Constrained MPC under closed-loop uncertainty

The importance of closed-loop uncertainty predictions in robust model-predictive control (MPC) has been discussed by a number of authors in previous years [(A. Bemporad, 1998), (D. Mayne, 2000), (B. Kouvaritakis, 2000)]. The proposed controllers often rely upon invariant sets and require that input constraints are inactive at the final steady-state [(B. Kouvaritakis, 2000), (M. V. Kothare et al., 1996)]. The controller discussed in this paper avoids this limiting assumption while maintaining robust output constraint handling. This paper emphasises the often negative effects of probabilistic input constraints and proposes a method based upon multiple uncertainty regions to deal with these effects. The proposed controller solves a second-order cone program (SOCP) at each execution in order to determine the set of control moves that optimizes the expected performance of the closed-loop system while maintaining the uncertain process outputs and inputs within their allowable bounds. Case studies illustrate the performance of the new controller when plant/model mismatch is present.