In this paper, we propose a general decentralised probabilistic control framework for a class of complex stochastic systems with switching modes. Probabilistic state space models are exploited to characterise the subsystems’ dynamical behaviours constituting a complex dynamical system, thus providing a complete description of the subsystems components. To address the variations in the operational modes of the subsystems, the Mixture Density Network (MDN) is applied here to identify the subsystems modes and provides estimates for the system dynamic distributions. Besides, to harmonise the actions between the subsystems, the probabilistic message passing methodology is utilised to provide communication between neighbouring subsystems. Based on the MDN model and the neighbours subsystems information via message passing, the general solution of the fully probabilistic decentralised randomised controller which minimises the Kullback-Leibler divergence (KLD) between the actual and its ideal distributions is then obtained. Moreover, a numerical example is presented to illustrate the effectiveness and the usefulness of our novel proposed framework.

在本文中，我们为一类具有切换模式的复杂随机系统提出了一个通用的分散概率控制框架。利用概率状态空间模型来表征构成复杂动态系统的子系统的动态行为，从而提供子系统组件的完整描述。为了解决子系统运行模式的变化，这里应用混合密度网络 (MDN) 来识别子系统模式并提供系统动态分布的估计。此外，为了协调子系统之间的动作，使用概率消息传递方法来提供相邻子系统之间的通信。基于MDN模型和邻居子系统信息通过消息传递，然后获得了最小化实际分布和理想分布之间的 Kullback-Leibler 散度 (KLD) 的完全概率分散随机控制器的一般解决方案。此外，还提供了一个数值示例来说明我们提出的新框架的有效性和实用性。