Distributed Formation of Balanced and Bistochastic Weighted Diagraphs in Multi-Agent Systems

Consensus strategies find a variety of applications in distributed coordination and decision making in multi-agent systems. In particular, average consensus plays a key role in a number of applications and is closely associated with two classes of digraphs, weight-balanced (for continuous-time systems) and bistochastic (for discrete-time systems). A weighted digraph is called balanced if, for each node, the sum of the weights of the edges outgoing from that node is equal to the sum of the weights of the edges incoming to that node. In addition, a weight-balanced digraph is bistochastic if all weights are nonnegative and, for each node, the sum of weights of edges incoming to that node and the sum of the weights of edges out-going from that node is unity; this implies that the corresponding weight matrix is column and row stochastic (i.e., doubly stochastic). We propose two distributed algorithms: one solves the weight-balance problem and the other solves the bistochastic matrix formation problem for a distributed system whose components (nodes) can exchange information via interconnection links (edges) that form an arbitrary, possibly directed, strongly connected communication topology (digraph). Both distributed algorithms achieve their goals asymptotically and operate iteratively by having each node adapt the (nonnegative) weights on its outgoing edges based on the weights of its incoming links (i.e., based on purely local information). We also provide examples to illustrate the operation, performance, and potential advantages of the proposed algorithms.Comment: 18 pages, 10 figures, submitted to European Control Conference (ECC) 201

Distributed Weight Balancing in Directed Topologies

This doctoral thesis concerns novel distributed algorithms for weight balancing over directed (communication) topologies. A directed topology (digraph) with nonnegative (or positive) weights assigned on each edge is weight-balanced if, for each node, the sum of the weights of in-coming edges equals the sum of the weights of out-going edges. The novel algorithms introduced in this thesis can facilitate the development of strategies for generating weight balanced digraphs, in a distributed manner, and find numerous applications in coordination and control of multi-component systems. In the first part of this thesis, we introduce a novel distributed algorithm that operates over a static topology and solves the weight balancing problem when the weights are restricted to be nonnegative integers. In the second part of the thesis, we present a novel distributed algorithm which solves the integer weight balancing problem in the presence of arbitrary (time-varying and inhomogeneous) delays that might affect the transmission at a particular link at a particular time. In the third part of this thesis, we present a novel distributed algorithm for obtaining admissible and balanced integer weights for the case when there are lower and upper weight constraints on the communication links. In the fourth part of this thesis we present a novel distributed algorithm which solves the integer weight balancing problem under lower and upper weight constraints over the communication links for the case where arbitrary (time-varying and inhomogeneous) time delays and possible packet drops affect the transmission at a particular link at a particular time.Comment: doctoral thesi