Faculty Advisor

Suzanne L. Weekes

Faculty Advisor

Zhikun Hou

Faculty Advisor

Raymond R. Hagglund

Faculty Advisor

Mikhail F. Dimentberg

Faculty Advisor

John J. Sullivan


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.


Worcester Polytechnic Institute

Degree Name



Mechanical Engineering

Project Type


Date Accepted





Stochastic Optimal Control, Dynamic Programming, Hamilton-Jacobi-Bellman equation, Random Vibration, Energy Balance method, Vibration, Control theory, Mathematical optimization, Stochastic control theory