| This dissertation addresses the problem of path planning for unmanned combat aerial vehicles (UCAVs) in the presence of radar-guided surface-to-air missiles (SAMs). The radars, collocated with SAM launch sites, operate within the structure of an Integrated Air Defense System (IADS) that permits communication and cooperation between individual radars.; The problem is formulated in the framework of the interaction between three sub-systems: the aircraft, the IADS, and the missile. The main features of this integrated model are: The aircraft radar cross section (RCS) depends explicitly on both the aspect and bank angles; hence, the RCS and aircraft dynamics are coupled. The probabilistic nature of IADS tracking is accounted for; namely, the probability that the aircraft has been continuously tracked by the IADS depends on the aircraft RCS and range from the perspective of each radar within the IADS. Finally, the requirement to maintain tracking prior to missile launch and during missile flyout are also modeled. Based on this model, the problem of UCAV path planning is formulated as a minimax optimal control problem, with the aircraft bank angle serving as control.; Necessary conditions of optimality for this minimax problem are derived. Based on these necessary conditions, properties of the optimal paths are derived. These properties are used to discretize the dynamic optimization problem into a finite-dimensional, nonlinear programming problem that can be solved numerically. Properties of the optimal paths are also used to initialize the numerical procedure.; A homotopy method is proposed to solve the finite-dimensional, nonlinear programming problem, and a heuristic method is proposed to improve the discretization during the homotopy process. Based upon the properties of numerical solutions, a method is proposed for parameterizing and storing information for later recall in flight to permit rapid replanning in response to changing threats.; Illustrative examples are presented that confirm the standard flying tactics of "denying range, aspect, and aim," by yielding flight paths that "weave" to avoid long exposures of aspects with large RCS. |
