In this report, a control method for the stabilization of periodic orbits for a class of one- and two-dimensional discrete-time systems that are topologically conjugate to symbolic dynamical systems is proposed and applied to a population model in an ecosystem and the Smale horseshoe map. A periodic orbit is assigned as a target by giving a sequence in which symbols have periodicity. As a consequence, it is shown that any periodic orbits can be globally stabilized by using arbitrarily small control inputs. This work is a new attempt to systematically design a control system based on symbolic dynamics in the sense that one estimates the magnitude of control inputs and analyzes the Lyapunov stability.
symbolic dynamics, global stability, chaos control
37B10, 74H65, 93D15