Synthesis of control system by approximation method for switching surface

The problem of control synthesis of spacecraft decent in Martian atmosphere is considered. The optimal control is to deliver minimum to maximal G-force and direct hit into terminal conditions allowing some variations in initial conditions. For various initial conditions an optimal control is shown to have similar shape and one switch in sign that depends on initial conditions. The moment of switching is suggested to be approximated depending on initial conditions. An example of control synthesis is given.