How to Find Minimum-Fuel Controllers, AIAA
Ross, I. Michael
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Spacecraft guidance and control (G & C) problems are uniquely different from similar problems arising in other control systems because the amount of fuel consumed by a proposed G and C algorithm dictates its engineering feasibility. Despite this stringent requirement, it has become quite prevalent, particularly in the recent formation keeping literature, to recast space G & C problems in terms of a quadratic cost or ignore propellant consumption altogether. In this paper, we show that the proper cost functions to use are lp-variants of the L1-norm of the control and not the popular quadratic forms. The penalty for not using the L1-norm is significantly more propellant consumption and undesirable continuous thrusting. An illustrative double-integrator problem is used to demonstrate that the fuel penalty incurred for using quadratic costs is at least 18 percent and could be as high as fifty percent. Techniques for solving the nonsmooth L1-optimal control problem for nonlinear dynamical systems are discussed. An example low-thrust orbit transfer problem is formulated and solved to illustrate the techniques.
The article of record as published may be located at http://arc.aiaa.orgApproved for public display, distribution unlimitedProceedings of AIAA Guidance, Navigation, and Control Conference ; Paper no. AIAA 2004-5346, Providence, Rhode Island, Aug. 16-19, 2004
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