Abstract
This paper proposes a novel probabilistic framework for the design of probabilistic message passing mechanism for complex and large dynamical systems that are operating and governing under a decentralized way. The proposed framework considers the evaluation of probabilistic messages that can be passed between mutually interacting quasi-independent subsystems that will not be restricted by the assumption of homogeneity or conformability of the subsystems components. The proposed message passing scheme is based on the evaluation of the marginal density functions of the states that need to be passed from one subsystem to another. An additional contribution is the development of stochastic controllability analysis of the controlled subsystems that constitute a complex system. To facilitate the understanding and the analytical analysis of the proposed message passing mechanism and the controllability analysis, theoretical developments are demonstrated on linear stochastic Gaussian systems.
Highlights
Complex systems are ubiquitous in nature and man-made systems
PROBLEM FORMULATION As discussed in the introduction section, this paper considers a fully probabilistic decentralized control framework where each subsystem in the complex system is controlled based on its local information and uncertain information provided by the external signals from the neighbouring subsystems states estimated via probabilistic message passing
Information diffusion will be achieved through probabilistic message passing in order to update the knowledge of the subsystems about their external inputs which will be achieved by using probabilistic inference methods
Summary
Complex systems are ubiquitous in nature and man-made systems. They appear in a wide range of domains including neuronal [1], intracellular, ecological [2], and engineering and infrastructure [3]. Recent developments on distributed and decentralized control still suffer from the lack of a reliable message passing framework that can operate efficiently under the presence of heterogenous or uncertain complex systems components [12]–[15]. R. Herzallah: Probabilistic Message Passing for Decentralized Control of Stochastic Complex Systems from the external environment and neighboring subsystems. A fully probabilistic framework for the design of decentralized controllers and probabilistic message passing is developed where local controllers, systems models, and communications between the subsystems of a complex system are characterized by probability density functions.
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