In this paper, we propose an event-based sampling policy to implement a constraint-tightening, robust MPC method. The proposed policy enjoys a computationally tractable design and is applicable to perturbed, linear time-invariant systems with polytopic constraints. In particular, the triggering mechanism is suitable for plants with no centralized sensory node as the triggering mechanism can be evaluated locally at each individual sensor. From a geometrical viewpoint, the mechanism is a sequence of hyperrectangles surrounding the optimal state trajectory such that robust recursive feasibility and robust stability are guaranteed. The design of the triggering mechanism is cast as a constrained parametric-in-set optimization problem with the volume of the set as the objective function. Reparameterized in terms of the set vertices, we show that the problem admits a finite tractable convex program reformulation and a linear program relaxation. Several numerical examples are presented to demonstrate the effectiveness and limitations of the theoretical results.

In this paper, an event-triggering approach is proposed for a robust model predictive control method. The approach is applicable to constrained, linear time-invariant systems with bounded, additive disturbances. At each triggering instant, the triggering mechanism is designed online using a linear programming approach. Intuitively, the mechanism is a sequence of hyper-rectangles that surround the optimal state trajectory, over the prediction horizon. Standard analyses of robust feasibility and robust stability of the closed-loop, event-triggered control system are conducted. A numerical example is presented to show benefits of the proposed approach. In particular and under the assumption that the disturbance has a uniform distribution, we further study some statistical properties of the generated triggering instants.

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.