This paper is concerned with devising nonlinear optimal guidance for intercepting a stationary target with a desired impact time. According to Pontryagin’s maximum principle, 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 the 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 the current state and time-to-go to the optimal guidance command. Therefore, the trained network eventually can generate impact-time-constrained 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.

本文关注的是设计非线性最优制导以拦截具有所需撞击时间的静止目标。根据庞特里亚金极大原理，建立了非线性最优截获问题解的若干最优性条件；并给出了相应的最优控制结构。利用最优性条件，我们制定了一个参数化系统，使其解空间与非线性最优截取问题的解空间相同。因此，参数化系统的简单传播，不使用任何优化方法，足以生成足够的采样数据，用于从当前状态和时间到最佳制导命令的映射。凭借通用逼近定理，前馈神经网络，由生成的数据训练，能够表示从当前状态和时间到最佳制导命令的映射。因此，经过训练的网络最终可以在恒定时间内生成受冲击时间约束的非线性最优引导。最后，通过仿真对所开发的非线性最优制导进行了举例和研究，表明非线性最优制导律的性能优于现有的拦截制导律。