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A universal framework for nabla nonlinear distributed optimisation algorithms
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DOI：10.1080/00207721.2025.2507841.png)
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Abstract
En 中文
This paper introduces a novel state-space approach to handle nonlinear systems. The distributed optimisation problem is decomposed into consensus and optimality subproblems according to their functionalities. Specifically, it designs an average input tracker and an average state observer to address these two subproblems, thereby constructing a discrete-time fractional distributed optimisation algorithm framework for nonlinear systems. A mild input law is provided, and its convergence is proven by constructing a Lyapunov function. The input law allows for a broader range of objective functions, demonstrating the flexibility of the framework. Since the fractional order belongs to the interval $ (0, 1] $ (0,1], the framework can degenerate to an integer form when necessary. Using the constructed framework, two distributed optimisation algorithms are developed: one based on mean estimation and another based on the push-sum protocol. The effectiveness of these algorithms is validated through four numerical simulations.
Keywords:
Distributed optimisation
nabla fractional difference and sum
multi-agent system
fractional difference inequalities
control theory
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