Abstract:

This paper is concerned with devising the nonlinear optimal guidance for overload-constrained interceptor to hit a target at a desired impact time. Firstly, the theoretical model for the nonlinear optimal guidance problem is established, and optimality conditions for the optimal trajectory are derived in virtue of Pontryagin's maximum principle and saturation function method. Secondly, by embedding the optimality conditions into a parameterized family of Hamiltonian trajectories, a parameterized set of differential equation for optimal trajectories is formulated, which allows one to use a simple numerical integration to generate the dataset of the mapping from the flight state to the optimal guidance command. Then, a feedforward neural network is trained by the dataset to approximate the mapping from flight state to the optimal guidance command. As a consequence, the nonlinear optimal guidance command can be generated by the trained neural network within milliseconds. Finally, numerical simulations are performed to demonstrate and verify the effectiveness of the proposed nonlinear optimal guidance law.

Key words: overload constraints, impact time control, nonlinear optimal guidance, parameterization of Hamiltonian trajectories, feedforward neural network