Extended trajectory shaping guidance laws

An extended cost function was proposed on the basis of a power function about missile remain time-to-go. According to Schwartz inequality, a family of extended optimal guidance law with both position and impact angle constraints was deduced and two kinds of extended trajectory shaping guidance laws were derived. For different missile seeker, autopilot dynamics weighted states, different system dynamics order and different exponential n of the cost function, the non-dimensional acceleration, non-dimensional position and angle miss distance of the first kind trajectory shaping guidance system was studied on the restraint that final impact angle was introduced into the system. It is concluded that the position and angle miss-distance produced by the final impact angle can approach to zero when the missile terminal guidance time is about 15 times as much of the system lag time. It will result in a more oscillatory position miss response when the system dynamics order increases. And when the exponential number n increases, the position and angle miss distance can be much worse. Finally, it shows that a fast response missile seeker is more effective than a fast autopilot response to reduce the system position and angle miss distance.