M.Sc Thesis | |

M.Sc Student | Nadav Balhance |
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Subject | Cooperative Guidance Law for Intra-salvo Tracking |

Department | Department of Aerospace Engineering |

Supervisors | Professor Shima Tal |

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This thesis is concerned with cooperative geometrical guidance of two missiles pursuing a single maneuvering target. The goal of the guidance law is to enable interception while reducing the variability of the look angle between the two missiles during the engagement. Three cooperative guidance laws were derived to achieve this goal. The derivation of the cooperative guidance laws is done by linearizing the equations of the engagement and formulating a special linear quadratic optimal control problem. The solution of this problem is used subsequently to derive the three guidance laws. The first guidance law, the FLA1, is a closed-loop guidance law, which was derived by a standard type linear quadratic representation of the problem. Its goal is to minimize the look angles variability with respect to fixed predefined values. The next guidance law, the MVLA2, is a feedforward guidance law, i.e. it is composed not only by a feedback of the current state but also by the initial state. The MVLA2 was derived by a non-standard type linear quadratic representation of the problem. Its goal is to minimize the look angles variability with respect to some reference values, which are not predefined. These reference values are calculated as a function of the initial conditions to minimize the cost function value. The CMVLA1 is a closed-loop version of the MVLA2.

The last guidance law, the MVLA1, is a better feedforward implementation of the MVLA2, in which the optimal reference values are not updated during a nonlinear scenario as in the CMVLA1 and the MVLA2.

The cost function for all three offered guidance laws includes miss distance terms, control effort terms and look angle variability terms for both missiles.

The non-standard type extension of the classical linear quadratic problem consists of a cost function, which is minimized simultaneously by the control input and the constant look angles that the missiles try to achieve. This way, the problem becomes a min-min problem, which is solved in two stages.

All three guidance laws were derived based on a linearized formulation of the kinematics and a linearized definition of the look angle. The guidance laws were derived for a known constant maneuver of the target and for ideal adversaries' dynamics.

The performance of the guidance laws is investigated by using linear and nonlinear planar simulations. It was shown that the look angle variability can be controlled with an allowable miss distance. It was also shown that by reducing the demand for lower variability of the look angles, the offered guidance laws become very similar to the well-known augmented proportional navigation. When a demand for lower variability of the look angles does exist, the trajectories are reshaped to lower the look angles variability.

A comparative study that investigates the differences between the three offered guidance laws shows that the MVLA1 is the preferable guidance law for the case where no specific values of look angles were predefined.