Bio-Inspired Collective Decision-Making in Game Theoretic Models and Multi-Agent Systems

Collective decision-making can be investigated in a variety of different contexts, from opinion dynamics to swarm robotics. In the context of honeybee swarms, the evolutionary dynamics corresponding to the honeybee consensus problem can be studied via game theoretic tools. Evolutionary game theory provides the necessary tools to capture the relevant aspects for the decision-making process, whereas mean-field game theory serves well as a framework to analyse the optimal response of a large number of interacting players, even in the case of adversarial disturbance, where the aim is to ensure the robustness of the system to worst-case deterministic perturbations. The interactions among players, often originating in the corresponding real system from a social or physical structure, e.g. humans or animals for social and nodes of a power network for physical, can be captured by means of a network. In this thesis, the model originating in the context of bio-inspired collective decision-making is formulated in a game theoretic framework. The study of the corresponding consensus problem is carried out by analysing the stability property of the system and the corresponding optimal strategies in the presence of an adversarial disturbance. A threshold is identified to prevent a situation of deadlock, which happens when the population is stuck in a scenario where no option has predominantly taken over. The analysis is then extended to compartmental models, which share similarities with the original system and gives insight on asymmetric evolutions of the system. Through this link, other relevant applications are considered, such as duopolistic competition in marketing and virus propagation in smart grids. Finally, structured environments are explored as an extension to the original model, and the structure is captured by means of undirected graphs or of the Barabási-Albert scale-free (SF) complex network model

Topology Reconstruction of Dynamical Networks via Constrained Lyapunov Equations

The network structure (or topology) of a dynamical network is often unavailable or uncertain. Hence, we consider the problem of network reconstruction. Network reconstruction aims at inferring the topology of a dynamical network using measurements obtained from the network. In this technical note we define the notion of solvability of the network reconstruction problem. Subsequently, we provide necessary and sufficient conditions under which the network reconstruction problem is solvable. Finally, using constrained Lyapunov equations, we establish novel network reconstruction algorithms, applicable to general dynamical networks. We also provide specialized algorithms for specific network dynamics, such as the well-known consensus and adjacency dynamics.Comment: 8 page