A modified backward integration method for optimal control problems with degenerate equilibrium points

We present a new numerical indirect method to solve optimal control problems with degenerate equilibrium points. When the optimal control problem is autonomous, the corresponding canonical system becomes an autonomous system of ordinary differential equations. Combining the well-known blow-up technique of vector fields with the classic backward integration method, and focusing on a specific type of degenerate singular points, we develop a new method that is both easy to implement and able to deal with complex problems.