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arXiv · 1608.01590

Compositional abstraction for networks of control systems: A dissipativity approach

Majid Zamani·Murat Arcak
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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.

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Majid Zamani, Murat Arcak. 2016-08-04. Compositional abstraction for networks of control systems: A dissipativity approach. https://arxiv.org/abs/1608.01590

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