Decentralized parameter estimation by consensus based stochastic approximation

Consensus-based decentralized real-time identification of large-scale systems

“…Therefore, one concludes, according to Stanković et al (2011b), that there exists for t large enough such a T > 0 that…”

“…, κ, and 1 ≤ κ ≤ |N (k, l) * | (| ·| denotes cardinality of a given set). Assume, for the sake of simplicity, that κ = 1 and |C 0 | = 0, implying that C * is irreducible and primitive (generalizations can be done following directly, Stanković et al, 2011b). By (A.4) and (A.5), for t large enough there exists such a τ 1 > 0 that Π(t, t − τ 1 ) = C (t) · · · C (t − τ 1 ) ≻ 0 a.s. (A ≻ 0 signifies that all the elements of a matrix A are positive).…”

“…Consequently, lim t→∞ ∥Φ(t, τ )∥ ∞ = 0 a.s. for any fixed τ , (Chen, 2002). Generalizations to κ > 1 can be done applying directly the methodology from Stanković et al (2011b).…”

Adaptive sensor networks for consensus based distributed estimation

“…However, having in mind that in Algorithm A the estimates are already obtained by exploiting local measurements, it could be expected that the additional interchange of the sensed data themselves might not have a significant effect; our claim is that a careful tuning of the gains c ij (t) can result into a much more efficient and effective tool. b) Introduction of the consensus term at the prediction level in Algorithm A, and not already at the filtering level as in Algorithm B, is beneficial from the point of view of increasing noise immunity, having in mind an additional spacial averaging of current residuals from the neighborhood implicit to Algorithm A [15]. Assuming that we have (2) and (3) (L could be the steady state Kalman gain or any other constant gain), the whole network implementing Algorithm A can be compactly represented by…”

A decentralized algorithm for balancing a strongly connected weighted digraph

“…It can be effectively used to model for instance wireless sensor networks, teams of robots or social dynamics, [1]- [3]. Several interesting problems arise in the context of multi-agent systems, ranging from distributed estimation [4] to collaborative data fusion [5].…”