Citation
Marcella Gomez, Seungil You, Richard Murray. "Time-Delayed Feedback Channel Design: Discrete Time H-Infinity Approach". American Control Conference 2014, June, 2013.

Abstract
This paper proposes a method of improving performance of scalar discrete-time systems with substantial delay by adding additional delayed feedback channels (i.e. imposing a distributed delay feedback). The optimal weights for the added feedback channels are found using optimization techniques. In particular, we reduce the H1 norm of the closed loop transfer function with multiple delayed feedback using techniques from static output feedback design. We impose constraints on the feedback gain in order to highlight the effectiveness of the distribution. In this manner, improvement on performance is a result of the distribution and not a change in the overall effective gain. The concept of applying a multiple delayed feedback channel is inspired by biological systems, where substantial delays can be present in feedback control. To show the effectiveness of this idea we apply our method to an example of a scalar genetic autoregulatory network. The constraint on the gain allows one to implement the feedback in a genetic regulatory network without having to change the reaction rates. A possible method of synthesizing such a system in a wet lab is explained in more detail. Finally, stability results indicate the possibility of stabilizing an unstable system with added delayed feedbacks (by adding larger delays). This approach may also be applicable to systems with large delays in which simple controllers are needed due to limitations in computational power. This paper motivates and provides preliminary results towards direct design of purely delay based controllers for network systems with large delays.

Electronic downloads

• http://www.cds.caltech.edu/~murray/preprints/gym14-acc_s.pdf

• HTML

  Marcella Gomez, Seungil You, Richard Murray. <a
  href="http://www.terraswarm.org/pubs/147.html"
  >Time-Delayed Feedback Channel Design: Discrete Time
  H-Infinity Approach</a>, American Control Conference
  2014, June, 2013.

• Plain text

  Marcella Gomez, Seungil You, Richard Murray.
  "Time-Delayed Feedback Channel Design: Discrete Time
  H-Infinity Approach". American Control Conference 2014,
  June, 2013.

• BibTeX

  @inproceedings{GomezYouMurray13_TimeDelayedFeedbackChannelDesignDiscreteTimeHInfinity,
      author = {Marcella Gomez and Seungil You and Richard Murray},
      title = {Time-Delayed Feedback Channel Design: Discrete
                Time H-Infinity Approach},
      booktitle = {American Control Conference 2014},
      month = {June},
      year = {2013},
      abstract = {This paper proposes a method of improving
                performance of scalar discrete-time systems with
                substantial delay by adding additional delayed
                feedback channels (i.e. imposing a distributed
                delay feedback). The optimal weights for the added
                feedback channels are found using optimization
                techniques. In particular, we reduce the H1 norm
                of the closed loop transfer function with multiple
                delayed feedback using techniques from static
                output feedback design. We impose constraints on
                the feedback gain in order to highlight the
                effectiveness of the distribution. In this manner,
                improvement on performance is a result of the
                distribution and not a change in the overall
                effective gain. The concept of applying a multiple
                delayed feedback channel is inspired by biological
                systems, where substantial delays can be present
                in feedback control. To show the effectiveness of
                this idea we apply our method to an example of a
                scalar genetic autoregulatory network. The
                constraint on the gain allows one to implement the
                feedback in a genetic regulatory network without
                having to change the reaction rates. A possible
                method of synthesizing such a system in a wet lab
                is explained in more detail. Finally, stability
                results indicate the possibility of stabilizing an
                unstable system with added delayed feedbacks (by
                adding larger delays). This approach may also be
                applicable to systems with large delays in which
                simple controllers are needed due to limitations
                in computational power. This paper motivates and
                provides preliminary results towards direct design
                of purely delay based controllers for network
                systems with large delays.},
      URL = {http://terraswarm.org/pubs/147.html}
  }
  

Posted by Mila MacBain on 16 Oct 2013.