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This paper is concerned with devising the nonlinear optimal guidance forintercepting a stationary target with a fixed impact time. According toPontryagin's Maximum Principle (PMP), some optimality conditions for thesolutions of the nonlinear optimal interception problem are established, andthe structure of the corresponding optimal control is presented. By employingthe optimality conditions, we formulate a parameterized system so that itssolution space is the same as that of the nonlinear optimal interceptionproblem. As a consequence, a simple propagation of the parameterized system,without using any optimization method, is sufficient to generate enough sampleddata for the mapping from current state and time-to-go to the optimal guidancecommand. By virtue of the universal approximation theorem, a feedforward neuralnetwork, trained by the generated data, is able to represent the mapping fromcurrent state and time-to-go to the optimal guidance command. Therefore, thetrained network eventually can generate fixed-impact-time nonlinear optimalguidance within a constant time. Finally, the developed nonlinear optimalguidance is exemplified and studied through simulations, showing that thenonlinear optimal guidance law performs better than existing interceptionguidance laws.

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