Constrained Dynamic Control Allocation in the Presence of Singularity and Infeasible Solutions

TL;DR

This paper introduces a modified control allocation method using pseudo inverse and SVD techniques to effectively handle singularities and infeasible solutions in complex control systems, ensuring reliable performance.

Contribution

It presents a novel analytical control allocation approach that manages singularities and infeasibility with predictable computational complexity, outperforming traditional optimization methods.

Findings

Successfully handles singularities and infeasible solutions

Maintains computational efficiency with predictable complexity

Demonstrates effectiveness through simulation results

Abstract

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.