Lebesgue-Approximation Model Predictive Control of Nonlinear Sampled-Data Systems

Abstract

This article studies discrete-time implementation of model predictive control (MPC) algorithms in continuous-time nonlinear sampled-data systems. We present a discrete-time and aperiodic nonlinear MPC algorithm to stabilize continuous-time nonlinear dynamics, based on the Lebesgue approximation model (LAM). In this LAM-based MPC (LAMPC), the sampling instants are triggered by a self-triggered scheme, and the predicted states and transition time instants in the optimal control problem are calculated in an aperiodic manner subject to the LAM. Sufficient conditions are derived on feasibility and stability of the resulting closed-loop systems. According to these conditions, the parameters in LAMPC are designed with the guarantee of exclusion of Zeno behavior. Meanwhile, it is shown that the periodic task model is a special case in our framework with appropriate choice of the parameters in the LAM. Simulation results indicate that LAMPC can dynamically adjust the computation periods and has the potential to reduce the computational costs compared with periodic approaches.