Controllability of Flow‐Conservation Transportation Networks with Fractional‐Order Dynamics

Abstract

In this paper, we adapt the fractional derivative approach to formulate the flow-conservation transportation networks, which consider the propagation dynamics and the users’ behaviors in terms of route choices. We then investigate the controllability of the fractional-order transportation networks by employing the Popov-Belevitch-Hautus rank condition and the QR decomposition algorithm. Furthermore, we provide the exact solutions for the full controllability pricing controller location problem, which includes where to locate the controllers and how many controllers are required at the location positions. Finally, we illustrate two numerical examples to validate the theoretical analysis.

Novel Controller Design for Finite-Time Synchronization of Fractional-Order Nonidentical Complex Dynamical Networks under Uncertain Parameters

“…In biology, it includes the structure and function of biological systems [4,5]. In physics, it involves the reliability and stability of power systems [6], transportation networks [7], etc. Therefore, complex networks have attracted a large number of researchers from many fields.…”