Minimum Number of Probes for Brain Dynamics Observability
Sergio Pequito, Paul Bogdan, George Pappas

Citation
Sergio Pequito, Paul Bogdan, George Pappas. "Minimum Number of Probes for Brain Dynamics Observability". 54th IEEE Conference on Decision and Control, 306-311, 15, December, 2015.

Abstract
In this paper, we address the problem of placing sensor probes in the brain such that the system dynamics' are generically observable. The system dynamics whose states can encode for instance the fire-rating of the neurons or their ensemble following a neural-topological (structural) approach, and the sensors are assumed to be dedicated, i.e., can only measure a state at each time. Even though the mathematical description of brain dynamics is (yet) to be discovered, we build on its observed fractal characteristics and assume that the a good model of the brain activity satisfies the following properties: (i) linear time-varying, or (ii) fractional-order dynamics. Although the sensor placement explored in this paper is particularly considering the observability of brain dynamics, the proposed methodology applies to any fractional-order linear system. Thus, the main contributions of this paper are twofold: (i) we show how to place the minimum number of dedicated sensors for continuous-time linear switching systems, i.e., a sequential description of the dynamics by a finite collection of linear time-invariant systems that can change over time, that ensures the system to be generically observable; and (ii) we show how to place the minimum number of dedicated sensors to ensure generic observability in discrete-time fractional-order systems for a specified finite interval of time. Finally, an illustrative example of the main results is provided using brain activity data.

Electronic downloads

Internal. This publication has been marked by the author for TerraSwarm-only distribution, so electronic downloads are not available without logging in.

Citation formats

• HTML

  Sergio Pequito, Paul Bogdan, George Pappas. <a
  href="http://www.terraswarm.org/pubs/531.html"
  >Minimum Number of Probes for Brain Dynamics
  Observability</a>, 54th IEEE Conference on Decision
  and Control, 306-311, 15, December, 2015.

• Plain text

  Sergio Pequito, Paul Bogdan, George Pappas. "Minimum
  Number of Probes for Brain Dynamics Observability".
  54th IEEE Conference on Decision and Control, 306-311, 15,
  December, 2015.

• BibTeX

  @inproceedings{PequitoBogdanPappas15_MinimumNumberOfProbesForBrainDynamicsObservability,
      author = {Sergio Pequito and Paul Bogdan and George Pappas},
      title = {Minimum Number of Probes for Brain Dynamics
                Observability},
      booktitle = {54th IEEE Conference on Decision and Control},
      pages = {306-311},
      day = {15},
      month = {December},
      year = {2015},
      abstract = {In this paper, we address the problem of placing
                sensor probes in the brain such that the system
                dynamics' are generically observable. The system
                dynamics whose states can encode for instance the
                fire-rating of the neurons or their ensemble
                following a neural-topological (structural)
                approach, and the sensors are assumed to be
                dedicated, i.e., can only measure a state at each
                time. Even though the mathematical description of
                brain dynamics is (yet) to be discovered, we build
                on its observed fractal characteristics and assume
                that the a good model of the brain activity
                satisfies the following properties: (i) linear
                time-varying, or (ii) fractional-order dynamics.
                Although the sensor placement explored in this
                paper is particularly considering the
                observability of brain dynamics, the proposed
                methodology applies to any fractional-order linear
                system. Thus, the main contributions of this paper
                are twofold: (i) we show how to place the minimum
                number of dedicated sensors for continuous-time
                linear switching systems, i.e., a sequential
                description of the dynamics by a finite collection
                of linear time-invariant systems that can change
                over time, that ensures the system to be
                generically observable; and (ii) we show how to
                place the minimum number of dedicated sensors to
                ensure generic observability in discrete-time
                fractional-order systems for a specified finite
                interval of time. Finally, an illustrative example
                of the main results is provided using brain
                activity data.},
      URL = {http://terraswarm.org/pubs/531.html}
  }
  

Posted by Sergio Pequito on 27 Mar 2015.
Groups: services