Many problems in multiagent networks can be solved through distributed learning (state estimation) of linear dynamical systems. In this paper, we develop a partial-diffusion Kalman filtering (PDKF) algorithm, as a fully distributed solution for state estimation in the multiagent networks with limited communication resources. In the PDKF algorithm, every agent (node) is allowed to share only a subset of its intermediate estimate vectors with its neighbors at each iteration, reducing the amount of internode communications. We analyze the stability of the PDKF algorithm and show that the algorithm is stable and convergent in both mean and mean-square senses. We also derive a closedform expression for the steady-state mean-square deviation criterion. Furthermore, we show theoretically and by numerical examples that the PDKF algorithm provides a trade-off between the estimation performance and the communication cost that is extremely profitable.

We propose an event-triggered game-theoretic strategy for managing the power grids demand side, capable of responding to changes in consumer preferences or the price parameters coming from the wholesale market. The relationship between the retailer and the residential consumers is modeled as one-leader, N-follower Stackelberg game. We provide a detailed characterization of the household appliances to reflect the reality and improve the efficiency of the demand response (DR). Moreover, to consider all the appliances' essentials, the consumer's objective function is formulated as a mixed integer non-linear program (MINLP), which, unlike conventional procedures, is solved via an integrated method. The proposed method consists of a day-ahead stage, in which the DR problem is solved for the next scheduling horizon, and a real-time stage which runs repeatedly to tackle the change in the parameters and adapt to the new condition. For any change in the grid, the consumers use the estimated optimal parameters (given by the original objective function) and develop another Stackelberg game based solution to maximize the satisfaction level. Given the appliances of multi-class nature, the proposed method is shown to be very tractable for ancillary services and reducing the mismatch between the renewable power generation and the load demand.

Partial diffusion-based recursive least squares (PDRLS) is an effective method for reducing computational load and power consumption in adaptive network implementation. In this method, each node shares a part of its intermediate estimate vector with its neighbors at each iteration. PDRLS algorithm reduces the internode communications relative to the full-diffusion RLS algorithm. This selection of estimate entries becomes more appealing when the information fuse over noisy links. In this paper, we study the steady-state performance of PDRLS algorithm in presence of noisy links and investigate its convergence in both mean and mean-square senses. We also derive a theoretical expression for its steady-state meansquare deviation (MSD). The simulation results illustrate that the stability conditions for PDRLS under noisy links are not sufficient to guarantee its convergence. Strictly speaking, considering nonideal links condition adds a new complexity to the estimation problem for which the PDRLS algorithm becomes unstable and do not converge for any value of the forgetting factor.

In partial diffusion-based least mean square (PDLMS) scheme, each node shares a part of its intermediate estimate vector with its neighbors at each iteration. In this paper, besides being involved in more general PDLMS scheme, we figure out how the noisy links affect deterioration of network performance during the exchange of weight estimates. We investigate the steady state mean square deviation (MSD) and derive a theoretical expression for it. We demonstrate that the PDLMS algorithm is stable and convergent in both mean and mean-square sense under non-ideal links. However, unlike the established statements on PDLMS scheme under ideal links, the trade-off between MSD performance and the number of selected entries of the intermediate estimate vectors as a sign of communication cost is mitigated. Strictly speaking, considering non-ideal links condition adds a new complexity to MSD relation that has a noticeable effect on its performance. This term violates the tradeoff between communication cost and estimation performance of the networks in comparison to noise-free condition on the links. Our simulation results substantiate the effect of noisy links on PDLMS algorithm and verify the theoretical findings. They match well with theory.

The performance of partial diffusion Kalman filtering (PDKF) algorithm for the networks with noisy links is studied here. A closed-form expression for the steady-state mean square deviation is then derived and theoretically shown that when the links are noisy, the communication-performance tradeoff, reported for the PDKF algorithm, does not hold. Additionally, optimal selection of combination weights is investigated and a combination rule along with an adaptive implementation is motivated. The results confirm the theoretical outcome.