Nonlinear Optimal Guidance for Fixed-Time Impact on a Stationary Target

TL;DR

This paper develops a neural network-based nonlinear optimal guidance law for intercepting a stationary target within a fixed impact time, leveraging Pontryagin's Maximum Principle and universal approximation to achieve real-time performance.

Contribution

It introduces a novel method combining optimal control theory and neural networks to generate fixed-time impact guidance without real-time optimization.

Findings

The guidance law outperforms existing methods in simulations.

The approach enables real-time guidance command generation.

The method effectively approximates the optimal control mapping.

Abstract

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.