simple model problem from vehicle dynamics.