Probabilistic message passing control for complex stochastic switching systems

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.