A Lyapunov function for the combined system-optimizer dynamics in inexact model predictive control

In this paper, an asymptotic stability proof for a class of methods inexact nonlinear model predictive control is presented. General Q-linearly convergent online optimization are considered and result derived the setting where limited number iterations optimizer carried out per sampling time. Under assumption Lipschitz continuity solution, we explicitly construct Lyapunov function combined system-optimizer dynamics, which shows that can be obtained if time sufficiently short. The results constitute extension to existing attractivity hold in simplified inequality constraints either not present or inactive region attraction considered. Moreover, with respect established on robust suboptimal control, develop framework takes into account optimizer’s dynamics does require decrease objective across iterates. By extending these results, gap between theory practice standard real-time iteration strategy bridged broader guaranteed.