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• W4132638 abstract "Chaotic response is related to a dense set of unstable periodic orbits (UPOs) and the system often visits the neighborhood of each one of them. Moreover, chaos has sensitive dependence to initial condition, which implies that the system evolution may be altered by small perturbations. Chaos control is based on the richness of chaotic behavior and may be understood as the use of tiny perturbations for the stabilization of an UPO embedded in a chaotic attractor. It makes this kind of behavior to be desirable in a variety of applications, since one of these UPO can provide better performance than others in a particular situation. Due to these characteristics, chaos and many regulatory mechanisms control the dynamics of living systems. Inspired by nature, it is possible to imagine situations where chaos control is employed to stabilize desirable behaviors of mechanical systems. Under this condition, these systems would present a great flexibility when controlled, being able to quickly change from one kind of response to another. Literature presents some contributions related to the analysis of chaos control in mechanical systems. Andrievskii and Fradkov (2004) and Savi et al. (2006) present an overview of applications of chaos control in various scientific fields. There are different techniques employed to perform chaos control (Savi et al., 2006), however, the inspirational idea of these methods is the well-known OGY method (Ott et al., 1990), which is a discrete technique that considers small perturbations promoted in the neighborhood of the desired orbit. This contribution proposes a robust controller that can be applied to stabilize UPOs of chaotic attractors. The adopted approach is based on the sliding mode control strategy and enhanced by a stable adaptive fuzzy inference system to cope with modeling inaccuracies and external disturbances that can arise. The boundedness of all closed-loop signals and the convergence properties of the tracking error are analytically proven using Lyapunov’s direct method and Barbalat’s lemma. The general procedure is applied to a nonlinear pendulum that presents chaotic response (De Paula et al., 2006). Numerical simulations are carried out showing the stabilization of some UPOs of the chaotic attractor showing an effective response, demonstrating the controller performance." @default.
• W4132638 created "2016-06-24" @default.
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• W4132638 date "2007-01-01" @default.
• W4132638 modified "2023-09-26" @default.
• W4132638 title "An Adaptive fuzzy sliding mode controller applied to a chatoic pendulum" @default.
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