Discrete-time Incremental ISS: A framework for Robust NMPC

In this paper, Incremental Input-to-State Stability is studied as a system theoretic framework to address the challenges of robust nonlinear model predictive control. In the first part of the paper, a Lyapunov framework for Incremental Input-to-State Stability of nonlinear discrete-time dynamical systems is established. In the second part, Incremental Input-to-State Stability is shown to lead to an efficient MPC method for disturbed nonlinear systems. Based on the Incremental Input-to-State Stability Lyapunov function, a tightening of the constraints is proposed. Satisfaction of the tightened constraints can be guaranteed under the disturbances. By this concept, a robust nonlinear model predictive control problem is handled and the effectiveness is shown through an example from the literature.