This thesis develops approximate dynamic programming (ADP) strategies suitable for process control problems aimed at overcoming the limitations of MPC, which are the potentially exorbitant on-line computational requirement and the inability to consider the future interplay between uncertainty and estimation in the optimal control calculation. The suggested approach solves the DP only for the state points visited by closed-loop simulations with judiciously chosen control policies. The approach helps us combat a well-known problem of the traditional DP called 'curse-of-dimensionality,' while it allows the user to derive an improved control policy from the initial ones. The critical issue of the suggested method is a proper choice and design of function approximator. A local averager with a penalty term is proposed to guarantee a stably learned control policy as well as acceptable on-line performance. The thesis also demonstrates versatility of the proposed ADP strategy with difficult process control problems. First, a stochastic adaptive control problem is presented. In this application an ADP-based control policy shows an "active" probing property to reduce uncertainties, leading to a better control performance. The second example is a dual-mode controller, which is a supervisory scheme that actively prevents the progression of abnormal situations under a local controller at their onset. Finally, two ADP strategies for controlling nonlinear processes based on input-output data are suggested. They are model-based and model-free approaches, and have the advantage of conveniently incorporating the knowledge of identification data distribution into the control calculation with performance improvement.

This thesis considers the problem of performance modeling, analysis and control of capacitated re-entrant lines. Specifically, the first part of the thesis develops an analytical framework for the modeling, analysis and control of capacitated re-entrant lines, which is based on Generalized Stochastic Petri nets (GSPN) framework. The corresponding scheduling problem is systematically formulated, and the structure of the optimal policy is characterized and compared to that identified for "traditional" re-entrant lines. The second part of thesis addresses the problem of developing a systematic and computationally effective method for computing the optimal scheduling policy for any given configuration of capacitated re-entrant line. Specifically, the underlying scheduling problem is transformed to a Markov Decision Process (MDP) problem and an algorithm that systematically generates the MDP formulation for any given fab configuration is developed. The third part of thesis develops an effective approximating scheme based on the Neuro-Dynamic Programming (NDP) theory. In its general definition, the NDP method seeks the approximation of the optimal relative value function of the underlying MDP formulation by a parameterized function. Hence, an approximating structure for the considered problem is proposed and the quality of the generated approximations is systematically assessed. More specifically, this part of the thesis develops a set of "feature" functions and the mathematical apparatus necessary to evaluate the considered approximating scheme through a numerical experiment. The obtained results indicate that good quality approximations can be achieved by considering a set of features that characterize the distribution of the running process instances to the various processing stages and their lower order interactions. The last part of the thesis exploits the performance models developed in its earlier parts in order to provide an analytical characterization of the optimality of various deadlock resolution strategies for Markovian resource allocation systems under the objective of maximizing throughput.