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

• Propose an efficient, constrained H∞ NMPC with guaranteed ISS w.r.t. bounded disturbances.
• Use piecewise affine H∞ control and augmented PLDI models to decrease conservatism of NMPC.
• Use PLDI method to turn the non-convex min–max problem into a semi-definite programming.
• Present a sufficient condition in form of LMIs to ensure the ISS of the proposed NMPC scheme.
• Apply the proposed NMPC to some fast systems, such as mass-carts and vehicular platoon.

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.