M.Sc Student | Heller Carmit |
---|---|

Subject | Pursuer Maneuver Minimization by Softly Constrained Optimal Guidance |

Department | Department of Aerospace Engineering |

Supervisors | Professor Yoseph Ben-Asher |

Dr. Isaac Yaesh | |

Full Thesis text |

When designing a guidance law, one
should take into consideration both the missile limitations requiring small
maneuver accelerations, and the final miss distance requiring the maneuvering
to be as large as possible. The suggested new guidance law is derived from a
cost function that minimizes the weighted sum of miss distance and normal
accelerations both to the power of *q*, where *q* is an even number.
This formulation of the cost function leads to minimization of the maximal
acceleration, as the value of *q* increases, rather than the total energy.
This cost function is referred to as "Hyper-quadratic", thus naming
the new guidance law "*HQN*".

The problem formulation involves
the relative displacement, *x _{1}*, the closing velocity,

*u
= - ((2q-1)/(q-1))*(x _{1}(t) + x_{2}(t) *t_{go} +
0.5*w_{0}*t_{go}^{2} )/ t_{go}^{2}*

The optimal guidance law, that
tends to minimize the maximum absolute maneuver is achieved when *q* tends
to infinity, leading to *N'=2*.

Next the problem of differential
game optimization, where both u and w take part in the minimization and
maximization of the cost function respectively, is solved. The optimal pursuit
maneuver and optimal evasion maneuver are derived using a Riccati equation
approach. In this case the optimal *u* and *w* are found to be
function of *N'* and the maneuverability ratio (*MR*). For *q* *=
2* we obtain the navigation constant: *N' = 3/(1- MR ^{-1})*,
and for

In order to gain a deeper insight
into the resulting family of guidance laws, a comparison is offered to the
Pareto optimal set of mixed *L _{2}/L_{q}* guidance laws.
The comparison reveals that the family of guidance laws which were obtained by
even

Finally, *HQN* performance in
various cases is analyzed and compared to the corresponding performance of some
well known guidance laws: Proportional Navigation (*PN*) for one sided
optimization and Differential game Law (*DGL*) for differential games.
This study shows that *HQN* achieves very small miss distance values while
maintaining low lateral acceleration.