Synchronization of Chaotic Systems with Bounded Controls

Abstract

Real-world dynamical systems are nonlinear in nature and require bounded controls due to electrical, mechanical and other input limitations. The present paper proposes a method to synchronize chaotic systems with controls subject to magnitude and rate constraints. The method consists in decomposing the driven system into a stabilizable linear part and a nonlinear part. Then, the nonlinear part is generated together with the drive signals through an exosystem and taken as disturbances for the driven system. Numerical simulations using two well-known chaotic systems are performed to validate the proposed method. The output synchronization is successfully achieved in a short settling time within the actuator output magnitude and rate bounds and is shown experimentally to be robust against process noise due to the underlying internal model control concept of the proposed synchronization method.