A New Approach to Model Predictive Control Based on Two Degrees of Freedom Control and B-Splines Input Shaping

Abstract

The purpose of this article is to reduce some technical difficulties related to the complexity of stability and feasibility analysis of Model Predictive Control (MPC) as well as to reduce the complexity of the relative optimization procedure. The new approach is based on a two degrees of freedom control scheme where the output $r(k)$ of a feedforward input estimator is used as input forcing the closed-loop system $\Sigma _f$ . This latter is given by the feedback connection of a Linear Time Invariant (LTI) plant with a dynamic output controller. The task of the controller is to guarantee the stability of $\Sigma _f$ , as well as the fulfillment of hard constraints for any $r(k)$ satisfying an “ a priori ” determined admissibility condition. The input $r(k)$ is computed through the online minimization of a quadratic cost functional and is applied to $\Sigma _f$ according to the usual MPC strategy. To simplify the constrained optimization problem, the input $r(k)$ forcing $\Sigma _f$ is assumed to be given by a B-spline function. This greatly decreases the number of decision variables of the online optimization procedure because B-splines are universal approximators which admit a parsimonious parametric representation. Moreover such parameterization allows us to reformulate the minimization of the cost functional as a box Constrained Least Squares (CLS) problem. It is shown that stability and recursive feasibility of the adopted MPC strategy are guaranteed in advance, regardless the chosen prediction horizon.