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.

翻译：在分布式模型预测控制（MPC）中，每个采样时刻的控制输入通过分布式算法求解有限时域内的大规模最优控制问题（OCP）计算得到。通常，此类算法需要子系统之间进行多轮（实际上近乎无限轮）通信才能收敛，这在计算层面和（无线系统的）能量层面均是主要缺陷。针对这些挑战，我们提出一种次优分布式MPC方案，通过维持大规模OCP的运行时解估计并在每个采样时刻对其进行更新，将总通信负担同样在时间上均匀分布。我们证明，在满足一定正则性条件下，若每个采样时刻的通信预算足够大，所得到的次优MPC控制律能够恢复最优MPC的定性鲁棒稳定性性质。