On stabilization of equilibria using predictive control with and without pulses

  • Authors:

  • Elena Braverman;Eduardo Liz

  • Affiliations:

  • Department of Mathematics, University of Calgary, 2500 University Drive N.W., Calgary, AB, Canada T2N 1N4;Departamento de Matemática Aplicada II, Universidade de Vigo, Campus Marcosende, 36310 Vigo, Spain

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2012

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Abstract

Consider a chaotic difference equation x"n"+"1=f(x"n). 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.