A control vector parameterization(CVP) based numerical approach is proposed for free time optimal control
problems. By using a time-scaling factor, free time optimal control problem is converted into a fixed time one, and the final
time is defined as an optimization parameter. Based on CVP method, the resulted optimal control problem is reformulated as
a nonlinear programming(NLP) problem. By constructing the Hamiltonian functions of objective and constraint functions,
the adjoint functions are solved to obtain the gradients of objective and constraint functions. The numerical solution is
obtained by using the sequential quadratic programming(SQP) method. For the control switched optimal control problems,
a mesh refinement strategy is presented to improve the optimal solution. A simulation on a fed-batch reactor optimal control
problem shows the effectiveness of the proposed approach.