Stability and Robustness of Distributed Suboptimal Model Predictive Control

TL;DR

This paper proposes a suboptimal distributed MPC approach that reduces communication requirements by maintaining and updating a running solution estimate, while preserving stability properties under certain conditions.

Contribution

It introduces a novel suboptimal distributed MPC scheme that distributes communication over time and maintains robustness, addressing computational and energy challenges.

Findings

The suboptimal MPC recovers stability properties of optimal MPC.

The scheme reduces communication burden in distributed control.

Robustness is maintained under regularity conditions.

Abstract

In distributed model predictive control (MPC), the control input at each sampling time is computed by solving a large-scale optimal control problem (OCP) over a finite horizon using distributed algorithms. Typically, such algorithms require several (virtually, infinite) communication rounds between the subsystems to converge, which is a major drawback both computationally and from an energetic perspective (for wireless systems). Motivated by these challenges, we propose a suboptimal distributed MPC scheme in which the total communication burden is distributed also in time, by maintaining a running solution estimate for the large-scale OCP and updating it at each sampling time. We demonstrate that, under some regularity conditions, the resulting suboptimal MPC control law recovers the qualitative robust stability properties of optimal MPC, if the communication budget at each sampling time is large enough.