Compositional Abstraction for Networks of Control Systems: A Dissipativity Approach

In this paper, we propose a compositional scheme for the construction of abstractions for networks of control systems by using the interconnection matrix and joint dissipativity-type properties of subsystems and their abstractions. In the proposed framework, the abstraction, itself a control system (possibly with a lower dimension), can be used as a substitution of the original system in the controller design process. Moreover, we provide a procedure for constructing abstractions of a class of nonlinear control systems by using the bounds on the slope of system nonlinearities. We illustrate the proposed results on a network of linear control systems by constructing its abstraction in a compositional way without requiring any condition on the number or gains of the subsystems. We use the abstraction as a substitute to synthesize a controller enforcing a certain linear temporal logic specification. This example particularly elucidates the effectiveness of dissipativity-type compositional reasoning for large-scale systems.