Strange attractor identification and state observation under sparse measurements

Abstract

In this paper, a new method of strange attractor identification, under sparse measurement, is proposed this method is based on the concept of compressive sensing. For this, some particular impulsive observers have been presented and adding a decision scheme linked to diagnosis method, the identification of the strange attractor and state observation are done. Some simulations results are given in order to highlight the well founded of the proposed design.

From restricted isometry property to observability under sparse measurement

“…[12] Under assumption 4 and for bounded sampling periods θ k , it is always possible to design an observer of the type (10) which converges asymptotically to the states of system (9).…”

“…[11] Given the system (9) and the observer (11), then ∀ε > 0, there exists β max > ε, a maximum sampling period θ max > 0 and a reset matrix R, such that for every initial condition x(0) < β max , the observation error (12) converges to a ball of radius ε + ε * .…”

“…More precisely, we propose a sufficient condition related to the observability and distinguishability of hybrid systems that will allows us to detect and reconstruct the non-measured states of a continuous linear system with sparse measurements. An answer to the question iv) for linear systems is given in [11] and for chaotic systems in [12] and will be used here to illustrate the answer to the question v). More precisely, an impulsive observer which bypasses the optimization algorithm, under certain conditions, will be presented in this work.…”