Influence of Discretization in Dynamically Embedded Model Predictive Control

The paper analyzes the closed-loop stability of Dynamically Embedded Model Predictive Control for input-constrained continuous-time nonlinear systems. Given a stabilizing continuous-time optimal control problem, the proposed method performs a discrete approximation to obtain a finite number of optimization variables. The resulting optimization problem is then embedded into a dynamic feedback law that evolves in parallel to the system. Using Input-to-State Stability, it is shown that the dynamic interconnection between the ideal continuous-time model predictive controller and the dynamically embedded solver is asymptotically stable for a sufficiently small discretization step and sufficiently fast solver dynamics. Numerical results, however, highlight a counter-intuitive behavior: as the discretization step decreases, the stability of the closed-loop system tends to deteriorate. This suggests that, although the discretization should be sufficiently accurate to correctly capture the behavior of the system, oversampling the system dynamics may be just as harmful as undersampling. Copyright (c) 2023 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)