Robust stability in predictive control with soft constraints

In this paper we take advantage of the primary and dual Youla parameterizations for setting up a soft constrained model predictive control (MPC) scheme for which stability is guaranteed in face of norm-bounded uncertainties. Under special conditions guarantees are also given for hard input constraints. In more detail, we parameterize the MPC predictions in terms of the primary Youla parameter and use this parameter as the online optimization variable. The uncertainty is parameterized 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 optimization as a constraint on the induced gain of the optimization variable. We illustrate the method with a numerical simulation example.