Adaptive feedback control and synchronization of non-identical chaotic fractional order systems

Zaid M. Odibat (1)

1 ULH - Université Le Havre Normandie

This paper addresses the reliable synchronization problem between two non-identical chaotic fractional order systems. In this work, we present an adaptive feedback control scheme for the synchronization of two coupled chaotic fractional order systems with different fractional orders. Based on the stability results of linear fractional order systems and Laplace transform theory, using the master-slave synchronization scheme, sufficient conditions for chaos synchronization are derived. The designed controller ensures that fractional order chaotic oscillators that have non-identical fractional orders can be synchronized with suitable feedback controller applied to the response system. Numerical simulations are performed to assess the performance of the proposed adaptive controller in synchronizing chaotic systems.

Mots clés: Chaos synchronization; Fractional order system; Caputo fractional derivative; Stability; Feedback control

Zaid M. Odibat. Adaptive feedback control and synchronization of non-identical chaotic fractional order systems. Nonlinear Dynamics, 2009, 60 (4), pp.479-487. ⟨10.1007/s11071-009-9609-6⟩. ⟨hal-00568401⟩