Boundary controllability of a system modelling a partially immersed obstacle

In this paper, we address the problem of boundary controllability for the one-dimensional nonlinear shallow water system, describing the free surface flow of water as well as the flow under a fixed gate structure. The system of differential equations considered can be interpreted as a simplified model of a particular type of wave energy device converter called oscillating water column. The physical requirements naturally lead to the problem of exact controllability in a prescribed region. In particular, we use the concept of nodal profile controllability in which at a given point (the node) time-dependent profiles for the states are required to be reachable by boundary controls. By rewriting the system into a hyperbolic system with nonlocal boundary conditions, we at first establish the existence and uniqueness of the semi-global classical solution for the system, then get the local controllability and that of nodal profile using a constructive method. In addition, based on this constructive process, we provide an algorithmic concept to calculate the required boundary control function for generating a solution for solving this control problem.

Network controllability mediates the relationship between rigid structure and flexible dynamics

ABSTRACTPrecisely how the anatomical structure of the brain supports a wide range of complex functions remains a question of marked importance in both basic and clinical neuroscience. Progress has been hampered by the lack of theoretical frameworks explaining how a structural network of relatively rigid inter-areal connections can produce a diverse repertoire of functional neural dynamics. Here, we address this gap by positing that the brain’s structural network architecture determines the set of accessible functional connectivity patterns according to predictions of network control theory. In a large developmental cohort of 823 youths aged 8 to 23 years, we found that the flexibility of a brain region’s functional connectivity was positively correlated with the proportion of its structural links extending to different cognitive systems. Notably, this relationship was mediated by nodes’ boundary controllability, suggesting that a region’s strategic location on the boundaries of modules may underpin the capacity to integrate information across different cognitive processes. Broadly, our study provides a mechanistic framework that illustrates how temporal flexibility observed in functional networks may be mediated by the controllability of the underlying structural connectivity.AUTHOR SUMMARYPrecisely how the relatively rigid white matter wiring of the human brain gives rise to a diverse repertoire of functional neural dynamics is not well understood. In this work, we combined tools from network science and control theory to address this question. Capitalizing on a large developmental cohort, we demonstrated that the ability of a brain region to flexibly change its functional module allegiance over time (i.e., its modular flexibility), was positively correlated with its proportion of anatomical edges projecting to multiple cognitive networks (i.e., its structural participation coefficient). Moreover, this relationship was strongly mediated by the region’s boundary controllability, a metric capturing its capacity to integrate information across multiple cognitive domains.