On stabilization of equilibria using predictive control with and without pulses

Consider a chaotic difference equation xn+1=f(xn)xn+1=f(xn). We focus on the problem of control of chaos using a prediction-based control (PBC) method. If ff has a unique positive equilibrium, it is proved that global stabilization of this equilibrium can be achieved under mild assumptions on the map ff; if ff 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.