An extension to chaos control via Lie derivatives: Fully linearizable systems

摘要

Chaos control comprises two basic problems: (i) suppression and (ii) synchronization. In this sense, the Lie derivative has been a powerful mathematical tool to deal with chaos control problems. The Lie derivative consists in the derivative of output-state variable(s) observed from measurements-along the vector field. Since a vector field assigns a vector space at any point of the space state for a given dynamical system, the Lie derivative of the output along such vector field signifies the directional derivative of the system observed from the measured state variable (or variables for multiple output systems). The Lie derivative signifies the direction of the dynamical system motion at any point belonging to space state. Hence, from this information, a control law can be designed for inducing a desired behavior. Nevertheless, for a chosen output, Lie derivative procedure can yield an unstable control law, which cannot deal with the chaos control. In this contribution, an extension to previous results about Lie derivatives in dynamical systems is presented. Thus, the chaos control can be achieved by the extension in face to points of singularity.