An Optimal Missile Guidance Law with a Jerk Constraint

摘要

The Proportional Navigation guidance law (PN) has been in use forrndecades within many tactical and strategic missiles due to its simple implementationrnand high accuracy. In some applications, however, therernmight arise implementation problems, for instance in the application of arndesign constraint on the jerk (first derivative of the acceleration) for thernmissile. An example of such a constraint is a missile, using Thrust VectorrnControl (TVC), which requires the entire missile body to be tilted in orderrnto perform a maneuver. From design considerations, the rate of bodyrnrotation may be limited, thus limiting the rate of acceleration change, orrnin other words, the jerk. The main purpose of this work is to developrnan optimal guidance law which minimizes the cost on the jerk, thus takingrninto account the limit on this property. This paper demonstrates,rnby introducing a jerk limit to the common PN and APN (AugmentedrnProportional Navigation) laws and showing that a miss occurs, under arncertain jerk limit, that the foregoing motivation is justified. The new jerkrnlimited guidance law (JLG) is developed by means of Cauchy-Schwartzrninequality, ensuring its optimality. JLG is then compared to the commonrnPN, APN and their variations (PN5 and APN5) and found to performrnwell, yet slightly inferior to PN in the case of an heading error and to performrnbetter than all other guidance laws for the case of target maneuver.rnThe results of this comparison also demonstrate the capability to tunernthe performance of JLG by the right choice of a jerk limit value (withinrnthe design limit on the missile) to achieve better results in terms of missrndistance.