A Decentralized Event-Based Approach for Robust Model Predictive Control

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 hyper-rectangles 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. Re-parameterized 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.