Optimization of Allocation and Launch Conditions of Multiple Missiles for Three-Dimensional Collaborative Interception of Ballistic Targets

We consider the integrated problem of allocation and control of surface-to-air-missiles for interception of ballistic targets. Previous work shows that using multiple missile and utilizing collaborative estimation and control laws for target interception can significantly decrease the mean miss distance. However, most of these methods are highly sensitive to initial launch conditions, such as the initial pitch and heading angles. In this work we develop a methodology for optimizing selection of multiple missiles to launch among a collection of missiles with prespecified launch coordinates, along with their launch conditions. For the interception we use 3-DoF models for missiles and the ballistic target. The trajectory of the missiles is controlled using three-dimensional extensions of existing algorithms for planar collaborative control and estimation laws. Because the dynamics of the missiles and nature of the allocation problem is highly nonlinear and involves both discrete and continuous variables, the optimization problem is cast as a mixed integer nonlinear programming problem (MINP). The main contribution of this work is the development of a novel probabilistic search algorithm for efficiently solving the missile allocation problem. We verify the algorithm by performing extensive Monte-Carlo simulations on different interception scenarios and show that the developed approach yields significantly less average miss distance and more efficient use of resources compared to alternative methods.