Researcher: Asad Ullah Awan
Supervisor: Prof. Majid Zamani
Host: Technische Universität München (TUM), Germany
Secondments:
1) Eindhoven University of Technology (TUE), The Netherlands
2) Scania, Sweden

For large interconnected control systems, controller design to achieve some complex specifications in a reliable and cost effective way is a challenging task. One direction which has been explored to overcome this challenge is to use a simpler (e.g. lower dimension) (in)finite approximation (abstraction) of the given system as a replacement in the controller design process. This allows for a design of a controller for the abstraction, which can be refined to the one for the original complex system.

Rather than treating the interconnected system in a monolithic manner, an approach which severely restricts the capability of existing techniques to deal with many number of subsystems, compositional schemes provide network-level certifications from main structural properties of the subsystems and their interconnections. Recently, a compositional framework for the construction of infinite abstractions of networks of control systems has been proposed using dissipativity theory. In this result, a notion of storage function is proposed which describes joint dissipativity properties of control systems and their abstractions. This notion is used to derive compositional conditions under which a network of abstractions approximate a network of the concrete subsystems.

In this project, we derive conditions under which compositional abstractions of networks of stochastic hybrid systems can be constructed using the interconnection topology and joint dissipativity-type properties of subsystems and their abstractions. In the proposed framework, the abstraction, itself a stochastic hybrid system (possibly with a lower dimension), can be used as a substitute of the original system in the controller design process. Moreover, we derive conditions for the construction of abstractions for a specific class of stochastic hybrid systems.

Publications:

  1. A. U. Awan and M. Zamani. Compositional abstraction of interconnected control systems under dynamic interconnection topology. The 56th IEEE Conference on Decision and Control, December 2017, to appear.
  2. A. U. Awan and M. Zamani. Compositional abstractions of networks of stochastic hybrid systems: A dissipativity approach. The 20th World Congress of the International Federation of Automatic Control, pp. 16374-16379, July 2017.