A sparse H ∞ controller synthesis perspective on the reconfiguration of brain networks*

Complex networked systems are the norm in the modern world with the human brain being one of the most complex networks. The control of such systems is a difficult task due to the interactions among the individual elements of the system. In this paper the design of sparse feedback controllers for complex networks is considered. Specifically, an $H$ ∞ controller synthesis problem with D stability constraints is formulated and solved for networks with different topological features. This formulation allows us to examine tradeoffs between control performance, controller sparsity and speed of closed-loop response. We applied this formulation to synthetic networks and the Macaque visual cortical network, assuming Laplacian node dynamics. The results show that as the requested response becomes faster, the control performance improves, and the feedback gain matrix becomes sparser but with larger non-zero entries. This is analogous to the observation that functional brain networks during high cognitive demand adopt a more efficient but also costlier configuration. This analogy suggests a possible connection between cognitive control and closed-loop control under sparse feedback.