Adaptive control of spatiotemporal chaos in coupled map lattices

In this paper, a new discrete adaptive method is proposed in order to control spatiotemporal chaos in coupled map lattices. The proposed method is an adaptive control which is based on the quasi sliding mode control design. It is a general method for tracking the control of spatiotemporal chaotic systems modeled by using coupled map lattices, and is robust with respect to unmodeled dynamic, unknown parameters, and bounded disturbance. The robustness of stability of the controlled system based on the Lyapunov direct method is proved even though bounds of disturbance are unknown. The unknown parameters of the model are updated with an adaptive algorithm, which is an extension of the gradient algorithm with a deadzone function. Diffusively coupled map lattice is used as an example to show the suitability of the method. Simulation results reveal the robustness and the applicability of the method in controlling spatiotemporal chaos in coupled map lattice models.