Terminal-Set-Based Optimal Stochastic Guidance

Abstract

In stochastic interception scenarios, an intercepting missile only has uncertain information about the target state, as this information is obtained from noisy measurements. The true dynamics of the target are also unavailable to the intercepting missile, so, instead, the interceptor can assume that the target possesses ideal dynamics, which amounts to adopting the worst-case scenario. Moreover, even when linear models and Gaussian noises are assumed, the notorious curse of dimensionality renders the straightforward optimal solution to this problem intractable in real-time. To alleviate the computational burden, this work uses an approach based on the notion of terminal sets to present an optimal interception strategy for stochastic scenarios. We show that using this approach greatly reduces the computational effort, as the number of modes diverges quadratically in time instead of exponentially. Another computational burden reduction is achieved via a novel decomposition of the interceptor’s terminal set. These results render the proposed strategy implementable in real-time, as the horizon is sufficiently short at the endgame stage of the engagement. A Monte Carlo simulation study is used to demonstrate the performance of the novel guidance law in stochastic scenarios, and to show that it achieves real-time performance despite its (still) considerable computational burden.