Di Meglio, Anna (2020) Modeling, analysis, and control of complex networks in the presence of temporality and coevolution. [Tesi di dottorato]

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Abstract

In the last decades, complex dynamical networks have attracted the attention of a highly heterogeneous community. Indeed, they are a suitable tool to study the emergence of collective behaviors in ensembles of coupled dynamical systems. Under simplifying and standard assumptions on the individual dynamics and on the static interaction topology, the control of such collective behaviors is now quite assessed. However, a deeper understanding is required when the structures of the interconnections change with time. Spurred by the belief that achieving insights on the interplay between the node dynamics and the time-varying topology could be beneficial from a control perspective, in this thesis, we focus on modeling and control of what we called evolving networks. In the first part of the thesis, we deal with the so-called temporal networks, i.e., networks whose structure changes in time, and show how their optimal control can be challenging in a realistic scenario in which only a probabilistic, instead of deterministic, knowledge of the topology is available. Indeed, controlling a large static network, while keeping the control energy limited, has always been a chimera. Recent results suggested that deterministic knowledge of network temporality can be exploited to substantially reduce the energy required to control the network. In a more realistic scenario, we illustrate that the temporality can be exploited to our advantage only provided that the variability of the network structure matches the intrinsic time scales of the nodes we aim to control. Considering a time-varying law is not the only way to account for the evolution of network structure. In the second part of the thesis, we introduce the more general concept of coevolving networks, in which both the nodes and the structure dynamically evolve in an interdependent fashion. We exploit the potential of this modeling framework in a socio-economic context and then show how the laws governing the coevolution of the network topology and of the node dynamics can be properly tuned to achieve specific control goals. In line with the idea of relaxing standard assumptions, and verifying if we can still gain advantage from the networked nature of complex networks, in the third part of the thesis, we focus on special static networks (networks endowed with symmetries and networks whose structures can be negatively weighted) that can provide further challenges and opportunities for control design.

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