Pósfai Márton
(Közép-európai Egyetem)
Controllability and complex networks
Absztrakt: Due to its important applications, there is considerable interest in understanding how complex systems can be influenced by external interventions. This is a challenging problem for many reasons, one key difficulty is the fact the components of the system form a complex network. In the past decade, structural controllability of linear dynamics has emerged as an important framework for network control. It exploits the connection between graph combinatorics and linear algebra, making it possible to answer control related questions relying on network structure only. The canonical setup of structural controllability assumes a directed network with linear dynamics driven by the weighted adjacency matrix. It was shown that the minimum number of independent external signals needed to fully control such a system can be determined by finding a maximum matching in the underlying network. This connection has far reaching consequences: I will show how control is affected by emergent properties of complex networks, such as scale-free degree distributions and structural phase transitions. I will show how structural controllability can be extended to incorporate additional complexities beyond simple networks, including temporal networks, multi-layer/multi-timescale networks, and control energy constraints. Finally, I will discuss the limitations of the framework, alternative approaches and open questions in the field.
