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Showing 1 to 10 of 10 for “"stochastic averaging"”.
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Stochastic Averaging for Mechanical Systems
… These systems are studied when driven by stochastic forcing. The analysis presented is based on the theory of stochastic averaging. This theory provides a mathematically rigorous method to reduce the number of differential equations required to describe the long term evolution of dynamical …
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Stochastic Averaging Correctors for a Noisy Hamiltonian System With Discontinuous Statistics
… here certain perturbed test functions for stochastic averaging of a noisy planar Hamiltonian system containing a homoclinic orbit. The noise is assumed to be small and have skewness at the homoclinic orbit. Following Sowers, we center our efforts on a singular perturbations problem in a …
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Stochastic Stability and Nonlinear Control in Mechanical Systems
… two dynamical systems under small intensity stochastic excitations is investigated. The method of stochastic averaging is used to derive a set of approximate Ito equations which are then examined to obtain the almost-sure stability conditions. The sample properties of the process are based on …
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Stochastically Perturbed Dynamics of Hamiltonian Systems Near 1:1-Resonance
… of trajectories on the averaged dynamics of stochastically perturbed two-degrees of freedom integrable systems is emphasized throughout the study. The extension of the method of stochastic averaging on graphs to 1:1-resonant Hamiltonian systems forms the other major aspect of this work.
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Rotor Blade Flap-Lag Stability and Response in Forward Flight in Turbulent Flows
… turbulence and applying a special case of the stochastic averaging procedure, equations are developed which describe the stochastic first and second moments of the perturbations in flap and lead-lag angles due to turbulence.
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On informational nudging and control of payoff-based learning
… alternatives. Each alternative brings a certain stochastic reward/payoff to the decision maker. The decision maker/user repeatedly chooses from the set of alternatives so as to maximize the reward she obtains. The user remembers her past experiments and builds an estimate of the reward of each …
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Dynamics of Randomly Perturbed Nonlinear Structural and Mechanical Systems With Resonances
… system and achieve a model-reduction through stochastic averaging. The solution of the reduced model can be approximated by a Markov process. Depending on the strength of the noise, the reduced Markov process takes its values on a line or on a graph with certain gluing conditions at the …
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A Problem From Hamiltonian Mechanics With Time -Periodic Coefficients, Small Noise, and Degeneracy
… to a Markov process on a stratified space. The averaging combines the deterministic time averaging of periodic coefficient, and the stochastic averaging of the resulting system. The corresponding strata of the reduced space are a two-sphere, a point and a line segment. Special attention is given …
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Stochastic Algorithms in Riemannian Manifolds and Adaptive Networks
… combination of adaptive network algorithms and stochastic geometric dynamics has the potential to make a large impact in distributed control and signal processing applications. However, both literatures contain fundamental unsolved problems. The thesis is thus in two main parts. In part I, we …
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Dimensional reduction in nonlinear estimation of multiscale systems
State or signal estimation of stochastic systems based on measurement data is an important problem in many areas of science and engineering. The true signal is usually hidden, evolving according to its own dynamics, and observations are usually corrupted and possibly incomplete. The goal is to …