A multivariable nonlinear algebraic loop as a QP with applications to MPC

In this paper we consider an alternative approach to implementing Model Predictive Control (MPC). We show that solving a class of quadratic programming (QP) problems is equivalent to solving a class of well-posed nonlinear algebraic loops. These algebraic loops are closely related to that found in static anti-windup synthesis. It therefore follows that certain classes of MPC can be implemented in a form that is a direct generalisation of the standard anti-windup structure. Implementations for classes of MPC are then derived for both regulator and tracking problems. Several alternative iterative algorithms for solving the algebraic loop are then presented. Some simulation results are also provided, with an example computational comparison to active set and interior point based MPC.