Title page for ETD etd-050205-152657

Document Type	thesis
Author Name	Leising, Sophie
URN	etd-050205-152657
Title	Nonlinear controller synthesis for complex chemical and biochemical reaction systems
Degree	MS
Department	Chemical Engineering
Advisors	Nikolaos Kazantzis, Advisor David DiBiasio, Department Head
Keywords	model predictive control discrete-time model continuous-time model nonlinear systems Lyapunov design
Date of Presentation/Defense	2005-05-02
Availability	restricted
Abstract The present research study is comprised of two main parts. The first part aims at the development of a systematic system-theoretic framework that allows the derivation of optimal chemotherapy protocols for HIV patients. The proposed framework is conceptually aligned with a notion of continuous-time model predictive control of nonlinear dynamical systems, and results in an optimal way to control viral replication, while maintaining low antiretroviral drug toxicity levels. This study is particularly important because it naturally integrates powerful system-theoretic techniques into a clinically challenging problem with worldwide implications, namely the one of developing chemotherapy patterns for HIV patients that are effective and do not induce adverse side-effects. The second part introduces a new digital controller design methodology for nonlinear (bio)chemical processes, that reflects contemporary necessities in the practical implementation of advanced process control strategies via digital computer-based algorithms. The proposed methodology relies on the derivation of an accurate sampled-data representation of the process, and the subsequent formulation and solution to a nonlinear digital controller synthesis problem. In particular, for the latter two distinct approaches are followed that are both based on the methodological principles of Lyapunov design and rely on a short-horizon model-based prediction and optimization of the rate of “energy dissipation” of the system, as it is realized through the time derivative of an appropriately selected Lyapunov function. First, the Lyapunov function is computed by solving the discrete Lyapunov matrix equation. In the second approach however, it is computed by solving a Zubov-like functional equation based on the system’s drift vector field. Finally, two examples of a chemical and a biological reactor that both exhibit nonlinear behavior illustrate the main features of the proposed digital controller design method.
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