Cooperative Differential Games Guidance Laws for Imposing a Relative Intercept Angle

A cooperative guidance law for a team of interceptors trying to intercept, from multiple directions, an evading target is proposed. An example scenario of interest is that of intercepting an aerial target, such as a ballistic missile, from multiple directions. The engagement is analyzed in the framework of a linear quadratic zero-sum two-person differential game, where the team of interceptors constitutes one of the adversaries and the target the other. An arbitrary number of interceptors, each having linear dynamics, is considered. The obtained guidance law for the team of interceptors enables enforcement of a relative geometry in between the group of missiles and the target. Such an approach is superior (in the sense of the required control effort) to that where each interceptor independently enforces, using a one-on-one strategy, a preselected intercept angle that satisfies the relative intercept requirement. A nonlinear two-dimensional simulation is used to investigate the performance of the obtained cooperative guidance law. It is shown that the proposed guidance law is superior to the optimal-control-based cooperative guidance law when the target is unpredictable and that the interceptors' acceleration requirements are comparable to conventional guidance laws that do not impose an angular constraint at interception.