In this talk, I will be discussing two aspects of consensus in multi-agent systems. 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 Laplacian are no longer symmetric in such cases either. In the first part of my talk, I will be considering such 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-? 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 limit 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 consensus of double integrators over a digraph. The second part of the talk will focus on the cycle digraph, which is at the heart of cyclic pursuit, and we shall obtain necessary and sufficient conditions for convergence of discrete time heterogeneous cyclic pursuit in both synchronous and asynchronous modes. We shall see how the set of points where the agents rendezvous may expand due to the heterogeneity in the gain of cyclic pursuit and explore the possibility of using negative gains. Finally, the talk will conclude by looking at another variant of discrete time cyclic pursuit- heterogeneous deviated cyclic pursuit. In this case, we shall discuss sufficient conditions of stability and show how the reachable set may also expand when the deviations of the agents are heterogeneous.
Dwaipayan Mukherjee is currently a Post-doctoral fellow at the Faculty of Aerospace Engineering, Technion- Israel Institute of Technology. His research is funded by a fellowship of the Israel Council for Higher Education. He received his B. E. (2007) from Jadavpur University, Kolkata, in Electrical Engineering, and M.Tech. (2009) in Control Systems Engineering (Department of Electrical Engineering) from the Indian Institute of Technology, Kharagpur. In 2014, he defended his doctoral thesis titled ‘Cyclic Pursuit- Variants and Applications’ at the Indian Institute of Science, Bangalore, Dept. of Aerospace Engineering. His research interests include networked dynamic systems, co-operative control, cyber-physical systems, and control theory.