Constrained Dynamic Control Allocation in the Presence of Singularity   and Infeasible Solutions
  Reliable controllers with high flexibility and performance are necessary for the control of intricate, advanced, and expensive systems such as aircraft, marine vessels, automotive vehicles, and satellites. Meanwhile, control allocation has an important role in the control system design strategies of such complex plants. Although there are many proposed control allocation methodologies, few papers deal with the problems of infeasible solutions or system matrix singularity. In this paper, a pseudo inverse based method is employed and modified by the null space, least squares, and singular value decomposition concepts to handle such situations. The proposed method could successfully give an appropriate solution in both the feasible and infeasible sections in the presence of singularity. The analytical approach guarantees the solution with pre-defined computational burden which is a noticeable privilege than the linear and quadratic optimization methods. Furthermore, the algorithm complexity is proportionately grown with the feasible, infeasible, and singularity conditions. Simulation results are used to show the effectiveness of the proposed methodology. 
David Buzorgnia and Ali Khaki-Sedigh
math.OC