Stable constrained MPC without terminal constraint

Sufficient conditions to guarantee stability of model predictive control (MPC) strategies require the use of a terminal cost function and a terminal constraint region. This paper gives a procedure for removing the terminal constraint while maintaining asymptotic stability. This is especially interesting when the system is unconstrained on the state. In this case, the computational burden of the optimization problem does not have to be increased by introducing terminal state constraints due to stabilizing reasons. A region in which terminal constraint can be removed from the optimization problem is characterized. Two methods are proposed to enlarge this region: increasing the prediction horizon and weighting the terminal cost. Furthermore, procedures to calculate the stabilizing prediction horizon and the weighting factor for a given initial state are presented. Combining both, any stabilizable state can be controlled. The presented results are illustrated by the application to a CSTR.