Infinitesimal interconnection variation in nonlinear networked systems

We propose a novel infinitesimal variation for a nonlinear networked system's behavior when its interconnection topology changes discontinuously. We introduce a variational derivative of system output with respect to the connectivity, and derive an analytic formula for the derivative using an adjoint formulation. We provide bounds relating the discontinuous change in system behavior to the proposed continuous infinitesimal variation. The variational derivative can be used as the sensitivity of the system output to the interconnection topology. The separability of the variational derivative allows us to develop a tractable algorithm for an interconnection pursuit problem applicable to optimization in biochemical reaction networks.