An M-matrix based Efficient Algorithm for Model Predictive Control of Input Constrained Linear Systems

This paper discusses an on-line approach to Model Predictive Control (MPC) of input constrained linear systems. First, it is shown that an example of MPC with one-side input constraints is reduced into the Linear Complementarity (LC) problem with an M-matrix, which can be more efficiently solved by the existing special algorithm than the other general algorithms such as the Lemke method. However, in the case of both-side input constraints, which is more practical from the control engineering points of view, it can not be reduced into the LC problem with an M-matrix. Thus, next, a new algorithm for the case of both-side input constraints is proposed in this paper. The effectiveness of the proposed algorithm is shown by a numerical simulation.