Input‐to‐state stability of contractive EMPC of non‐linear systems with bounded disturbances

Abstract

In this work, the authors consider the robust control problem of model predictive control (MPC) for economic criterion optimisation of constrained uncertain non-linear systems with unknown but bounded additive disturbances. The authors propose a robust economic MPC (EMPC) scheme with guaranteed input-to-state stability (ISS) to solve the robust control problem. By imposing a modified Lyapunov-based contractive constraint, the optimal control problem of the EMPC is formulated based on the nominal state prediction of the uncertain system. Then some sufficient conditions of Lipschitz continuity and terminal elements are derived to guarantee recursive feasibility and ISS of the EMPC with respect to the disturbance by the arguments of robust invariant sets and ISS. Two examples consisting of a chemical reaction process and a vehicle system are used to demonstrate the effectiveness of the proposed scheme.