The model predictive control (MPC) of large-scale systems should adopt a distributed optimization approach, where controllers for the constituent subsystems optimize their control actions and iterations are used to coordinate their decisions. The real-time implementation of MPC, however, usually allows very limited time for computation and inevitably needs to be terminated early. In this work, we propose a splitting algorithm for distributed optimization analogous to forward-backward splitting (FBS), where ${\ell }_1$ and quadratic penalties are imposed on the violation of interconnecting relations among the subsystems. By designing the involved parameters based on dissipative analysis, the iterations result in the monotonic decrease of a plant-wide Lyapunov function, which we call Lyapunov envelope, thus maintaining closed-loop stability under distributed MPC despite early termination and yielding improving control performance as the allowed computational time or number of iterations increases. The proposed Lyapunov envelope algorithm is tested on an industrial-scale vinyl acetate monomer process.

大型系统的模型预测控制 (MPC) 应采用分布式优化方法，其中组成子系统的控制器优化其控制动作并使用迭代来协调其决策。然而，MPC 的实时实现通常允许非常有限的计算时间并且不可避免地需要提前终止。在这项工作中，我们提出了一种类似于前向后向分裂（FBS）的分布式优化分裂算法，其中${\ell }_1$对违反子系统之间的互连关系施加二次惩罚。通过基于耗散分析设计涉及的参数，迭代导致全厂 Lyapunov 函数单调递减，我们称之为 Lyapunov 包络，从而在分布式 MPC 下保持闭环稳定性，尽管提前终止并提高控制性能，因为允许的计算时间或迭代次数增加。建议的 Lyapunov 包络算法在工业规模的乙酸乙烯酯单体过程中进行了测试。