Missile Guidance Law Based on New Analysis and Design of SDRE Scheme

A three-dimensional missile guidance law is designed, based on new analysis of the classical state-dependent Riccati equation (SDRE) scheme, and a novel alternative strategy that ensures the pointwise solvability of SDRE analytically. Specifically, regarding the design flexibility of nonunique state-dependent coefficients (SDCs), the classical SDRE usually follows an empirical guideline to select an SDC. The feasibility of such SDCs must be pointwise examined to ensure the solvability of the corresponding SDRE, which causes considerable online computational burden. In this paper, a necessary and sufficient condition on the feasibility of SDCs is analytically formulated based on reduced dimensionality and can be easily determined offline. Remarkably, this condition also reveals a pitfall that the classical SDRE guidance law becomes unsolvable as the line-of-sight rates are nulled, which conflicts with the widely acknowledged guidance objective. To resolve such a conflict, an alternative, computationally efficient, and more systematic construction of SDCs is proposed to guarantee feasibility and eliminate online examination of solvability of the SDRE. In the simulations of intercepting a maneuvering target, the SDRE guidance law that is based on the alternative SDC construction outperforms the classical SDRE scheme, as well as the guidance law that combines the proportional navigation and sliding mode control.