Optimizing the end-point state-weighting matrix in model-based predictive control

In this paper a linear model-based predictive control (MPC) algorithm is presented, for which nominal closed-loop stability is guaranteed. The input is obtained by minimizing a quadratic performance index over a finite horizon plus an end-point state (EPS) penalty, subject to input, state and output constraints. Under certain conditions, the weighting matrix in the EPS penalty enables one to specify an invariant ellipsoid in which the input, state and output constraints are satisfied. In existing MPC algorithms this weighting matrix is calculated off-line. The main contribution of this paper is to incorporate the calculation of the EPS-weighting matrix into the on-line optimization problem of the controller. The main advantage of this approach is that a natural and automatic trade-off between feasibility and optimality is obtained. This is demonstrated in a simulation example.