Robust stability in constrained predictive control through the Youla parameterisations

In this article we take advantage of the primary and dual Youla parameterisations to set up a soft constrained model predictive control (MPC) scheme. In this framework it is possible to guarantee stability in face of norm-bounded uncertainties. Under special conditions guarantees are also given for hard input constraints. In more detail, we parameterise the MPC predictions in terms of the primary Youla parameter and use this parameter as the on-line optimisation variable. The uncertainty is parameterised in terms of the dual Youla parameter. Stability can then be guaranteed through small gain arguments on the loop consisting of the primary and dual Youla parameter. This is included in the MPC optimisation as a constraint on the induced gain of the optimisation variable. We illustrate the method with a numerical simulation example.