Mathias Hudoba de Badyn, Dillon R. Foight, Daniel Calderone, Mehran Mesbahi, Roy S. Smith
备注：
8 pages, 3 figures. Accepted to the 24th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2020), which has been postponed to August 2021. This version is the extended paper, which includes the proofs that were submitted for review
We consider network structures that optimize the $\mathcal{H}_2$ norm of weighted, time scaled consensus networks, under a minimal representation of such consensus networks described by the edge Laplacian. We show that a greedy algorithm can be used to find the minimum-$\mathcal{H}_2$ norm spanning tree, as well as how to choose edges to optimize the $\mathcal{H}_2$ norm when edges are added back to a spanning tree. In the case of edge consensus with a measurement model considering all edges in the graph, we show that adding edges between slow nodes in the graph provides the smallest increase in the $\mathcal{H}_2$ norm.
This paper examines the $\mathcal{H}_\infty$ performance problem of the edge agreement protocol for networks of agents operating on independent time scales, connected by weighted edges, and corrupted by exogenous disturbances. $\mathcal{H}_\infty$-norm expressions and bounds are computed that are then used to derive new insights on network performance in terms of the effect of time scales and edge weights on disturbance rejection. We use our bounds to formulate a convex optimization problem for time scale and edge weight selection. Numerical examples are given to illustrate the applicability o…
This paper proposes model reduction approaches for consensus network systems based on a given clustering of the underlying graph. Namely, given a consensus network system of time-scaled agents evolving over a weighted undirected graph and a graph clustering, a parameterized reduced consensus network system is constructed with its edge weights and nodal time-scales as the parameters to be optimized. H-infinity- and H-2-based optimization approaches are proposed to select the reduced network parameters such that the corresponding approximation errors, i.e., the H-infinity- and H-2-norms of the e…
In this paper, we consider the privacy preservation problem in both discrete- and continuous-time average consensus algorithms with strongly connected and balanced graphs, against either internal honest-but-curious agents or external eavesdroppers. A novel algorithm is proposed, which adds edge-based perturbation signals to the process of consensus computation. Our algorithm can be divided into two phases: a coordinated scrambling phase, which is for privacy preservation, and a convergence phase. In the scrambling phase, each agent is required to generate some perturbation signals and add them…
We present a multi-agent algorithm for multi-objective optimization problems, which extends the class of consensus-based optimization methods and relies on a scalarization strategy. The optimization is achieved by a set of interacting agents exploring the search space and attempting to solve all scalar sub-problems simultaneously. We show that those dynamics are described by a mean-field model, which is suitable for a theoretical analysis of the algorithm convergence. Numerical results show the validity of the proposed method.
We consider a class of multi-agent cooperative consensus optimization problems with local nonlinear convex constraints where only those agents connected by an edge can directly communicate, hence, the optimal consensus decision lies in the intersection of these private sets. We develop an asynchronous distributed accelerated primal-dual algorithm to solve the considered problem. The proposed scheme is the first asynchronous method with an optimal convergence guarantee for this class of problems, to the best of our knowledge. In particular, we provide an optimal convergence rate of $\mathcal{O(…
We consider the consensus interdiction problem (CIP), in which the goal is to maximize the convergence time of consensus averaging dynamics subject to removing a limited number of network edges. We first show that CIP can be cast as an effective resistance interdiction problem (ERIP), in which the goal is to remove a limited number of network edges to maximize the effective resistance between a source node and a sink node. We show that ERIP is strongly NP-hard, even for bipartite graphs of diameter three with fixed source/sink edges, and establish the same hardness result for the CIP. We then …
In this paper, we study the robustness of the event-triggered consensus algorithms against frequency-domain uncertainties. It is revealed that the sampling errors resulted by event triggering are essentially images of linear finite-gain $\mathcal{L}_2$-stable operators acting on the consensus errors of the sampled states and the event-triggered mechanism is equivalent to a negative feedback loop introduced additionally to the feedback system. In virtue of this, the robust consensus problem of the event-triggered network systems subject to additive dynamic uncertainties and network multiplicati…
We propose a new decentralized average consensus algorithm with compressed communication that scales linearly with the network size n. We prove that the proposed method converges to the average of the initial values held locally by the agents of a network when agents are allowed to communicate with compressed messages. The proposed algorithm works for a broad class of compression operators (possibly biased), where agents interact over arbitrary static, undirected, and connected networks. We further present numerical experiments that confirm our theoretical results and illustrate the scalabilit…
