Nonlinear Optimal Guidance for Intercepting Moving Targets

Abstract: This paper introduces a nonlinear optimal guidance framework for guiding a pursuer to intercept a moving target, with an emphasis on real-time generation of optimal feedback control for a nonlinear optimal control problem. Initially, considering the target moves without maneuvering, we derive the necessary optimality conditions using Pontryagin's Maximum Principle. These conditions reveal that each extremal trajectory is uniquely determined by two scalar parameters. Analyzing the geometric property of the parameterized extremal trajectories not only leads to an additional necessary condition but also allows to establish a sufficient condition for local optimality. This enables the generation of a dataset containing at least locally optimal trajectories. By studying the properties of the optimal feedback control, the size of the dataset is reduced significantly, allowing training a lightweight neural network to predict the optimal guidance command in real time. Furthermore, the performance of the neural network is enhanced by incorporating the target's acceleration, making it suitable for intercepting both uniformly moving and maneuvering targets. Finally, numerical simulations validate the proposed nonlinear optimal guidance framework, demonstrating its better performance over existing guidance laws.