Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Department of Electrical and Computer Engineering

First Advisor

Meir Pachter, PhD


This dissertation explores optimal path planning for air vehicles. An air vehicle exposed to illumination by a tracking radar is considered and the problem of determining an optimal planar trajectory connecting two prespecified points is addressed. An analytic solution yielding the trajectory minimizing the received radar energy reflected from the target is derived using the Calculus of Variations. Additionally, the related problem of an air vehicle tracked by a passive sensor is also solved. Using the insights gained from the single air vehicle radar exposure minimization problem, a hierarchical cooperative control law is formulated to determine the optimal trajectories that minimize the cumulative exposure of multiple air vehicles during a rendezvous maneuver. The problem of one air vehicle minimizing exposure to multiple radars is also addressed using a variational approach, as well as a sub-optimal minimax argument. Local and global optimality issues are explored. A novel decision criterion is developed determining the geometric conditions dictating when it is preferable to go between or around two radars. Lastly, an optimal minimum time control law is obtained for the search and target identification mission of an autonomous air vehicle. This work demonstrates that an awareness of the consequences of embracing sub-optimal and non-globally optimal solutions for optimization problems, such as air vehicle path planning, is essential.

AFIT Designator


DTIC Accession Number