Aeroassisted orbital maneuvering using Lyapunov optimal feedback control

For advanced space transportation systems, such as the National Aerospace Plane or the Orbital Transfer Vehicle, the use of aeroassisted orbital transfer from a high Earth orbit to a low Earth orbit will require an optimizing closed-loop feedback controller, not only to achieve significant fuel savings, but also to compensate for large, unpredictable fluctuations in atmospheric density. We present a Lyapunov optimal function minimizing feedback control algorithm incorporating a preferred direction of motion at each state of the system, opposite to the gradient of a specified "descent function." Lyapunov optimal feedback control is compared to an approximate minimum-fuel calculus of variations open-loop optimal control algorithm based on the 1962 U.S. Standard Atmosphere. The performance of the two controllers is simulated against both the 1962 U.S. Standard Atmosphere and an atmosphere corresponding to the STS-6 Space Shuttle flight, which contains density fluctuations on the order of + 40% compared to the U.S. Standard Atmosphere. In the STS-6 atmosphere the calculus of variations open-loop controller fails to achieve optimal atmospheric exit conditions. In fact, it fails to exit the atmosphere. The Lyapunov optimal feedback controller is able to achieve not only atmospheric exit, despite the ± 40% density fluctuations in the STS-6 atmosphere, but also achieves essentially the optimal (minimum-fuel) exit conditions.