Robust interval observers for global Lipschitz uncertain chaotic systems

In this paper we develop and apply a robust interval observer to estimate the unknown variables of uncertain chaotic systems. We consider that bounds of the uncertainties are known and propose an observer that computes guaranteed upper and lower bounds for the unknown variables. We show that the proposed observer converges asymptotically toward a bounded error, leading to an original scheme of observer-based synchronization. The method is applied to the estimation of the variables of Chua’s chaotic system.

Research highlights
► A first bounding of chaotic systems is introduced, using interval observers.
► The observer has a novel structure, considering perfect knowledge and uncertainties on the parameters of the chaotic system.
► The estimation performance of the proposed method can be evaluated online.
► The final estimation error converges toward a bounded quantity.