Performance Improvement in Noisy Linear Consensus Networks with Time-Delay
For researchers working on consensus networks, this work provides computationally efficient methods to improve network performance under time-delay, though the improvements are incremental over existing approaches.
This paper analyzes the H2 norm performance of noisy linear consensus networks with time-delay, showing it is a convex function of Laplacian eigenvalues and coupling weights. It proposes a tight convex approximation and three graph modification methods (growing, re-weighting, sparsifying) that achieve near-optimal performance with lower complexity than existing methods.
We analyze performance of a class of time-delay first-order consensus networks from a graph topological perspective and present methods to improve it. The performance is measured by network's square of H-2 norm and it is shown that it is a convex function of Laplacian eigenvalues and the coupling weights of the underlying graph of the network. First, we propose a tight convex, but simple, approximation of the performance measure in order to achieve lower complexity in our design problems by eliminating the need for eigen-decomposition. The effect of time-delay reincarnates itself in the form of non-monotonicity, which results in nonintuitive behaviors of the performance as a function of graph topology. Next, we present three methods to improve the performance by growing, re-weighting, or sparsifying the underlying graph of the network. It is shown that our suggested algorithms provide near-optimal solutions with lower complexity with respect to existing methods in literature.