Analysis and control of nonlinear stochastic systems

Analysis and control of stochastic systems is an active research subject that has a broad range of engineering applications. A limited class of problems yield analytical solutions for nonlinear systems under stochastic excitations. The objective of this PhD dissertation is to analyze nonlinear stochastic systems and to achieve a deeper understanding of the methods to investigate and design various types of controllers. We develop mathematical tools for the stability analysis and address the issues of feedback stabilization, optimal controls, time delay and approximate techniques to assess the control performance of such systems.; We use Stochastic Averaging (SA) to obtain an approximate equation for the PDF of the amplitude process using Stratonovich-Khasminskii limit theorem. A predetermined feedback form is used to study the effect of the feedback gains. For the transient analysis a further approximation is employed using the Rayleigh closure. Performance charts for the feedback gains are compiled and robustness issues are addressed. Extensive numerical simulations are compared to the estimated system response.; Based on the PDF formulation we extend the control method to the steady state optimal control of stochastic systems. The infinite hierarchy of the moment equations are closed using a Rayleigh approximation and we compared the computational effort to find the optimal control gains with both SA and Rayleigh approximation. The effect of control effort weighting in the cost function is also addressed. We also use the feedback controls that render the exact steady state PDF of the nonlinear system response. We determine the control gains by minimizing a performance index, which includes the moment tracking error and the control penalty. We demonstrate that the approach yields the covariance control formulation when the control effort is not penalized. The exact PDF makes the solution process of optimization very efficient and accurate. We create accurate tables of expectations of system responses for two nonlinear examples.; We extend the semi discretization method to stochastic systems with time delay. We propose exact drift mapping method to account for the stochastic components in the system to evaluate the effect of feedback control gains. Stability charts for feedback control gains are also compiled. (Abstract shortened by UMI.)...