Model-based predictive control for Hammerstein systems

Abstract

Hammerstein systems are a class of systems represented by a static nonlinearity at the input followed by a linear dynamic block. In the paper the static input nonlinearity is transformed into a polytopic description. The remaining uncertain linear model is used in a MPC algorithm of which the optimization problem involves minimization of a linear objective function subject to linear matrix inequalities (LMIs), which is a convex problem. A procedure is presented to remove a number of LMIs from the optimization problem, prior to solving it. By means of an iterative procedure the conservatism of the polytopic description can be reduced. Nominal closed loop stability of this Hammerstein MPC algorithm is guaranteed. A comparison is presented between the proposed algorithm and an algorithm which removes the nonlinearity from the control problem via an inversion.