A Comparison of Control Allocation Methods in the Presence of Parametric Model Uncertainty

When allocating redundant effectors to virtual control commands, linear (generalized
inverse) allocators have historically been used on aircraft and spacecraft. While simple to
implement, generalized inverses are unable to realize a significant portion of the attainable
moments. To address this drawback, the control allocation problem can also be formulated as a
linear programming or quadratic programming problem and solved using convex optimization based
solvers. These approaches have been shown to access a larger set of attainable moments,
however, little work has been done to understand the performance of convex optimization-based
control allocation in the presence of parametric model uncertainty. This paper seeks to compare
the performance of several control allocation approaches, including two forms of generalized
inverse allocators, the pseudo inverse and minimum-variance, and the linear programming
and quadratic programming approach in the presence of parametric model uncertainty. The
performance of these four allocators were tested on an aircraft model in the presence of
realistic parametric model uncertainty and the convex optimization approaches were shown to
outperform the generalized inverses.