Chaotic Systems Reconstruction

Abstract

This chapter deals with the multiple model approach based chaotic systems reconstruction. The approach is based on the design of unknown inputs multiple observers using Linear Matrix Inequalities ($\mathcal{L}\mathcal{M}\mathcal{I}$) formulation. The objective is to estimate state variables of a multiple model subject to unknown inputs affecting both states and outputs of the system. Uncertainties affecting state matrices of the system are also considered for both continuous-time and discrete-time multiple models. In order to improve the performances of the observer, poles placement in an $\mathcal{L}\mathcal{M}\mathcal{I}$ region is also studied. Numerical examples are given to illustrate the effectiveness the given results. Application dealing with chaotic synchronization and message decoding are also given by considering chaotic multiple model subject to hidden message. The proposed approach can be also used in a chaotic cryptosystem procedure where the plaintext (message) is encrypted using chaotic signals at the drive system side. The resulting ciphertext is embedded to the output and/or state of the drive system and is sent via public channel to the response system. The plaintext is retrieved via the synthesis approach, i.e. the designed unknown input multiple observer.