固定时间撞击静止目标的非线性最优制导
Nonlinear Optimal Guidance for Fixed-Time Impact on a Stationary Target
AI总结：
本文研究固定时间拦截静止目标的非线性最优制导，基于PMP构建参数化系统生成数据并训练前馈神经网络以表示最优制导映射，仿真表明该制导律优于现有方法。
摘要：
本文研究设计非线性最优制导，以在固定撞击时间拦截静止目标。根据Pontryagin极大值原理（PMP），建立了非线性最优拦截问题解的一些最优性条件，并给出了相应最优控制的结构。利用这些最优性条件，我们构建了一个参数化系统，使其解空间与非线性最优拦截问题的解空间相同。因此，对参数化系统进行简单传播，无需使用任何优化方法，就足以为从当前状态和剩余时间到最优制导指令的映射生成充足的采样数据。借助泛逼近定理，由生成数据训练的前馈神经网络能够表示从当前状态和剩余时间到最优制导指令的映射。因此，训练后的网络最终能在恒定时间内生成固定撞击时间的非线性最优制导。最后，通过仿真对所开发的非线性最优制导进行了演示和研究，表明该非线性最优制导律优于现有的拦截制导律。
英文摘要：
This paper is concerned with devising the nonlinear optimal guidance for intercepting a stationary target with a fixed impact time. According to Pontryagin's Maximum Principle (PMP), some optimality conditions for the solutions of the nonlinear optimal interception problem are established, and the structure of the corresponding optimal control is presented. By employing the optimality conditions, we formulate a parameterized system so that its solution space is the same as that of the nonlinear optimal interception problem. As a consequence, a simple propagation of the parameterized system, without using any optimization method, is sufficient to generate enough sampled data for the mapping from current state and time-to-go to the optimal guidance command. By virtue of the universal approximation theorem, a feedforward neural network, trained by the generated data, is able to represent the mapping from current state and time-to-go to the optimal guidance command. Therefore, the trained network eventually can generate fixed-impact-time nonlinear optimal guidance within a constant time. Finally, the developed nonlinear optimal guidance is exemplified and studied through simulations, showing that the nonlinear optimal guidance law performs better than existing interception guidance laws.
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