In recent years there has been increased research activity in the area of Func- tional Data Analysis. Methodology from finite dimensional multivariate analysis has been extended to the functional data setting giving birth to Functional ANOVA, Functional Principal Components Analysis, etc. In particular, some studies have pro- posed inferential techniques for various functional models that have connections to well known areas such as mixed-effects models or spline smoothing. The methodol- ogy used in these cases is computationally intensive since it involves the estimation of coefficients in linear models, adaptive selection of smoothing parameters, estimation of variances components, etc. This dissertation proposes a wide-ranging modeling framework that includes many functional linear models as special cases. Three widely used tools are con- sidered: mixed-effects models, penalized least squares, and Bayesian prediction. We show that, in certain important cases, the same numerical answer is obtained for these seemingly different techniques. In addition, under certain assumptions, an applica- tion of a Kalman filter algorithm is shown to improve the order of computations, by two orders of magnitude, for point and interval estimates (with n being the sample size). A functional data analysis setting is used to exemplify our results.

No / Since batch reactors are generally applied to produce a wide variety of specialty products, there is a great deal of interest to enhance batch operation to achieve high quality and purity product while minimizing the conversion of undesired by-product. The use of process optimization in the control of batch reactors presents a useful tool for operating batch reactors efficiently and optimally. In this work, we develop an approach, based on an on-line dynamic optimization strategy, to modify optimal temperature set point profile for batch reactors. Two different optimization problems concerning batch operation: maximization of product concentration and minimization of batch time, are formulated and solved using a sequential optimization approach. An Extended Kalman Filter (EKF) is incorporated into the proposed approach in order to update current states from their delayed measurement and to estimate unmeasurable state variables. A nonlinear model-based controller: generic model control algorithm (GMC) is applied to drive the temperature of the batch reactor to follow the desired profile. A batch reactor with complex exothermic reaction scheme is used to demonstrate the effectiveness of the proposed approach. The simulation results indicate that with the proposed strategy, large improvement in batch reactor performance, in term of the amount of a desired product and batch operation time, can be achieved compared to the method where the optimal temperature set point is pre-determined.