Chance-Constrained Distributed Optimization with Shared States

doi:10.3390/math14091420

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Chance-Constrained Distributed Optimization with Shared States

2026-04-23

Mugenga, Ineza Remy *

Abebe Geletu

Mirau, Silas

李朴 (Pu Li)

DOI：10.3390/math14091420

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Abstract

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Interconnected systems have attracted significant attention in numerous engineering ap-plications such as energy, water, and oil, as well as gas distribution networks. However,due to their high complexity, it is enormously difficult to ensure a reliable and effectivecooperation of such interconnected systems under limited communication and interactioncapacities. In addition, uncertainty consideration poses further challenges in developing anefficient distributed optimization approach to such interconnected systems. Furthermore,satisfying the constraints of shared states between subsystems under uncertainty leadsto conflict issues and has not been properly studied yet. This study proposes a chance-constrained distributed optimization approach to the optimal operation of interconnectedsystems by considering conflicting reliability levels of satisfying shared state constraints. Acompromised reliability level for such constraints is determined by an averaged weighting.We establish that the optimal cost is Lipschitz-continuous with respect to the compromisedreliability level, providing a theoretical basis for quantifying the marginal cost of reliability,and we show that the compromise is robust to perturbations in the subsystem weights. Wedevelop a numerical solution framework based on the inner-outer approximation method.For the efficient computation of the high-dimensional integrals, we use Hoeffding's in-equality to determine a suitable sample size. The optimal operation of three interconnectedenergy distribution networks is used as a case study to demonstrate the proposed approach.

Keywords:

interconnected systems

uncertainty

shared state

chance constraint

distributed optimization

inner-outer approximation

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