The rapid development of technology and economy has led to the development of chemical processes, large-scale manufacturing equipment, and transportation networks, with their increasing complexity. These large systems are usually composed of many interacting and coupling subsystems. Moreover, the propagation and perturbation of uncertainty make the control design of such systems to be a thorny problem. In this study, for a complex system composed of multiple subsystems suffering from multiplicative uncertainty, not only the individual constraints of each subsystem but also the coupling constraints among them are considered. All the constraints with the probabilistic form are used to characterize the stochastic natures of uncertainty. This paper first establishes a centralized model predictive control scheme by integrating overall system dynamics and chance constraints as a whole. To deal with the chance constraint, based on the concept of multi-step probabilistic invariant set, a condition formulated by a series of linear matrix inequality is designed to guarantee the chance constraint. Stochastic stability can also be guaranteed by the virtue of nonnegative supermartingale property. In this way, instead of solving a non-convex and intractable chance-constrained optimization problem at each moment, a semidefinite programming problem is established so as to be realized online in a rolling manner. Furthermore, to reduce the computational burdens and amount of communication under the centralized framework, a distributed stochastic model predictive control based on a sequential update scheme is designed, where only one subsystem is required to update its plan by executing optimization problem at each time instant. The closed-loop stability in stochastic sense and recursive feasibility are ensured. A numerical example is employed to illustrate the efficacy and validity of the presented algorithm in this study.

技术和经济的快速发展导致化学工艺、大型制造设备和运输网络的发展，其复杂性日益增加。这些大型系统通常由许多相互作用和耦合的子系统组成。此外，不确定性的传播和扰动使此类系统的控制设计成为一个棘手的问题。在这项研究中，对于一个由多个子系统组成的复杂系统存在乘法不确定性，不仅考虑了每个子系统的个体约束，还考虑了它们之间的耦合约束。所有具有概率形式的约束都用于表征不确定性的随机性。本文首先通过将整体系统动力学和机会约束整合为一个整体，建立了集中模型预测控制方案。针对机会约束，基于多步概率不变集的概念，设计了一个由一系列线性矩阵不等式构成的条件来保证机会约束。随机稳定性也可以通过非负上鞅性质来保证。这样，就不再求解每个时刻的非凸、难处理的机会约束优化问题，而是建立半定规划问题，以滚动方式在线实现。此外，为了减少集中式框架下的计算负担和通信量，设计了一种基于顺序更新方案的分布式随机模型预测控制，其中只需一个子系统通过在每个时刻执行优化问题来更新其计划。保证了随机意义上的闭环稳定性和递归的可行性。一个数值例子被用来说明本研究中提出的算法的有效性和有效性。