Intelligent quadratic optimal synchronization of uncertain chaotic systems via LMI approach

This paper proposes an intelligent quadratic optimal control scheme via linear matrix inequality (LMI) approach for the synchronization of uncertain chaotic systems with both external disturbances and parametric perturbations. First, a four-layered neural fuzzy network (NFN) identifier is constructed to estimate system nonlinear dynamics. Based on the NFN identifier, an intelligent quadratic optimal controller is developed with robust hybrid control scheme, in which H∞ optimal control and variable structure control (VSC) are embedded to attenuate the effects of external disturbances and parametric perturbations. The adaptive tuning laws of network parameters are derived in the sense of the Lyapunov synthesis approach to ensure network convergence, and the sufficient criterion for existence of the controller is formulated in the linear matrix inequality (LMI) form to guarantee the quadratic optimal synchronization performance. Finally, a numerical simulation example is illustrated by the chaotic Chua’s circuit system to demonstrate the effectiveness of our scheme.