Approximate dissipativity and performance bounds for interconnected systems

We consider the interconnection of dissipative systems through coupling costs in a distributed economic MPC context. Our goal is to provide a structured dissipativity property for the overall system emerging from the subsystems' local dissiaptivity properties and their interconnection. However, following this bottom-up approach, only in very few cases we can expect to establish dissipativity of the overall system based on a minimal set of assumptions. Hence, in this work we introduce the concept of approximate dissipativity, which still allows us to make statements on the system performance, albeit somewhat unsharp. We verify approximate dissipativity for the overall system under cost interconnection of the subsystems, and we demonstrate how this concept can constructively be exploited when adding a new subsystem to the network.