A Sufficient Condition for Stability of Sampled–data Model Predictive Control using Adaptive Time–mesh Refinement

Abstract

In this work, we address through model predictive control (MPC) a constrained nonlinear plant described by a continuous-time dynamical model, which naturally leads to a sampled-data control system. The numerical solution of the optimal control problems involved in MPC must utilize, eventually, some form of discretization. Nevertheless, there are several advantages in maintaining a continuous-time model until later stages. One advantage is that we can devise numerical procedures which, by exploiting additional freedom in selecting the discretization points, are more efficient when continuous-time models are used. Here, we discuss an extension to MPC of an Adaptive Mesh Refinement (AMR) algorithm, which has shown to be efficient in solving nonlinear optimal control problems. We derive a sufficient condition that guarantees that an MPC scheme using an adaptive time-mesh refinement algorithm preserves stability.