On the disturbance model in the robustification of explicit predictive control

This article deals with the predictive control for linear systems, described in a explicit form as piecewise affine (PWA) state feedback laws. The main goal is to reduce the sensitivity of these schemes with respect to the model uncertainties. This objective can be attained by considering worst-case (min–max) formulations, optimisation over the control policies or tube predictive control. Such comprehensive approaches may lead to fastidious on-line optimisation, thus reducing the range of application. In the present note, a two-stage predictive strategy is proposed, which in the first place synthesises an analytical (continuous and piecewise linear) control law based on the nominal model and secondly robustifies the control law in the neighbourhood of the equilibrium point (the feedback gain obtained for the unconstrained control problem – most often assimilated to the LQR gain). How the disturbance model corresponding to the unconstrained control robustification can be used to improve the robustness of the PWA control law is also shown.