Stable Predictive Control Horizons

The stability theory of predictive and adaptive predictive control for processes of linear and stable nature is based on the hypothesis of a physically realisable driving desired trajectory (DDT). The formal theoretical verification of this hypothesis is trivial for processes with a stable inverse, but it is not for processes with an unstable inverse. The extended strategy of predictive control was developed with the purpose of overcoming methodologically this stability problem and it has delivered excellent performance and stability in its industrial applications given a suitable choice of the prediction horizon. From a theoretical point of view, the existence of a prediction horizon capable of ensuring stability for processes with an unstable inverse was proven in the literature. However, no analytical solution has been found for the determination of the prediction horizon values which guarantee stability, in spite of the theoretical and practical interest of this matter. This article presents a new method able to determine the set of prediction horizon values which ensure stability under the extended predictive control strategy formulation and a particular performance criterion for the design of the DDT generically used in many industrial applications. The practical application of this method is illustrated by means of simulation examples.