The Grainger College of Engineering
Aerospace Engineering

Conway Group’s Control Theory Among Journal’s Most Downloaded Papers

8/11/2014 Susan Mumm, Aerospace Engineering Media Specialist

Bruce Conway and Pradipto Ghosh theorize on optimal feedback controllers for dynamic systems.

Written by Susan Mumm, Aerospace Engineering Media Specialist

This graphic shows a collection of optimal time histories for the lift coefficient (one of two controls) for a AOTV (aero-assisted orbital transfer vehicle). This is a spacecraft that deliberately enters the atmosphere and uses lift and drag to modify the orbit, before exiting the atmosphere and re-entering orbit. The object is to change the orbit inclination while using as little fuel as possible. The many green time histories are for different initial conditions.
This graphic shows a collection of optimal time histories for the lift coefficient (one of two controls) for a AOTV (aero-assisted orbital transfer vehicle). This is a spacecraft that deliberately enters the atmosphere and uses lift and drag to modify the orbit, before exiting the atmosphere and re-entering orbit. The object is to change the orbit inclination while using as little fuel as possible. The many green time histories are for different initial conditions.
A research paper by Aerospace Engineering at Illinois Emeritus Prof. Bruce A. Conway and his graduate student appeared in July on the Journal of Guidance, Control, and Dynamics' list of the most downloaded papers for the past 12 months.

“Near-Optimal Feedback Strategies Synthesized Using a Spatial Statistical Approach” by graduate student (now recent PhD) Pradipto Ghosh and Conway concerns finding optimal feedback (closed-loop) controllers for dynamic systems. This has been a difficult problem for many decades, with no straightforward solution having been developed, according to Conway.

He and Pradipto give several examples of the application of their method, one of which is the recovery of a spacecraft from insertion into an initial orbit that is slightly lower than originally planned.

“The approach taken in the paper is to use the open-loop optimal strategies, which are easier to find but of course lack the ability to compensate for unmodeled errors, to find an approximation for the optimal feedback control,” Conway said.

This graphic shows just one time history for the same lift coefficient control but for a new initial condition (or perturbation), i.e. one not represented in the first graphic. The green line is the optimal open-loop control found from this new initial condition; this is the “true” solution. The dashed line is the optimal feedback control using kriging interpolation among the “family” of optimal trajectories shown in the first graph. There is a very good correspondence.
This graphic shows just one time history for the same lift coefficient control but for a new initial condition (or perturbation), i.e. one not represented in the first graphic. The green line is the optimal open-loop control found from this new initial condition; this is the “true” solution. The dashed line is the optimal feedback control using kriging interpolation among the “family” of optimal trajectories shown in the first graph. There is a very good correspondence.
“This is done by a type of interpolation; we find a “family” of optimal trajectories, determined from different initial conditions, that hopefully encompasses (or “encloses" or “bounds") the deviations from the nominal trajectory that will be found in flight.

“We then use a method, universal kriging, developed by a South African mining engineer to predict mineral concentrations in unsampled locations in a field that had previously never been applied to such dynamic systems. The kriging method does the interpolation among the previously computed optimal trajectories to find the feedback control for the system of interest in such a way as to minimize the predicted error.

“Since all of the time-consuming computation of the open-loop trajectories can be done in advance, our controller is very fast, that is, suitable for use in real time onboard a vehicle.”
 

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This story was published August 11, 2014.