Nonlinear Optimal Guidance for Intercepting Stationary Targets with Impact-Time Constraints

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.