Parameter Identification of Chaotic and Hyper-Chaotic Systems Using Synchronization-Based Parameter Observer

A technique is introduced for identifying uncertain and/ or unknown parameters of chaotic and hyper-chaotic systems via using a synchronization-based parameter observer. The proposed technique is based on designing a state feedback controller and then solving for the unknown parameters using some simple parameter adaptive laws that require access to some or all of the states depending on the dynamical model of the systems. Two detailed cases utilizing chaotic and hyper-chaotic systems are used to exemplify the proposed observer when partial identification of the unknown parameters is considered, where the results demonstrated the effectiveness of the proposed method via comparing it with other methods reported in the literature, Furthermore, the feasibility of the designed observer on unknown-structure model and complex-variable model are verified through the theoretical analyses and simulation results, and the advantages and limitations of the synchronization-based parameter observer approach are discussed in detail.