Mechanical & Materials Engineering, Department of


Date of this Version



A THESIS Presented to the Faculty of The Graduate College at The University of Nebraska In Partial Fulfillment of Requirements For the Degree of Master of Science, Major: Mechanical Engineering, Under the Supervision of Professor Cho W. Solomon To. Lincoln Nebraska, September 2010 Copyright 2010 Celestin Nkundineza


Stochastic control is an important area of research in engineering systems that undergo disturbances. Controlling individual states in such systems is critical. The present investigation is concerned with the application of the stochastic optimal control strategy developed by To (2010) and its implementation as well as providing computed results of linear and nonlinear systems under stationary and nonstationary random excitations. In the strategy the feedback matrix is designed based on the achievement of the objectives for individual states in the system through the application of the Lyapunov equation for the system. Each diagonal element in the gain or associated gain matrix is related to the corresponding states. The strategy is applied to four dynamic engineering systems that are divided into two categories. One category includes two linear systems each of which has two degrees of freedom. The other category encompasses two nonlinear two-degree-of-freedom systems.

Computed results were provided for the optimal control of stationary and nonstationary random displacements. These results were obtained by employing the computer software, MATLAB and were represented graphically. The computed results include the time-dependent elements of the associated gain matrix. Three-dimensional graphical representations of the controlled mean squares of displacements against the two elements of the feedback gain matrix were included. The latter three-dimensional presentations are important for the design engineer who needs to choose elements of the gain matrix in order to achieve a specific objective in certain states of the system.