Discrete Time Formulation of Quasi Infinite Horizon Nonlinear Model Predictive Control Scheme with Guaranteed Stability

The quasi infinite horizon NMPC formulation developed by Chen and Allgöwer [1998] provides a systematic method to characterize the terminal set needed to ensure nominal stability of a system controlled using finite horizon NMPC formulation at an unstable operating point. Their approach, however, has been developed for continuous time NMPC formulations. Real time implementation of an NMPC scheme using microprocessors, however, makes model discretization inevitable. In this work, a discrete time version of the quasi infinite NMPC formulation is developed, which is particularly suited for operating a system at an unstable operating point. Also, a novel approach is developed for characterization of the terminal region that makes use of the discrete time nonlinear model and that provides sufficient degrees of freedom to characterize the terminal region. The nominal closed loop system is then shown to be equi-asymptotically stable when controlled using the proposed discrete time QIH-NMPC. Efficacy of the proposed approach is demonstrated using a benchmark problem given by Chen and Allgöwer [1998]. The simulation study shows that the terminal regions for the discrete time case are relatively smaller than the terminal region for the continuous time case reported by Chen and Allgöwer [1998]. Also, the proposed discrete time QIH-NMPC is able to steer the state trajectories from specified feasible initial conditions to locations inside the terminal set within the specified prediction horizon and later converge to the unstable operating point.