Loading...

Estimation of nonlinear dynamic systems over communication channels

Sanjaroon, V ; Sharif University of Technology | 2018

860 Viewed
  1. Type of Document: Article
  2. DOI: 10.1109/TAC.2018.2797192
  3. Publisher: Institute of Electrical and Electronics Engineers Inc , 2018
  4. Abstract:
  5. Remote observation of the state trajectory of nonlinear dynamic systems over limited capacity communication channels is studied. It is shown that two extreme cases are possible: Either the system is fully observable or the error in estimation blows up. The key observation is that such behavior is determined by the relationship between the Shannon capacity and the Lyapunov exponents; the well-known characterizing parameters of a communication channel on one side, and a dynamic system from the other side. In particular, it is proved that for nonlinear systems with initial state x0, the minimum capacity of an additive white Gaussian noise channel required for full observation of the system in the mean square sense is ∑iκi(x0)Δi(x0), where Δi(x0) s and κi(x0) s denote distinct Lyapunov exponents and their multiplicity numbers, respectively. Conversely, if the capacity is less than E[∑i κi(x0)Δi(x0)], then observation is impossible. In order to show the universality of the result, we obtain the same observability conditions for the digital noiseless channel and the packet erasure channel in sure and almost sure senses, respectively. © 2018 IEEE
  6. Keywords:
  7. Capacity ; Lyapunov exponents ; Nonlinear dynamic systems ; Observability ; Channel capacity ; Communication channels (information theory) ; Differential equations ; Digital communication systems ; Dynamics ; Entropy ; Lyapunov functions ; Lyapunov methods ; Noise generators ; Nonlinear dynamical systems ; White noise ; AWGN channel ; Limited capacity ; Lyapunov exponent ; Noiseless channels ; Packet erasure channels ; Remote observation ; Shannon capacity ; Dynamical systems
  8. Source: IEEE Transactions on Automatic Control ; Volume 63, Issue 9 , 2018 , Pages 3024-3031 ; 00189286 (ISSN)
  9. URL: https://ieeexplore.ieee.org/document/8267266