Topic : Networked Dynamic Systems: Consensus and Formation Control
By: Dwaipayan Mukherjee
Event/Venue: IEEE Signal Processing Society Kolkata (Webinar)
Details: This talk delves into two aspects of networked dynamic systems– consensus in multiagent systems, and formation control. Consensus is a widely researched topic in the domain of multi-agent systems. The central idea in consensus is to achieve agreement in the states of agents while these agents communicate over a directed or undirected topology. In graph theoretic terms, the agents are the nodes of the network while the edges connecting the nodes depict the flow of information among the agents. A lot of work has been done on consensus of networks where the communication links are bidirectional (represented by undirected graphs). However, when the information flows over a directed graph, the analysis is rendered difficult owing to a lack of symmetry in the interconnections. The matrices associated with the directed graph, such as the Adjacency and the Laplacian are no longer symmetric in such cases either. The first part of this talk will be considering directed networks and looking at an edge version of the consensus protocol. It will be shown that this particular interpretation helps in analyzing the robustness of the network. Agents will be modelled as single integrators. The perturbation in our system appears in the form of uncertainty in edge weights. The system will be cast in the M-Δ form and a Nyquist criteria based bound on the stability of the same will be presented. A general result will be derived that is applicable to all digraphs having a globally reachable node. Subsequently, two special digraphs, the directed cycle and the directed acyclic graph will be considered, where the tolerable bound on the perturbation will be given a graph theoretic interpretation. The highlight of this study is that we shall use tools from control theory to obtain the stability bounds, instead of carrying out a spectral analysis of the Laplacian or other related matrices. Thereafter, a double integrator model for agents will be considered and a general consensus protocol presented, along with control theoretic tools for obtaining the bounds on perturbation. Finally, as a dual to the above problem, we shall look at the design problem, where the objective is to choose suitable edge weights that will ensure onsensus of double integrators over a digraph. The second part of the talk focuses on a bearing-only formation control law over directed cycles that exploits the properties of projection matrices. We shall discuss otions such as bearing-rigidity and contrast it with the notions of distance-rigidity. Further, we shall show how the interplay between stability of formation and its rigidity leads to interesting non-unique shapes.