A hybrid-systems approach to uncover complex networks behaviour
A synchronised school of fish swimming in the sea; a network of computer systems; the evolution of a flock of birds; the controlled motion of swarm satellites; the cooperation of several robotic systems to accomplish a common goal; social networks; water or electrical power distribution systems: these are examples of complex networks and collective behaviour. That is, a group of systems (normally, a big number of them) interconnected in a non-trivial and non-regular way. The key aspect of these networks is the complex nature of their interconnection topology, which defines the behaviour of the overall structure and entails the onset of complex dynamical phenomena not present in the individual systems.
Two key ideas are pivotal to propose a model for these systems: 1) individual elements following elementary behavioural rules can produce complex behavioural patterns, and 2) in many cases, individual elements achieve a global goal with minimal communication with other elements in the network, and without having a complete picture of the overall structure. This type of behaviour implies different discrete transitions and the interaction of different types of dynamics (discrete and continuous). Consequently, the hybrid-systems framework - characterised by the coupling of continuous-type and discrete-event dynamics - seems to be very adequate to improve the existing models of complex networks and to give answers to many questions concerning the stability of the network and its structure.The goal of this PhD project is to formulate the evolution and dynamical behaviour of complex networks within the hybrid-systems framework. The ultimate goal is to design robust and resilient systems, that is, systems capable of preserving stability and recovering from faults. The control or decision-making techniques to explore fall into distributed, cooperative and networked control techniques. This research covers multiple emerging applications from robotic systems to transportation and distribution networks, and from high-confidence healthcare to national security.