14,230 research outputs found
Asymptotic and finite-time almost global attitude tracking: representations free approach
In this paper, the attitude tracking problem is considered using the rotation
matrices. Due to the inherent topological restriction, it is impossible to
achieve global attractivity with any continuous attitude control system on
. Hence in this work, we propose some control protocols achieve almost
global tracking asymptotically and in finite time, respectively. In these
protocols, no world frame is needed and only relative state informations are
requested. For finite-time tracking case, Filippov solutions and non-smooth
analysis techniques are adopted to handle the discontinuities. Simulation
examples are provided to verify the performances of the control protocols
designed in this paper.Comment: arXiv admin note: text overlap with arXiv:1705.0282
Covariant Lyapunov vectors
The recent years have witnessed a growing interest for covariant Lyapunov
vectors (CLVs) which span local intrinsic directions in the phase space of
chaotic systems. Here we review the basic results of ergodic theory, with a
specific reference to the implications of Oseledets' theorem for the properties
of the CLVs. We then present a detailed description of a "dynamical" algorithm
to compute the CLVs and show that it generically converges exponentially in
time. We also discuss its numerical performance and compare it with other
algorithms presented in literature. We finally illustrate how CLVs can be used
to quantify deviations from hyperbolicity with reference to a dissipative
system (a chain of H\'enon maps) and a Hamiltonian model (a Fermi-Pasta-Ulam
chain)
Complex Dynamics and Synchronization of Delayed-Feedback Nonlinear Oscillators
We describe a flexible and modular delayed-feedback nonlinear oscillator that
is capable of generating a wide range of dynamical behaviours, from periodic
oscillations to high-dimensional chaos. The oscillator uses electrooptic
modulation and fibre-optic transmission, with feedback and filtering
implemented through real-time digital-signal processing. We consider two such
oscillators that are coupled to one another, and we identify the conditions
under which they will synchronize. By examining the rates of divergence or
convergence between two coupled oscillators, we quantify the maximum Lyapunov
exponents or transverse Lyapunov exponents of the system, and we present an
experimental method to determine these rates that does not require a
mathematical model of the system. Finally, we demonstrate a new adaptive
control method that keeps two oscillators synchronized even when the coupling
between them is changing unpredictably.Comment: 24 pages, 13 figures. To appear in Phil. Trans. R. Soc. A (special
theme issue to accompany 2009 International Workshop on Delayed Complex
Systems
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