A solution for constrained control allocation problem by using multi-parametric quadratic programming algorithm

Control allocation is an important part of a system. It implements the function that map the desired commanded forces from the controller into the commands of the different actuators. In this paper, the authors present an approach for solving constrained control allocation problem in vessel system by using multi-parametric quadratic programming (mp-QP) algorithm. The goal of mp-QP algorithm applied in this study is to compute a solution to minimize a quadratic performance index subject to linear equality and inequality constraints. The solution can be pre-computed off-line in the explicit form of a piecewise linear (PWL) function of the generalized forces and constrains. The efficiency of mp-QP approach is evaluated through a dynamic positioning simulation for a ship by using four tugboats with constraints about limited pushing forces and found to work well.