Robust design of predictive controllers in presence of unmodeled dynamics

In the last two decades two key issues have been in the focus of the attention of researchers working on the advancement of the methodologies for the control design of linear systems, i.e. robustness to model uncertainty and the presence of constraints on inputs and other system variables, giving rise to the very active research areas of Robust Identification and Control and of Model Predictive Control, respectively. There exist now well assessed methods of robust control design (H_∞, ℓ₁, μ, etc.) for various kinds of uncertainty descriptions. All the above methodologies provide linear controllers, while the Model Predictive Control (MPC) literature has shown that nonlinear controls, e.g. obtained by a receding horizon procedure, may give significant improvements over linear controllers in cases that constraints on inputs and other system variables have to be met. Indeed, the main issues typically pertaining MPC, i.e. feasibility of the on-line optimization, stability and performance are now largely understood for systems exactly described by linear models, while only recently robustness issues have been addressed in the MPC context. In turn, model uncertainty may be of two types, parametric or dynamic. In this paper an MPC design technique is proposed taking into account robustness versus dynamic model uncertainty.