Obtaining and employing state dependent parametrizations of prespecified complexity in constrained MPC

In this paper we propose a method of obtaining and employing state dependent parametrizations in order to reduce the on-line computational load in linear model predictive control (MPC). At the core of our results is the application of a data mining algorithm off-line to obtain a number of suitable parametrizations to approximate solutions of the MPC optimization problem. We show how to refine the parametrizations to achieve constraint satisfaction and employ them in an overall MPC scheme which provides guaranteed stability and constraint satisfaction at considerably reduced computational load. We apply the results in an illustrative example which shows the benefits of the proposed method.