On stabilization of equilibria using predictive control with and without pulses

Consider a chaotic difference equation xn+1 = f (xn). We focus on the problem of control of chaos using a prediction-based control (PBC)method. If f has a unique positive equilibrium, it is proved that global stabilization of this equilibrium can be achieved under mild assumptions on the map f ; if f has several positive equilibria, we demonstrate that more than one equilibrium can be stabilized simultaneously.We also show that it is still possible to stabilize an unstable equilibrium using a strategy of control with pulses, that is, the control is only applied after a fixed number of iterations. We illustrate our main results with several examples, mainly from population dynamics. © 2012 Elsevier Ltd. All rights reserved.