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A Boolean network is a finite dynamical system, whose variables take values from a binary set. The value update rule for each variable is a local function, i.e., it depends only on a selected subset of variables. Boolean networks have been widely used in modeling gene regulatory networks. We focus in this paper on a special class of Boolean networks, termed as conjunctive Boolean networks. A Boolean...
Consider a formation control problem in which agents in Euclidean space are tasked with stabilizing their positions at prescribed target distances from each other, and for which these distances are described by a rigid graph. There is a mismatch in target distances if there is a pair of neighboring agents i and j such that agent i aims to stabilize from agent j at a distance dij, but agent j from...
Formation control deals with the design of decentralized control laws that stabilize agents at prescribed distances from each other. We call any configuration a target configuration if it satisfies the inter-agent distance conditions. It is well known that when the distance conditions are defined via a rigid graph, there is a finite number of target configurations modulo rotations and translations...
In this paper, we consider a class of gradient flows that model rules by which a multi-agent system might approach to an equilibrium. The rules are quite simple to state, in fact they depend on a single attraction/repulsion function, but in the generality assumed here the analysis of the resulting flow presents several challenges. In part, these challenges arise from the natural invariance with respect...
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