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arXiv · 2609.27237

Stability Analysis of Decentralized Adaptive Control of Laterally Coupled Multi-Loop Thermosyphon System with Unknown System Parameters

Novel Kumar Dey·Yan Wu
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Abstract

A high dimensional bi-directionally coupled $N$-loop thermosyphon system in a tandem is modeled by $3N$ Lorenz type of differential equations. The fluid flow in each loop is driven by the heat source (Rayleigh numbers) as well as the moment and heat exchanges between the adjacent loops. The flow becomes chaotic when the Rayleigh numbers are large. A decentralized controller design via proportional local state feedback is employed to stabilize the chaotic flows in each loop. As a result of the stability analysis, we show that there exist lower bounds on the controller gains that guarantee global stability of the system. Under the scenario of unknown parameters, we augment the original system with additional dynamic equations of the feedback gains to adaptively determine the feasible gains that stabilize the system. The analysis also sheds insight on the role of thermal coupling in the stability of the control system, which allows us to extend the results to negative $z$-state coupling coefficient as well as a class of nonlinear $z$-state coupling functions. Numerical simulations further demonstrate the effectiveness of the proposed controller design

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Novel Kumar Dey, Yan Wu. 2026-09-23. Stability Analysis of Decentralized Adaptive Control of Laterally Coupled Multi-Loop Thermosyphon System with Unknown System Parameters. https://arxiv.org/abs/2609.27237

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