Trajectory Control in Nonlinear Networked Systems and Its Applications to Complex Biological Systems

The control of nonlinear networked systems is one of the challenging problems in the network science and engineering fields. Based on physical and realistic considerations, it is a critical goal to control the systems towards certain desired behaviors that are essential for the system's mission regarding a selected task in various fields. To explore a practical framework of controllability, in this study, we theoretically prove the existence of control functions that can drive the nonlinear networked system from one initial trajectory to another desired trajectory under the condition that the considered system is Lipschitz continuous and dissipative. In particular, we propose a strategy for identifying the driver nodes that need to be controlled and design a general form of control functions for realizing such a transition. Moreover, a graph theory--based algorithm is used to identify the driver nodes. Furthermore, we demonstrate the effectiveness of our theoretical results using a chaotic system and two biological systems, including a system of mammalian circadian rhythms and a complex disease-related system of hepatocellular carcinoma (HCC) by steering the systems towards their attractors, including point, periodic, and chaotic attractors. Numerical experiments reveal that controlling a single driver node is sufficient to drive a system to certain desired behaviors. More importantly, we also identify some critical biochemical molecules for controlling circadian rhythms and potential therapeutic strategies for curing or relieving HCC. These results suggest that our approach will provide a powerful tool for revealing molecular mechanisms of biological systems and identifying drug targets from the viewpoint of control theory.