Geodesic
A study on global stabilization of periodic orbits in discrete-time chaotic systems by using symbolic dynamics
Kybernetika, Tome 51 (2015) no. 1, pp. 4-19
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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.
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.
DOI : 10.14736/kyb-2015-1-0004
Classification : 37B10, 37N35, 74H65, 93D15
Keywords: symbolic dynamics; chaos control; global stability 
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Suzuki, Masayasu; Sakamoto, Noboru. A study on global stabilization of periodic orbits in discrete-time chaotic systems by using symbolic dynamics. Kybernetika, Tome 51 (2015) no. 1, pp. 4-19. doi: 10.14736/kyb-2015-1-0004

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