Decentralised fully probabilistic design for stochastic networks with multiplicative noise

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Abstract
In this paper, we present an innovative decentralised control framework, designed to address stochastic dynamic complex systems that are influenced by multiple multiplicative noise factors. Our advanced approach builds upon the foundation of conventional Decentralised Fully Probabilistic Design (DFPD) by refining the Riccati equation to accommodate multiple noise sources effectively. By embracing the inherent stochastic nature of complex systems, our methodology fully characterises their dynamic behaviours using probabilistic state–space models, delivering a comprehensive representation of subsystem components. Importantly, the DFPD approach also incorporates system and input constraints by characterising their corresponding ideal distributions, ensuring optimal functionality and performance while adhering to permissible boundaries. To further enhance system performance, we introduce a probabilistic message passing architecture that enables seamless communication between neighbouring subsystems and promotes harmonised decision-making among local nodes. To demonstrate the efficacy of our proposed framework, we employ a three-inverted pendulum system as a numerical example and compare its performance to that of the conventional DFPD. Through this comparison, we showcase the advantages of our novel decentralised control approach in handling complex systems with multiple noise factors.

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