| The dissertation considers the objective of specifying commands to redundant actuators under constraints, a problem commonly referred to as control allocation. Three optimization objectives are considered, namely, direct allocation, mixed ℓ 1-norm, and mixed ℓ2-norm. The direct allocation objective is considered under relaxed conditions allowing for coplanar controls and yields a greater understanding of the geometry of the attainable set. An approach using a spherical coordinate transformation of the set of attainable accelerations is presented as an alternative to conventional methods. It is potentially useful for applications that require fast execution but can tolerate significant off-line processing. The core of the dissertation focuses on the solution of control allocation problems using interior-point algorithms. The algorithms are described in detail with an emphasis on preferred implementations. Appropriate choices of stopping tolerances and of other algorithm parameters are studied. Results show that implementation of the algorithms is feasible, without requiring an excessive number of computations. Warm start strategies are also evaluated, with mixed results due to a large variability in the number of computations. Although the computational load of the interior-point method is found to be greater than existing methods for problems of small size, convergence to the optimal solution is found to be more uniform and predictable than the other methods. In addition, the properties of the algorithms scale very favorably with problem size, making them preferable in applications with a large number of actuators. The performances of the algorithms are evaluated using linearized state-space models of a C-17 transport aircraft and of a tailless fighter aircraft. |
