Robustness margins and robustification of nominal explicit MPC

The design of nominal linear predictive control is well understood nowadays with the parameters influencing the stability and the performance of the nominal closed loop. Structurally, this nominal closed loop represents a piecewise dynamical system and a natural question is the level of robustness of the nominal design. In this talk we will analyse the robustness margins of an explicit MPC controller for linear systems. A generic geometrical approach will be used to obtain robustness/fragility margins with respect to the positive invariance properties. Several robustness margins will be considered: the first one considers parametric uncertainties in the model, the second one correspond to the variation of the gain of the model and finally the last one correspond to the admissible neglected dynamics with respect to the nominal prediction model. For PWA control laws defined over a bounded region in the state space, it is shown that these margins can be described in terms of polyhedral sets in parameter space. In the second part of the talk, we will get back to some classical robustification procedures and look at the influence of such techniques in the case of nominal explicit MPC in order to cope with unmodelled dynamics of the plant to be controlled.