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A Newton-type method is investigated for online optimisation in nonlinear model predictive control, the so-called real-time iteration scheme. Only one Newton-type iteration is performed per sampling instant in this scheme, and control of the system and the solution of the optimal control problem are performed in parallel. In the resulting combined dynamics of system and optimiser, the actual feedback control in each step is based on the current solution estimate, and the solution estimates are at each sampling instant refined and transferred to the next optimisation problem by a specially designed transition. This approach yields an efficient online optimisation algorithm that has already been successfully tested in several applications. Due to the close dovetailing of system and optimiser dynamics, however, stability of the closed-loop system is not implied by standard nonlinear model predictive control results. A proof of nominal stability of the scheme is given 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–optimiser dynamics can be guaranteed to converge towards the origin from significantly disturbed system–optimiser states.
Diehl et al. (Fri,) studied this question.