Double generating functions method for finite time LQ optimal trajectory generation problems

For the finite time linear quadratic (LQ) optimal control problems, there exist many method solving it. This paper analyses the numerical stability of the optimal state and input trajectories generated by four kinds of methods. The direct method and the single generating function method may cause numerical instability and the double generating functions method proposed recently works well for LQ finite time optimal control problems. In addition, the double generating functions method gives the optimal state and input trajectories as the functions of boundary condition, where, the coefficient matrices which are not dependent on the boundary condition can be calculated in advance. Therefore, it is very useful for treating LQ optimal control problems with a family of boundary conditions. A numerical example shows the numerical stability of four kinds of methods.