  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. Herein 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 predictive
control cost function and by 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, networks with non-smooth
dynamics, as well as 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.
