Stability of nonlinear model predictive control in the presence of errors due to numerical online optimization

We present and investigate a Newton type method for online optimization in nonlinear model predictive control, the so called "real-time iteration scheme". In this scheme only one Newton type iteration is performed per sampling time, resulting in a fast online optimization algorithm. Due to the close dovetailing of system and optimizer dynamics, however, stability of the closed-loop system is not implied by standard nonlinear model predictive control results. In this paper, we give a proof of nominal stability of the scheme, which builds on concepts from both, NMPC stability theory and convergence analysis of Newton type methods. The principal result is that under some reasonable assumptions - the combined system-optimizer dynamics can be guaranteed to converge towards the origin from significantly disturbed system-optimizer states.