Robust MPC control based on a contractive sequence of sets

The closed loop formulation of the robust MPC has been shown to be a control technique capable of robustly stabilize uncertain nonlinear systems subject to constraints. This control technique mitigates the conservativeness derived from the open loop formulations but it is computationally too demanding or even untractable. This paper provides a way of overcoming the complexity of this technique. This is done by means of a sequence of sets. It is shown that it suffices to obtain a sequence of robust controllable sets. This sequence can be computed off-line using any tractable conservative procedure for the computation of the robust one-step set. Incorporating this sequence as a stabilizing constraint in the optimization problem, robust stability is guaranteed in case of suboptimal solutions or open loop approaches. Then, the optimization problem can be considerably simplified, yielding tractable approaches at the expense of performance. The proposed technique has been applied to a CSTR model.