Adaptive hybrid function projective synchronization of chaotic systems with fully unknown periodical time-varying parameters

Abstract

In this paper, an adaptive learning control approach is presented for the hybrid functional projective synchronization (HFPS) of different chaotic systems with fully unknown periodical time-varying parameters. Differential-difference hybrid parametric learning laws and an adaptive learning control law are constructed via the Lyapunov–Krasovskii functional stability theory, which make the states of two different chaotic systems asymptotically synchronized in the sense of mean square norm. Moreover, the boundedness of the parameter estimates are also obtained. The Lorenz system and Chen system are illustrated to show the effectiveness of the hybrid functional projective synchronization scheme.

Keywords

• adaptive learning control
• , chaotic system
• hybrid functional projective synchronization
• differential-difference mixed parametric learning law
• Lyapunov–Krasovskii function