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Presentation given at the AIAA/AAS Astrodynamics Specialists Conference in Minneapolis, MN, on 8/13/12.
The conference proceedings are available here: http://arc.aiaa.org/doi/abs/10.2514/6.2012-4425
Low-thrust trajectories result in challenging nonlinear optimization problems. To solve these problems, efficient and robust optimization techniques are required. The increasing complexity of such problems induces a rise in the computational intensity of the nonlinear solvers. The current work is based on a Hybrid Differential Dynamic Programming (HDDP) algorithm and aims at improving its computational efficiency. A quasi-Newton based method is presented to approximate the expensive second-order sensitivities in efforts to reduce computation times, while maintaining attractive convergence properties. A variety of quasi-Newton rank-one and rank-two updates are tested using several benchmark optimal control problems, including a simple spacecraft finite thrust trajectory problem. The quasi-Newton methods are used in this study to approximate the Hessian of the state transition functions, as opposed to the Hessian of the performance index like in classic optimization applications. Accordingly, the symmetric rank-one update is found to be most suitable for this HDDP application. The approximations are demonstrated to be sufficiently close to the true Hessian for the problems considered. In comparing the full second order version of HDDP with the quasi-Newton modification, the converged iteration counts are comparable while the run times for the quasi-Newton cases show up to an order of magnitude improvement. The speedups are demonstrated to increase with the problem dimension and the degree of coupling within the dynamic equations.
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