An optimal parameterized Newton-type structure-preserving doubling algorithm for impact angle guidance-based 3D pursuer/target interception engagement

Chin-Tien Wu

Abstract:

The proposed strategy, finite-time state-dependent Riccati equation (FT-SDRE)-based impact angle guidance, is
generally employed to solve the 3D pursuer/target interception model with fixed lateral accelerations. This article
expands its application to a general scenario where the lateral acceleration of a target may change. To achieve
this, we approximate the accelerations of the azimuth and elevation angles of the target in the inertial frame
via second-order finite difference schemes and develop a high-performance FT-SDRE algorithm with structurepreserving
doubling algorithms (SDAs). As a result, the update frequency of the controller can be increased, and
better guidance of the pursuer can be obtained to address the high maneuverability of the target during the entire
interception procedure. At every state of the FT-SDRE, a modified Newton–Lyapunov method is employed to solve
the continuous algebraic Riccati equation (CARE), and a new simplified SDA with adaptive optimal parameter
selection is proposed for solving the associated Lyapunov equation. Our numerical results demonstrate that the
FT-SDRE algorithm accelerated by our proposed methods is approximately three times faster than the FT-SDRE
algorithm, in which the MATLAB functions icare and lyap are used to solve the CARE and the Lyapunov equation,
respectively, throughout the entire interception procedure. In other words, the control frequency can be increased
threefold. In our benchmark cases where the target maneuvers with nonlinear lateral acceleration, the target can
be intercepted earlier via the proposed FT-SDRE algorithm.