We study the distributed model predictive control (DMPC) problem for a network of linear discrete-time subsystems in the presence of stochastic noise among communication channels, where the system dynamics are decoupled and the system constraints are coupled. The DMPC is cast as a stochastic distributed consensus optimization problem by modeling the exchanged variables as stochastic ones and a novel noisy alternating direction multiplier method (NADMM) is proposed to solve it in a fully distributed way. We prove that the sequences of the primal and dual variables converge to their optimal values almost surely (a.s.) with communication noise. Furthermore, a new stopping criterion and a DMPC scheme termed as current–previous DMPC (cpDMPC) are proposed, which guarantees deterministic termination even when the NADMM algorithm may not converge in a practical realization. Next, the strict analysis on the feasibility of the cpDMPC strategy and the closed-loop stability is carried out, and it is shown that the cpDMPC strategy is feasible at each time step and the closed-loop system is asymptotically stable. Finally, the effectiveness of the proposed NADMM algorithm is verified via an example.

我们研究了在通信通道之间存在随机噪声的情况下，线性离散时间子系统网络的分布式模型预测控制（DMPC）问题，其中系统动力学解耦且系统约束耦合。通过将交换变量建模为随机变量，将DMPC转换为随机分布共识优化问题，并提出了一种新颖的有噪交替方向乘数法（NADMM）以完全分布式的方式解决该问题。我们证明，基本变量和对偶变量的序列几乎可以确定地（与通信噪声一样）收敛到其最佳值。此外，提出了一种新的停止标准和一种称为当前以前的DMPC（cpDMPC）的DMPC方案，即使在实际实现中NADMM算法可能无法收敛时，也可以确保确定性终止。接下来，对cpDMPC策略的可行性和闭环稳定性进行了严格的分析，结果表明cpDMPC策略在每个时间步都是可行的，并且闭环系统是渐近稳定的。最后，通过实例验证了所提出的NADMM算法的有效性。