An adaptive nonlinear controller design for a class of uncertain chaotic systems with single input using linear model reference

This paper addresses a new linear model reference adaptive control scheme design for chaos control of a class of chaotic systems. The controller structure is introduced for second-order and high-order chaotic nonlinear systems, and all constant parameters and controller gain are assumed to be uncertain. Based on the adaptation rules invoked by the Lyapunov theory, a model reference adaptive controller technique with a single input is designed to attenuate the chaos of the uncertain chaotic system. A high-order filtered signal-based Lyapunov function is used to prove the asymptotic stability of the closed-loop error dynamics. To demonstrate the performance of the designed controller, the proposed method is applied to reduce parametric uncertainties and chaotic oscillations in 2D chaotic Gyro and 3D Genesio–Tesi chaotic systems. The outputs of a successful model reference tracking for different reference responses of chaotic systems are presented with simulation results. The simulation results exhibit that the proposed theoretical method has both viability and robustness against unknown controller gain, also making it suitable for the application of chaotic systems control for tracking the desired linear model reference system. Even further than these, the proposed method is to provide convenience in the synchronization of both transient and steady-state responses.