Online distributed tracking of generalized Nash equilibrium on physical networks

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.

Continuous-time fully distributed generalized Nash equilibrium seeking for multi-integrator agents

“…1], [15, Eq. 9] and is verified, for example, for games affected by a bounded process noise in the linear constraints [17,Lemma 5].…”

“…We then define the reference trajectory as (ω t ) t∈N . At each time-step, we propose to appropriately re-initialize the dynamic tracking of the estimated variables and, in the spirit of the iteration in (17), to apply a finite number of iterations of Algorithm 2. The resulting method is illustrated in Algorithm 3.…”

“…Despite its practical relevance, there are very few works that study the online GNE problem. The paper [17] proposes a regularized algorithm, which only achieves inexact convergence, and which is not fully-distributed. Instead, the authors of [18] develop an algorithm for the partial-decision information scenario, but that achieves sublinear regret only when the solution is asymptotically constant and for diminishing step sizes.…”