Abstract
In generalized Nash equilibrium (GNE) seeking problems over physical networks such as power grids, the enforcement of network constraints and time-varying environment may bring high computational costs. Developing online algorithms is recognized as a promising method to cope with this challenge, where the task of computing system states is replaced by directly using measured values from the physical network. In this paper, we propose an online distributed algorithm via measurement feedback to track the GNE in a time-varying networked resource sharing market. Regarding that some system states are not measurable and measurement noise always exists, a dynamic state estimator is incorporated based on a Kalman filter, rendering a closed-loop dynamics of measurement-feedback driven online algorithm. We prove that, with a fixed step size, this online algorithm converges to a neighborhood of the GNE in expectation. Numerical simulations validate the theoretical results.
Highlights
1.1 Background Generalized Nash Game (GNG) problems have received increasing attentions in recent years
We focus on the resource sharing market with the physical network constraint, which consists of three levels: market, prosumers, and network levels
4.1 Error of regularization In this subsection, we prove that Ft is a contractive mapping operator, and show that the offline algorithm converges to a neighborhood of the Generalized Nash equilibrium (GNE)
Summary
1.1 Background Generalized Nash Game (GNG) problems have received increasing attentions in recent years. Considering GNGs on physical networks, say, a networked power market, it may take a high computational cost to obtain system states, which follows the Kirchhoff law and depends on different operations. It turns to be much more challenging when parameters of the physical network are time-varying. Instead of being numerically computed, system states are directly measured from the physical system and fed back to drive the online algorithm, rendering a closed-loop algorithm via measurement feedback In this way, the algorithm can remarkably relieve the computational burden and respond much faster to the time-varying environment. It (2021) 1:6 can further allow to construct online tracking algorithms of GNEs in time-varying environments
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