Robust model predictive control with aperiodic actuation

We consider a control design problem using wireless sensor/actuator networks. Such systems need to operate within the limited resources of available battery life and bandwidth. To address these concerns, we take a model predictive control (MPC) approach for perturbed LTI systems with constraints on the admissible input and state sets. We propose a triggering mechanism (TM) that aims to reduce the number of MPC updates, with the goal to reduce the communication and computation loads. The TM uses trajectories that have been computed at the last update instant and a current measurement to determine whether or not to trigger an update. The TM consists of two parts: 1) inequalities that are functions of the error signal between the observed states and the predicted trajectories, guaranteeing recursive feasibility, and 2) a scalar inequality, that is a function of a weighted version of the value function at the last triggering instant, guaranteeing closed-loop convergence. Numerical simulations demonstrate the effectiveness of our TM in reducing the number of MPC updates, thereby possibly reducing the communication load as well.