Biomedical subjects

Elbert E N Macau

Publications and source records attributed to Elbert E N Macau.

5 recordsLinked to original sources

PubMed2006

Control of chaos and its relevancy to spacecraft steering.

In 1990, a seminal work named controlling chaos showed that not only the chaotic evolution could be controlled, but also the complexity inherent in the chaotic dynamics could be exploited to provide a unique level of flexibility and efficiency in technological uses of this phenomenon. Control of chaos is also making substantial contribution in the field of astrodynamics, especially related to the exciting issue of low-energy transfer. The purpose of this work is to bring up the main ideas regarding the control of chaos and targeting, and to show how these techniques can be extended to Hamiltonian situations. We give realistic examples related to astrodynamics problems, in which these techniques are unique in terms of efficiency related to low-energy spacecraft transfer and in-orbit stabilization.

Algorithms↗

PubMed2005

Using geometric control and chaotic synchronization to estimate an unknown model parameter.

We present a new parameter estimation procedure for nonlinear systems. Such technique is based on the synchronization between the model and the system whose unknown parameter is wanted. Synchronization is accomplished by controlling the model to make it follow the system. We use geometric nonlinear control techniques to design the control system. These techniques allow us to derive sufficient conditions for synchronization and hence for proper parameter estimation. As an example, this procedure is used to estimate a parameter of an example serving as a model.

Journal Article↗

PubMed2004

Analysis of chaotic saddles in high-dimensional dynamical systems: the Kuramoto-Sivashinsky equation.

This paper presents a methodology to study the role played by nonattracting chaotic sets called chaotic saddles in chaotic transitions of high-dimensional dynamical systems. Our methodology is applied to the Kuramoto-Sivashinsky equation, a reaction-diffusion partial differential equation. The paper describes a novel technique that uses the stable manifold of a chaotic saddle to characterize the homoclinic tangency responsible for an interior crisis, a chaotic transition that results in the enlargement of a chaotic attractor. The numerical techniques explained here are important to improve the understanding of the connection between low-dimensional chaotic systems and spatiotemporal systems which exhibit temporal chaos and spatial coherence.

Algorithms↗

PubMed2002

Driving trajectories in chaotic scattering.

In this work we introduce a general approach for targeting in chaotic scattering that can be used to find a transfer trajectory between any two points located inside the scattering region. We show that this method can be used in association with a control of chaos strategy to drive around and keep a particle inside the scattering region. As an illustration of how powerful this approach is, we use it in a case of practical interest in celestial mechanics in which it is desired to control the evolution of two satellites that evolve around a large central body.

Journal Article↗

PubMed2002

Active synchronization in nonhyperbolic hyperchaotic systems.

We propose a methodology to address the outstanding problem of synchronization in nonhyperbolic hyperchaotic physical systems. Our approach makes use of a controlling-chaos strategy that accomplishes the task by transmitting only one scalar signal even in the presence of noise.

Journal Article↗