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Multiagent systems consist of agents that locally exchange information through a physical network subject to a graph topology. Current control methods for networked multiagent systems assume the knowledge of graph topologies in order to…
We investigate the structure of connected graphs, not necessarily locally finite, with infinitely many ends. On the one hand we study end-transitive such graphs and on the other hand we study such graphs with the property that the…
We introduce a distributed control architecture for a class of heterogeneous, nonlinear dynamical agents moving in the "string" formation, while guaranteeing trajectory tracking, collision avoidance and the preservation of the formation's…
In this paper we consider complex dynamical networks modeled by means of state space systems running in discrete time. We assume that the dependency structure of the variables within the (nonlinear) network equations is known and use…
A directed acyclic network is considered where all the terminals need to recover the sum of the symbols generated at all the sources. We call such a network a sum-network. It is shown that there exists a solvably (and linear solvably)…
Neural network models in neuroscience allow one to study how the connections between neurons shape the activity of neural circuits in the brain. In this chapter, we study Combinatorial Threshold-Linear Networks (CTLNs) in order to…
Time-discrete dynamical systems on a finite state space have been used with great success to model natural and engineered systems such as biological networks, social networks, and engineered control systems. They have the advantage of being…
This paper addresses the bipartite consensus-control problem in open multi-agent systems containing both cooperative and antagonistic interactions. In these systems, new agents can join and new interactions can be formed over time.…
A drawback of the classic approach for complexity analysis of distributed graph problems is that it mostly informs about the complexity of notorious classes of ``worst case'' graphs. Algorithms that are used to prove a tight (existential)…
This paper addresses the distributed consensus protocol design problem for multi-agent systems with general linear dynamics and directed communication graphs. Existing works usually design consensus protocols using the smallest real part of…
In this paper, we aim to design sparse D-optimal (determinantoptimal) pose-graph SLAM problems through the synthesis of sparse graphs with the maximum weighted number of spanning trees. Characterizing graphs with the maximum number of…
The graphical notion of effective resistance has found wide-ranging applications in many areas of pure mathematics, applied mathematics and control theory. By the nature of its construction, effective resistance can only be computed in…
We study the behavior of solutions of mutually coupled equations in heterogeneous random graphs. Heterogeneity means that some equations receive many inputs whereas most of the equations are given only with a few connections. Starting from…
Heteroclinic structures organize global features of dynamical systems. We analyze whether heteroclinic structures can arise in network dynamics with higher-order interactions which describe the nonlinear interactions between three or more…
This paper addresses the behavior analysis problems for directed signed networks that involve cooperative-antagonistic interactions among agents. Of particular interest is to explore the convergence behaviors of directed signed networks…
In network flow problems, there is a well-known one-to-one relationship between extreme points of the feasibility region and trees in the associated undirected graph. The same is true for the dual differential problem. In this paper, we…
The relation between network structure and dynamics is determinant for the behavior of complex systems in numerous domains. An important long-standing problem concerns the properties of the networks that optimize the dynamics with respect…
Many dynamical systems, including thermal, fluid, and multi-agent systems, can be represented as weighted graphs. In this paper we consider whether the unstable states of such systems can be observed from limited discrete-time measurement,…
This paper addresses analytical aspects of deterministic, continuous-time dynamical systems defined on networks. The goal is to model and analyze certain phenomena which must be framed beyond the context of networked dynamical systems,…
Signed networks provide a principled framework for representing systems in which interactions are not merely present or absent but qualitatively distinct: friendly or antagonistic, supportive or conflicting, excitatory or inhibitory. This…