Robust event-triggered model predictive control of polytopic LPV systems: An input-to-state stability approach

Abstract

This paper addresses the problem of designing robust event-triggered tube-based model predictive control (TMPC) for constrained linear parameter-varying systems. The main challenge with implementing TMPC schemes in an event-triggered setup is that the assumption of feedback for all sampling times is not satisfied, which leads to an exponential growth of the predicted sets. First, a novel modification of homothetic TMPC is introduced to consider the effect of open-loop control between triggering times. At each sampling instant, the TMPC provides the maximal feasible number of open-loop steps and a sequence of control inputs, which can be applied in an open-loop fashion while satisfying the state and control constraints. Second, depending on the maximal number of open-loop steps, the triggering condition is derived based on the input-to-state stability (ISS) concept with the aim to reduce the communication traffic between sensors, controllers and actuators. Moreover, recursive feasibility and asymptotic stability of the closed-loop system are guaranteed. Simulation results demonstrate the efficacy of the proposed scheme while reducing the frequency of the update times.