Robust Predictive Control with Restricted Constraints to Cope with Estimation Errors

Abstract This paper addresses predictive regulation of linear discrete-time systems subject to persistent bounded disturbances and to state/control constraints. Previous work has dealt with the case of complete state information; here the output feedback case is addressed. The proposed nonlinear dynamic compensator is built according to the classical separation structure, i.e. consists of a state estimator and of a static feedback compensator using the state estimate. In turn, the state estimator is made up of a classical Luenberger observer which provides an asymptotic state estimate and of a set-membership estimator which recursively updates the uncertainty of that estimate. The static feedback compensator consists of a robust predictive controller with suitable constraint restrictions which take into account of the current state uncertainty as well as of the process disturbance and measurement noise. It is shown that the overall scheme guarantees an asymptotically stable behaviour under suitable assumptions on the set-membership state estimator and feasibility at the outset.