Robust self-triggered DMPC for linear discrete-time systems with local and global constraints

Abstract

In this paper, a novel robust distributed model predictive control with a self-triggered mechanism is proposed for a family of discrete-time linear systems with additive disturbances, local and global constraints. To handle the additive disturbances, a tube method is applied to achieve the robust satisfaction of local constraints. Meanwhile, a sequential constraints tightening method is proposed to guarantee the satisfaction of global coupled constraints. The optimization problem is constructed as a consensus problem of an augmented Lagrange function and is solved through a modified distributed alternative direction multiplier method. Furthermore, a self-triggered mechanism is adopted to help reduce the computation burden and accelerate system stabilization by skipping insignificant iteration steps in parallel ways. By clarifying the upper bound on tolerable bounded disturbances, two sufficient conditions about recursive feasibility of optimization problem and input-to-state stability of the closed-loop system are given, respectively. Finally, performances of the proposed scheme are illustrated by simulation examples.