Estimation of Nonlinear Dynamic Systems Over Communication Channels
| Autor: | Vahideh Sanjaroon, Babak Hossein Khalaj, Abolfazl S. Motahari, Alireza Farhadi |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Discrete mathematics
Physics 0209 industrial biotechnology Packet erasure channel 020206 networking & telecommunications Observable 02 engineering and technology Lyapunov exponent Computer Science Applications symbols.namesake Nonlinear system Channel capacity 020901 industrial engineering & automation Control and Systems Engineering 0202 electrical engineering electronic engineering information engineering symbols Entropy (information theory) Observability Electrical and Electronic Engineering Computer Science::Information Theory Communication channel |
| Zdroj: | IEEE Transactions on Automatic Control. 63:3024-3031 |
| ISSN: | 2334-3303 0018-9286 |
| Popis: | 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 $x_0$ , the minimum capacity of an additive white Gaussian noise channel required for full observation of the system in the mean square sense is $ \sum _i\kappa _i(x_0)\Delta _i (x_0)$ , where $\Delta _i (x_0)$ s and $\kappa _i(x_0)$ s denote distinct Lyapunov exponents and their multiplicity numbers, respectively. Conversely, if the capacity is less than $E[\sum _i \kappa _i(x_0)\Delta _i (x_0)]$ , 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. |
| Databáze: | OpenAIRE |
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