The behavioral approach to open and interconnected systems

The text is written in January 2009 for the group.

I have being reading this week the paper

J.C. Willems, The behavioral approach to open and interconnected systems, Control Systems Magazine, Volume 27, pages 46-99, 2007.

The paper is available at

There is also available a related presentation

Interconnected systems

and its extended version

The paper is about a general approach to model systems. The author starts with the input-output description widely accepted in control theory and demonstrates its deficiency to model physical systems. An alternative suggested in the paper is the behavioral approach where the system is defined though its behavior. The author also considers bond-graph modeling and compares it with the behavioral approach as well. In the final part of the paper the author goes in mathematical details and presents how linear time invariant differential system can be considered in the framework of the behavioral approach. While the previous parts of the paper are relatively easy to read and follow, the final part requires considerable concentration. I have to read it once more.

I like the paper very much, as while working with the input-output representation and bond-graph modeling I had exactly the same problems as discussed in the paper. Now I see how one can overcome them.

The paper has exceptional quality in appearance. It looks like a well designed encyclopedia with carefully chosen typesetting and illustrations. It is very unusual for a scientific paper.

Model reduction is not discussed in the paper but it seems that the behavioral approach may open for model reduction new views. It is worthy to noting that the author has already made a couple of talks on model reduction

P.S. On the site linked in the paper, I have found a nice video

It is amazing what engineers already can do.


2 responses to “The behavioral approach to open and interconnected systems”

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  1. Alex says:

    I’m very impressed with this theory too. And as you also found it very interesting and quite familiar in main points.

    But unfortunately there are still many open questions. first of all, most constructive methods exist only for LTI systems. Of course they are very deep and algebraic, but also very difficult for engineers. For nonlinear control systems something similar unavailable.
    But I think that in the future, this framework has become a popular language as the state space representation 🙂

  2. For example VHDL-AMS has modeling capability where physical systems are expressed through ports, like circuit elements. This means that the process is already underway.