Generalized Synchronization of Chaotic Systems Using a Symplectic Pseudospectral Optimal Control Method

Abstract

In this paper, the generalized synchronization of chaotic systems is formulated as a nonlinear optimal control problem where constraints on control variables are also considered. The nonlinear constrained optimal control problem is solved by a symplectic pseudospectral method. Via this method, chaotic synchronization problems under the following three different conditions are studied: (1) the master and the slave systems are identical but with different initial values; (2) the master and the slave systems are different but dimensionalities of two systems are same; (3) the master and the slave systems are of different dimensionalities. Numerical simulations demonstrate the effectiveness of the symplectic pseudospectral optimal control method. Master and slave systems are synchronized rapidly and constraints on control are strictly satisfied. By enlarging the weight parameters on the generalized error in the cost functional, it results in a more rapid synchronization.