A Variational Approach in Determination of Neighboring Optimal Guidance Law for Injection Problem

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An optimal trajectory design of a nonlinear injection into orbit problem with maximum velocity is investigated. This design includes an exact solution to the nonlinear two-point boundary value problem which determines optimal control history as well as optimal state trajectories in the open-loop form. Also, the Neighboring Optimal Control (NOC) law is utilized for finding nonlinear optimal closed-loop solution in the exact form which can protect the mission against the environment disturbances. The NOC law can produce time-variant feedback gains minimizing the performance measure to second order for perturbations from a nominal optimal path. Generally, this law is a function of perturbations appeared in states and constraints and can be computed using the backward sweep method. The simulation results indicate that the presented methodology can be successfully utilized in the real world application with good robustness to each noise or disturbance.
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Neighboring Optimal Control; Injection Into Orbit; Nonlinear Explicit Guidance

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