Actuation requirements in high dimensional oscillator systems

Understanding actuation needs for reconformation processes in high dimensional multi-stable systems is key to efficient nonlinear control design. Many solitary systems exhibit multiple equilibria and control of these systems when networked with others becomes a challenging task. In this paper we study a networked model in which each single entity contains multiple equilibria and a operational objective is to transition the entire coupled system from one equilibrium to another. We show that after a series of coordinate transformations, the structure of the system and mechanisms for internal resonance leading to this behavior become clear. We also characterize the amount of energy needed for such conformation change (the activation energy) both through numerical simulation and perturbation techniques. We find that unlike traditional Transition State Theories, the activation energy is a function of the spatial structure of such energy (it is not a constant number). We find that a reduced order model which results from averaging accurately predicts this activation energy in a very concise way.