Stabilizing chaos with predictive control

A novel approach to controlling chaos in discrete-time nonlinear autonomous systems is proposed. A desired unstable periodic orbit is stabilized by small control using the predicted trajectory of the system. The exact knowledge of the periodic orbit is not assumed, just its existence is required. The method developed is validated for one-dimensional and multi-dimensional mappings; its efficacy is demonstrated via numerical simulations of the mappings known from the literature, such as logistic, tent, cubic, and Henon maps. The method is simple in implementation, but its application is limited to systems with no exogenous disturbances and uncertainties in the model description. The approach looks highly promising and may have diverse applications.