Compositional abstraction for networks of control systems: A dissipativity approach
For control engineers, this work provides a scalable compositional abstraction framework that simplifies controller design for large-scale networked systems, though it is incremental as it extends existing dissipativity-based methods.
This paper proposes a compositional method for constructing abstractions of networks of control systems using dissipativity properties, enabling controller synthesis for large-scale systems without constraints on subsystem number or gains. The approach is demonstrated on a network of linear systems to enforce a linear temporal logic specification.
In this paper we propose a compositional scheme for the construction of abstractions for networks of control systems 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.