The method of singular perturbations is applied to the determination of the optimal range-fuel-time trajectory for an air-breathing missile. This method is shown to lead to the reduced-order "cruise-dash" model, and this model is used in the optimization study. Earlier work in this area is extended by the inclusion of two not heretofore considered limits on the dynamical system. The results of the earlier work are shown to hold throughout much of the velocity regime in which the missile operates, but operation in the very high and very low velocity ranges is shown to be sharply curtailed, with the optimal operating points being changed drastically in some cases. Also, the effect of the non-zero minimum admissible throttle setting and the resultant throttle-chattering on the solution of the control problem is examined in some detail. / M.S.

The engagement between an antiship missile and a ship’s defense system is investigated. The missile is equipped with proportional navigation guidance for homing in on its ship target. The ship’s defense system consists of a radar, an estimation system (the extended Kalman filter and the “jump filter” are used), and a gun system. The performance index is defined as the estimated number of hits (EHITS) of projectiles on the missile. The main objective of this dissertation is to determine maneuvering periods for the missile which minimize the EHITS to evade the ship’s gunfire under different engagement conditions. The maneuvering periods are design parameters in the missile’s controls of both the vertical and the horizontal planes. The engagement conditions are the follows: the maximum amplitude of the maneuvering functions, the homing in position of the missile on the ship, the measurement noise condition of the ship’s radar, and the missile’s model assumed in the ship’s filters. The missile’s control functions considered are periodic and of specific types (sinusoidal, square and sawtooth waveforms); therefore, the periods which minimize the EHITS in this study are suboptimal for the general engagement problem. Two methods are used to obtain the suboptimal periods: one is the ”brute force" method of computing the EHITS for certain equally spaced periods, the other uses an optimization software to search for the minimum point. The results show that the curve of EHITS vs. period is monotonically decreasing until it reaches a minimum point. The optimal period increases with an increase in measurement noise. Among the three waveforms used, the square wave gives the smallest optimal period and the sawtooth wave gives the largest one. The sinusoidal waveform with the period of 1.9 seconds is recommended. We consider the missile's performance against a perfect radar, a modern radar, and an earlier model radar. The optimum EHITS resulting from the optimal periods are between two and three EHITS for all three radars considered. / Ph. D.