Title page for ETD etd-0525101-111407

Document Type dissertation

Author Name Iourtchenko, Daniil V

URN etd-0525101-111407

Title Optimal Bounded Control and Relevant Response Analysis for Random Vibrations

Degree PhD

Department Mechanical Engineering

Advisors
Mikhail F. Dimentberg, Advisor
Raymond R. Hagglund, Committee Member
Zhikun Hou, Committee Member
Suzanne L. Weekes, Committee Member
John J. Sullivan, Graduate Committee Rep

Keywords
Stochastic Optimal Control
Dynamic Programming
Hamilton-Jacobi-Bellman equation
Random Vibration
Energy Balance method

Date of Presentation/Defense 2001-05-08

Availability unrestricted

Abstract
In this dissertation, certain problems of stochastic optimal control and relevant
analysis of random vibrations are considered. Dynamic Programming approach is used to
find an optimal control law for a linear single-degree-of-freedom system subjected to
Gaussian white-noise excitation. To minimize a system’s mean response energy, a
bounded in magnitude control force is applied. This approach reduces the problem of
finding the optimal control law to a problem of finding a solution to the Hamilton-Jacobi-Bellman
(HJB) partial differential equation. A solution to this partial differential equation
(PDE) is obtained by developed ‘hybrid’ solution method. The application of bounded in
magnitude control law will always introduce a certain type of nonlinearity into the
system’s stochastic equation of motion. These systems may be analyzed by the Energy
Balance method, which introduced and developed in this dissertation. Comparison of
analytical results obtained by the Energy Balance method and by stochastic averaging
method with numerical results is provided. The comparison of results indicates that the
Energy Balance method is more accurate than the well-known stochastic averaging
method.

Files
iourtchenko.pdf

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Document Type	dissertation
Author Name	Iourtchenko, Daniil V
URN	etd-0525101-111407
Title	Optimal Bounded Control and Relevant Response Analysis for Random Vibrations
Degree	PhD
Department	Mechanical Engineering
Advisors	Mikhail F. Dimentberg, Advisor Raymond R. Hagglund, Committee Member Zhikun Hou, Committee Member Suzanne L. Weekes, Committee Member John J. Sullivan, Graduate Committee Rep
Keywords	Stochastic Optimal Control Dynamic Programming Hamilton-Jacobi-Bellman equation Random Vibration Energy Balance method
Date of Presentation/Defense	2001-05-08
Availability	unrestricted
Abstract In this dissertation, certain problems of stochastic optimal control and relevant analysis of random vibrations are considered. Dynamic Programming approach is used to find an optimal control law for a linear single-degree-of-freedom system subjected to Gaussian white-noise excitation. To minimize a system’s mean response energy, a bounded in magnitude control force is applied. This approach reduces the problem of finding the optimal control law to a problem of finding a solution to the Hamilton-Jacobi-Bellman (HJB) partial differential equation. A solution to this partial differential equation (PDE) is obtained by developed ‘hybrid’ solution method. The application of bounded in magnitude control law will always introduce a certain type of nonlinearity into the system’s stochastic equation of motion. These systems may be analyzed by the Energy Balance method, which introduced and developed in this dissertation. Comparison of analytical results obtained by the Energy Balance method and by stochastic averaging method with numerical results is provided. The comparison of results indicates that the Energy Balance method is more accurate than the well-known stochastic averaging method.
Files	iourtchenko.pdf