Adaptive unstable periodic orbit stabilization of uncertain time-delayed chaotic systems subjected to input nonlinearity

This paper investigates stabilizing the unstable periodic orbits (UPO) of uncertain time-delayed chaotic systems with sector nonlinearity in input function. The article proposes an adaptive output feedback control design based on the Lyapunov–Krasovskii approach, to stabilize the periodic solutions of a broad class of time-delayed chaotic systems, with unknown time-delay and uncertainty. Finally, numerical simulations are presented to illustrate the effectiveness of the proposed method.

► We propose a controller for UPO stabilization of time-delayed chaotic systems.
► Chaotic systems contain unknown dynamics, uncertain parameters and input nonlinearity.
► The control scheme uses the output states instead of all system states to be known.
► The Lyapunov–Krasovskii approach is used to deal with time-delay in the system dynamics.
► Adaptive control is used to relax the assumptions of knowing the system parameters.