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 structure-preserving 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.

中文翻译：

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一种基于撞击角度制导的三维追击者/目标拦截交战的最优参数化牛顿型结构保持倍增算法


所提出的策略，基于有限时间状态依赖的 Riccati 方程 （FT-SDRE） 的撞击角制导，通常用于求解具有固定横向加速度的 3D 追击者/目标拦截模型。本文将其应用扩展到目标的横向加速度可能会发生变化的一般场景。为此，我们通过二阶有限差分方案近似目标在惯性系中的方位角和仰角的加速度，并开发了一种具有结构保持倍增算法 （SDA） 的高性能 FT-SDRE 算法。因此，可以提高控制器的更新频率，并可以更好地引导追击者，以解决整个拦截过程中目标的高机动性问题。在 FT-SDRE 的每种状态下，都采用改进的 Newton-Lyapunov 方法来求解连续代数 Riccati 方程 （CARE），并提出了一种具有自适应最优参数选择的新型简化 SDA 来求解相关的 Lyapunov 方程。我们的数值结果表明，我们提出的方法加速的 FT-SDRE 算法比 FT-SDRE 算法快大约三倍，其中 MATLAB 函数 icare 和 lyap 分别用于求解 CARE 和 Lyapunov 方程，贯穿整个拦截过程。换句话说，控制频率可以提高三倍。在我们的基准情况下，目标以非线性横向加速度进行机动，可以通过提出的 FT-SDRE 算法更早地拦截目标。