American Journal of Applied Sciences

Determination of Nonlinear Optimal Feedback Law for Satellite Injection Problem Using Neighboring Optimal Control

Hamed Hossein Afshari, Alireza Basohbat Novinzadeh and Jafar Roshanian

DOI : 10.3844/ajassp.2009.430.438

American Journal of Applied Sciences

Volume 6, Issue 3

Pages 430-438


An optimal trajectory design of a nonlinear satellite injection problem for transfer to a final target orbit by minimizing the time was investigated. Indeed, this design was an exact solution to the nonlinear two-point boundary value problem which determined optimal control history as well as optimal state trajectories in the open-loop form. Furthermore, the obtained optimal guidance strategy was exerted in the closed-loop form against the environment disturbances using neighboring optimal control method in the exact solution. Neighboring Optimal Control (NOC) law could produce time-variant feedback gains minimizing the performance measure to second order for perturbations from a nominal optimal path. Generally, this law was a function of perturbations appeared in the states and constraints and could be computed utilizing the backward sweep method. The simulation results indicated that the presented methodology was successfully utilized in the real world applications with good robustness to each noise or disturbance produced in each state variable.


© 2009 Hamed Hossein Afshari, Alireza Basohbat Novinzadeh and Jafar Roshanian. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.