Decentralised Fully Probabilistic Design for Stochastic Networks with Multiplicative Noise

In this paper, a novel decentralised control framework based on decentralised fully probabilistic design (DFPD) is proposed for a class of stochastic dynamic complex systems with multiple multiplicative noises. Compared with the existing conventional DFPD, the new procedure is improved by modifying the Riccati equation in order to deal with multiple multiplicative noises. Considering the stochastic nature of complex systems, the systems’ dynamical behaviours are fully charaterised by probabilistic state-space models. In this way, a complete description of the components of the subsystems is provided. In addition, probabilistic message passing architecture is introduced to provide communication between neighbouring subsystems and to harmonise the actions between the local nodes. To illuminate the effectiveness of the proposed framework, a three inverted pendulum system numerical example is presented and the results are compared with the conventional DFPD.