Convergence of the discrete-time nonlinear model predictive control with successive time-varying linearization along predicted trajectories

Abstract

Model predictive control techniques for nonlinear systems very often take advantage of nonlinear model linearization. The model can be linearized once or repeatedly. In the paper the second type of method is considered: successive model linearization along predicted state and input trajectories. The nonlinear behaviour is represented by recurrent set of linear time-varying models. Solution of such optimal non-linear model predictive control problem is mostly obtained in an iterative way where the most important step is the successive system linearization along predicted trajectory. The main aim of the paper is to analyse convergence of the considered NMPC method, discuss problems concerning necessary condition for the convergence and prove proposed solutions.