Control Node Selection Algorithm for Nonlinear Dynamic Networks

The coupled problems of selecting control nodes and designing control actions for nonlinear network dynamics are fundamental scientific problems with applications in many diverse fields. These problems are thoroughly studied for linear dynamics. However, in spite of a number of open research questions, methods for nonlinear network dynamics are less developed. As observed by various studies, the prevailing graph-based controllability approaches for selecting control nodes might result in significantly suboptimal control performance for nonlinear dynamics. We present a new, intuitive, and simple method for simultaneous control node selection and control sequence design for complex networks with nonlinear dynamics. The method is developed by incorporating the control node selection problem into an open-loop optimal control problem and by approximately solving the resulting mixed-integer optimization problem using a mesh adaptive direct search method. The developed framework is numerically robust and can deal with stiff networks and with control and actuator constraints. Good numerical performance of the method is demonstrated by testing it on prototypical Duffing oscillator and associative memory networks. The developed codes that can easily be adapted to models of other complex systems are available online.