Dynamic coupling design for nonlinear output agreement and time-varying flow control

TL;DR

This paper develops a dynamic coupling framework for nonlinear network systems to achieve output agreement under time-varying disturbances, with applications to flow control and microgrid management.

Contribution

It introduces necessary and sufficient conditions for output agreement in nonlinear networks, including incrementally passive systems, and applies these to flow control and microgrid regulation.

Findings

Conditions for output agreement derived for general nonlinear networks.

Internal model controllers can solve optimal routing in transportation networks.

Droop-controllers in microgrids are interpretable as internal model controllers.

Abstract

This paper studies the problem of output agreement in networks of nonlinear dynamical systems under time-varying disturbances, using dynamic diffusive couplings. Necessary conditions are derived for general networks of nonlinear systems, and these conditions are explicitly interpreted as conditions relating the node dynamics and the network topology. For the class of incrementally passive systems, necessary and sufficient conditions for output agreement are derived. The approach proposed in the paper lends itself to solve flow control problems in distribution networks. As a first case study, the internal model approach is used for designing a controller that achieves an optimal routing and inventory balancing in a dynamic transportation network with storage and time-varying supply and demand. It is in particular shown that the time-varying optimal routing problem can be solved by applying an internal model controller to the dual variables of a certain convex network optimization problem. As a second case study, we show that droop-controllers in microgrids have also an interpretation as internal model controllers.