Steering the dynamics by controlling the temporal interaction network

Abstract

Many real-world coupled dynamical systems have the interaction structure and strength that evolve or adapt over time. Here, we investigate how one can control the state of a system by tuning its temporal interaction network. We present a framework based on nonlinear optimal control, where one has control over the coupling matrix of a dynamical system. We show how to obtain the gradient of the Lagrangian function of the system using the adjoint method. We then focus on a linear time-variant system for which we illustrate the framework. Finally, we explore how the states at the nodes can be steered to target trajectories, by controlling the coupling matrix, imposing various constraint on its structure. The workflow presented here can be leveraged to steer the dynamics of systems with artificial or engineered interaction that is tunable.