Compositional abstraction for networks of control systems: A dissipativity approach

TL;DR

This paper introduces a compositional method for creating abstractions of control system networks using dissipativity properties, enabling scalable controller synthesis for complex systems.

Contribution

It presents a novel dissipativity-based framework for constructing system abstractions compositionally, applicable to nonlinear and linear control systems without size restrictions.

Findings

Successfully constructed abstractions for linear control networks

Enabled controller synthesis for complex systems with temporal logic specifications

Demonstrated effectiveness on large-scale control system networks

Abstract

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.