4,488 research outputs found
Limits on the Network Sensitivity Function for Multi-Agent Systems on a Graph
This report explores the tradeoffs and limits of performance in feedback control of interconnected multi-agent systems, focused on the network sensitivity functions. We consider the interaction topology described by a directed graph and we prove that the sensitivity transfer functions between every pair of agents, arbitrarily connected, can be derived using a version of the Mason's Direct Rule. Explicit forms for special types of graphs are presented. An analysis of the role of cycles points out that these structures influence and limit considerably the performance of the system. The more the cycles are equally distributed among the formation, the better performance the system can achieve, but they are always worse than the single agent case. We also prove the networked version of Bode's integral formula, showing that it still holds for multi-agent systems
Differential Inequalities in Multi-Agent Coordination and Opinion Dynamics Modeling
Distributed algorithms of multi-agent coordination have attracted substantial
attention from the research community; the simplest and most thoroughly studied
of them are consensus protocols in the form of differential or difference
equations over general time-varying weighted graphs. These graphs are usually
characterized algebraically by their associated Laplacian matrices. Network
algorithms with similar algebraic graph theoretic structures, called being of
Laplacian-type in this paper, also arise in other related multi-agent control
problems, such as aggregation and containment control, target surrounding,
distributed optimization and modeling of opinion evolution in social groups. In
spite of their similarities, each of such algorithms has often been studied
using separate mathematical techniques. In this paper, a novel approach is
offered, allowing a unified and elegant way to examine many Laplacian-type
algorithms for multi-agent coordination. This approach is based on the analysis
of some differential or difference inequalities that have to be satisfied by
the some "outputs" of the agents (e.g. the distances to the desired set in
aggregation problems). Although such inequalities may have many unbounded
solutions, under natural graphic connectivity conditions all their bounded
solutions converge (and even reach consensus), entailing the convergence of the
corresponding distributed algorithms. In the theory of differential equations
the absence of bounded non-convergent solutions is referred to as the
equation's dichotomy. In this paper, we establish the dichotomy criteria of
Laplacian-type differential and difference inequalities and show that these
criteria enable one to extend a number of recent results, concerned with
Laplacian-type algorithms for multi-agent coordination and modeling opinion
formation in social groups.Comment: accepted to Automatic
- …