In the past decades there has been onsiderable commercial and academic interest in methods for monitoring control system performance for linear systems. Far less has been written on control system performance for nonlinear dynamic / stochastic systems. This thesis presents research results on three control performance monitoring topics for the nonlinear systems: i) Controller assessment of a class of nonlinear systems: The use of autoregressive moving average (ARMA) models to assess the control loop performance for linear systems is well known. Classes of nonlinear dynamic / stochastic systems for which a similar result can be obtained are established for SISO discrete systems. For these systems, the performance lower bounds can be estimated from closed-loop routine operating data using nonlinear autoregressive moving average with exogenous inputs (NARMAX) models. ii) Variance decomposition of nonlinear systems / time series: We develop a variance decomposition approach to quantify the effects of different sources of disturbances on the nonlinear dynamic / stochastic systems. A method, called ANOVA-like decomposition, is employed to achieve this variance decomposition. Modifications of ANOVA-like decomposition are proposed so that the NOVA-like decomposition can be used to deal with the time dependency and the initial condition. iii) Parameter uncertainty effects on the variance decomposition: For the variance decomposition in the second part, the model parameters are assumed to be exactly known. However, parameters of empirical or mechanistic models are uncertain. The uncertainties associated with parameters should be included when the model is used for variance analysis. General solutions of the parameter uncertainty effects on the variance decomposition for the general nonlinear systems are proposed. Analytical solutions of the parameter uncertainty effects on the variance decomposition are provided for models with linear parameters. / Thesis (Ph.D, Chemical Engineering) -- Queen's University, 2007-10-17 16:02:26.376 / This work was sponsored by NSERC Discovery, NSERC Equipment, Shell Global Solutions, OGSST and QGA

Semidefinite programming is a powerful modeling tool for a wide range of optimization and feasibility problems. Its prevalent use in practice relies on the fact that a (nearly) optimal solution of a semidefinite program can be obtained efficiently in both theory and practice, provided that the semidefinite program and its dual satisfy the Slater condition. This thesis focuses on the situation where the Slater condition (i.e., the existence of positive definite feasible solutions) does not hold for a given semidefinite program; the failure of the Slater condition often occurs in structured semidefinite programs derived from various applications. In this thesis, we study the use of the facial reduction technique, originally proposed as a theoretical procedure by Borwein and Wolkowicz, as a preprocessing technique for semidefinite programs. Facial reduction can be used either in an algorithmic or a theoretical sense, depending on whether the structure of the semidefinite program is known a priori. The main contribution of this thesis is threefold. First, we study the numerical issues in the implementation of the facial reduction as an algorithm on semidefinite programs, and argue that each step of the facial reduction algorithm is backward stable. Second, we illustrate the theoretical importance of the facial reduction procedure in the topic of sensitivity analysis for semidefinite programs. Finally, we illustrate the use of facial reduction technique on several classes of structured semidefinite programs, in particular the side chain positioning problem in protein folding.