A coordinate‐transformation method for the numerical solution of nonlinear minimum‐time control problems

A new method is presented for the numerical solution of nonlinear minimum-time control problems where at least one of the state variables is monotone. A coordinate transformation converts the problem with fixed end point and free end time to one of free end point and fixed end time. The transformed problem can be solved efficiently by the use of the gradient method with penalty functions to force the system to achieve target values of state variables. Application of the method is illustrated by the synthesis of a minimum-time temperature path for the thermally initiated bulk polymerization of styrene.