A Robust Distributed Model Predictive Control Framework for Consensus of Multi-Agent Systems with Input Constraints and Varying Delays

This paper studies the consensus problem of general linear discrete-time multi-agent systems (MAS) with input constraints and bounded time-varying communication delays. We propose a robust distributed model predictive control (DMPC) consensus protocol that integrates the offline consensus design with online DMPC optimization to exploit their respective advantages. More precisely, each agent is equipped with an offline consensus protocol, which is a priori designed, depending on its immediate neighbors' estimated states. Further, the estimation errors propagated over time due to inexact neighboring information are proved bounded under mild technical assumptions, based on which a robust DMPC strategy is deliberately designed to achieve robust consensus while satisfying input constraints. Moreover, it is shown that, with the suitably designed cost function and constraints, the feasibility of the associated optimization problem can be recursively ensured. We further provide the consensus convergence result of the constrained MAS in the presence of bounded varying delays. Finally, two numerical examples are given to verify the effectiveness of the proposed distributed consensus algorithm

Resilient and constrained consensus against adversarial attacks: A distributed MPC framework

There has been a growing interest in realizing the resilient consensus of the multi-agent system (MAS) under cyber-attacks, which aims to achieve the consensus of normal agents (i.e., agents without attacks) in a network, depending on the neighboring information. The literature has developed mean-subsequence-reduced (MSR) algorithms for the MAS with F adversarial attacks and has shown that the consensus is achieved for the normal agents when the communication network is at least (2F+1)-robust. However, such a stringent requirement on the communication network needs to be relaxed to enable more practical applications. Our objective is, for the first time, to achieve less stringent conditions on the network, while ensuring the resilient consensus for the general linear MAS subject to control input constraints. In this work, we propose a distributed resilient consensus framework, consisting of a pre-designed consensus protocol and distributed model predictive control (DMPC) optimization, which can help significantly reduce the requirement on the network robustness and effectively handle the general linear constrained MAS under adversarial attacks. By employing a novel distributed adversarial attack detection mechanism based on the history information broadcast by neighbors and a convex set (i.e., resilience set), we can evaluate the reliability of communication links. Moreover, we show that the recursive feasibility of the associated DMPC optimization problem can be guaranteed. The proposed consensus protocol features the following properties: 1) by minimizing a group of control variables, the consensus performance is optimized; 2) the resilient consensus of the general linear constrained MAS subject to F-locally adversarial attacks is achieved when the communication network is (F+1)-robust. Finally, numerical simulation results are presented to verify the theoretical results