The augmented ideal proportional navigation guidance law is derived as the closed-loop nonlinear optimal feedback solution for maneuvering target interception. The derived guidance law minimizes a performance index that is similar to the range-weighted control energy of relative motion. The optimal solution is obtained without any linearization of the engagement kinematics or assumption of a near-collision course condition. A method to implement the optimal guidance solution for a constant-speed pursuer is also proposed.
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Cho et al. (2016) studied this question.
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