Compositional abstraction of interconnected control systems under dynamic interconnection topology

In this work, we derive conditions under which compositional abstractions of networks of control systems, interconnected via some dynamic interconnection topology, can be constructed using the dynamic interconnection and joint dissipativity-type properties of subsystems and their abstractions. In the proposed framework, the abstraction, itself a system (possibly with a lower dimension), can be used as a substitute of the original system in the controller design process. Moreover, we derive conditions for the construction of abstractions for a class of control systems involving nonlinearities satisfying an incremental quadratic inequality. We provide an example to illustrate the effectiveness of the proposed dissipativity-type compositional reasoning by reducing a 150-dimensional nonlinear system to a 3-dimensional one.