Effects of delays and network graphs on multi-agent network dynamics stability and performance

Dynamics of multi-agent systems (MAS) is influenced by communication/activation delays as well as network characteristics. Here, the aim is to design network graphs and develop control algorithms for a class of MAS considering critical the interplay between network delays and network graphs. Specifically, the network graphs influence not only the stability of MAS guaranteed when delay is less than a certain margin, delay margin, but also the performance, reaching speed of agents to a common steady state (consensus). This work is motivated by the counter-intuitive observation, small coupling strengths between agents can enhance their decay rate to consensus under relatively large inter-agent time delays. From this, it is shown that a certain network graph by edge elimination, zero coupling strengths, leads to faster consensus under larger time delays compared to the case with a complete graph. The design of this ideal network graph is influenced by factors including the inter-agent delay, the number of agents and eliminated edges, and the agents initial states. A statistical approach is developed to select the ideal network by using a cluster analysis in data mining. In this data driven approach, one reveals that the delay margin of the MAS is affected by how many and which edges are eliminated. In view of this, a systematic approach is established to design the network graphs rendering more delay tolerance of the MAS. This analytic approach is used to explain a self-regulating mechanism to counter delay-induced instability whereby this mechanism naturally restores stability by agents regrouping. These results provide parallelism to self-regulation and self-healing in collective behavior of nature-made MAS. Further advancements are reported in terms of how Proportional-Retarded (PR) protocols can be tuned for fast consensus in MAS. In particular, such protocols are proposed for a desired decay rate of MAS with double-integrator dynamics. Finally, the MAS model is extended considering non-delayed self-loops, and a computationally efficient mathematical framework is proposed to study the stability of such MAS which are large scale but cannot be conveniently decomposed into subsystems. This framework has the potential to design new control algorithms for achieving a desired delay margin. Dissertation Supervisor: Rifat Sipahi Title: Associate Professor