Stochastic Stability and Nonlinear Control in Mechanical Systems

Almost-sure asymptotic stability of 3 and 4 dimensional co-dimension 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 the boundary behavior of the associated scalar diffusion process of the amplitude Ito equations. This method is then applied to a linear, gyroscopic problem of a rotating shaft with a random loading demonstrating the conservative nature of mean square stability. In addition to stochastic excitations, many systems also undergo harmonic loading. The almost-sure stability of two degree-of-freedom systems subjected to both random and harmonic excitation is then investigated. In this analysis, stochastic averaging followed by a perturbation theoretic approximation is used to facilitate the solution of the multi-dimensional diffusive Markov process.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Aeronautical and Astronautical Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Talwar, Sanjiv

Contributors dc:contributor

• Namachchivaya, N. Sri

• Applied Mechanics
• Engineering, Aerospace

Identifier

(UMI)AAI9314948

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/72369