Input-to-state stability of efficient robust H∞ MPC scheme for nonlinear systems

Abstract

In this work, we present an efficient H∞ model predictive control (MPC) scheme with guaranteed input-to-state stability (ISS) for constrained nonlinear systems subject to unknown but bounded disturbances. The nonlinear system is represented by using some given inclusion polytope. The notion of ISS is introduced to derive the sufficient condition in terms of linear matrix inequalities (LMIs), which ensures the ISS of the closed-loop system. In order to reduce the online computational demand of MPC, the non-convex min–max optimization problem is converted to a minimization problem in form of LMIs. A suboptimal MPC algorithm is then addressed to further decrease the computational demand. The applicability of the proposed results is illustrated by two numerical examples of a mass-cart and a vehicular platoon.