The article presents a decentralized feedback optimization approach for networked systems, where communication between agents is limited or undesirable. The key idea is to approximate the overall input-output sensitivity matrix by its diagonal elements, allowing each agent to update its control input based only on local information.
The authors first show that the stationary points of the proposed decentralized controller coincide with the Nash equilibria of an underlying convex game. They then conduct a comprehensive analysis of the closed-loop stability and sub-optimality, deriving sufficient conditions for stability and bounding the distance between the globally optimal solution and the stationary point to which the decentralized controller converges.
The analysis is performed for two cases: when the plant is represented by its steady-state input-output map, and when the plant is modeled as a linear time-invariant (LTI) system. In the former case, the sub-optimality bound depends on the degree of diagonal dominance of the sensitivity matrix and the properties of the objective function. In the latter case, the authors show that the coupled errors involving the distance to the plant's steady state and the distance to the controller's equilibrium point decay to zero with a linear rate, provided that the steady-state map of the LTI plant satisfies the diagonal dominance condition.
The theoretical results are illustrated through numerical simulations of a voltage control problem in a direct current (DC) power grid, demonstrating the effectiveness of the decentralized controller and the tightness of the derived sub-optimality bound.
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by Wenb... om arxiv.org 04-01-2024
https://arxiv.org/pdf/2311.09408.pdfDiepere vragen