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Control Node Selection Algorithm for Nonlinear Dynamic Networks

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Document pages: 6 pages

Abstract: The coupled problems of selecting control nodes and designing control actionsfor nonlinear network dynamics are fundamental scientific problems withapplications in many diverse fields. These problems are thoroughly studied forlinear dynamics; however, in spite of a number of open research questions,methods for nonlinear network dynamics are less developed. As observed byvarious studies, the prevailing graph-based controllability approaches forselecting control nodes might result in significantly suboptimal controlperformance for nonlinear dynamics. Herein we present a new, intuitive, andsimple method for simultaneous control node selection and control sequencedesign for complex networks with nonlinear dynamics. The method is developed byincorporating the control node selection problem into an open-loop predictivecontrol cost function and by solving the resulting mixed-integer optimizationproblem using a mesh adaptive direct search method. The developed framework isnumerically robust and can deal with stiff networks, networks with non-smoothdynamics, as well as with control and actuator constraints. Good numericalperformance of the method is demonstrated by testing it on prototypical Duffingoscillator and associative memory networks. The developed codes that can easilybe adapted to models of other complex systems are available online.

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