English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We extend the notion of estimation entropy of autonomous dynamical systemsproposed by Liberzon and Mitra [1] to nonlinear dynamical systems withuncertain inputs with bounded variation. We call this new notion the{$\epsilon$}-estimation entropy of the system and show that it lower bounds thebit rate needed for state estimation. {$\epsilon$}-estimation entropyrepresents the exponential rate of the increase of the minimal number offunctions that are adequate for {$\epsilon$}- approximating any trajectory ofthe system. We show that alternative entropy definitions using spanning orseparating trajectories bound ours from both sides. On the other hand, we showthat other commonly used definitions of entropy, for example the ones in [1],diverge to infinity. Thus, they are potentially not suitable for systems withuncertain inputs. We derive an upper bound on {$\epsilon$}-estimation entropyand estimation bit rates, and evaluate it for two examples. We present a stateestimation algorithm that constructs a function that approximates a giventrajectory up to an {$\epsilon$} error, given time-sampled and quantizedmeasurements of state and input. We investigate the relation between{$\epsilon$}-estimation entropy and a previous notion for switched nonlinearsystems and derive a new upper bound for the latter, showing the generality ofour results on systems with uncertain inputs.

State Estimation of Continuous-time Dynamical Systems with Uncertain  Inputs with Bounded Variation: Entropy, Bit Rates, and Relation with Switched  Systems