Differential-algebraic equations are the most natural way to mathematically model many complex systems in science and engineering. Once the model is derived, it is important to optimize the design parameters and control it in the most robust and efficient way to maximize performance.
This book presents the latest theory and numerical methods for the optimal control of differential-algebraic equations. Readers will find the following features presented in a readable fashion so the results are accessible to the widest audience: the most recent theory, written by leading experts from a number of academic and nonacademic areas and departments, several state-of-the-art numerical methods, and real-world applications.
Audience: This book is intended for applied mathematicians, engineers, and computational scientists from a variety of disciplines who are interested in the optimal control of problems. It will be of interest to those developing methods and theory and those working on real-world applications, especially in control and chemical and mechanical engineering.
Contents: Chapter 1: DAEs, Control, and Optimization; Chapter 2: Regularization of Linear and Nonlinear Descriptor Systems; Chapter 3: Notes on Linearization of DAEs and on Optimization with Differential-Algebraic Constraints; Chapter 4: Spectra and Leading Directions for Linear DAEs; Chapter 5: StratiGraph Tool: Matrix Stratifications in Control Applications; Chapter 6: Descriptor System Techniques in Solving H2/Infinity-Optimal Fault Detection and Isolation Problems; Chapter 7: Normal Forms, High-Gain, and Funnel Control for Linear Differential-Algebraic Systems; Chapter 8: Linear-Quadratic Optimal Control Problems with Switch Points and a Small Parameter; Chapter 9: Mixed-Integer DAE Optimal Control Problems: Necessary Conditions and Bounds; Chapter 10: Optimal Control of a Delay PDE; Chapter 11: Direct Transcription with Moving Finite Elements; Chapter 12: Solving Parameter Estimation Problems with SOCX; Chapter 13: Control of Integrated Chemical Process Systems Using Underlying DAE Models; Chapter 14: DMPC for Building Temperature Regulation; Chapter 15: Dynamic Regularization, Level Set Shape Optimization, and Computed Myography; Chapter 16: The Application of Pontryagin s Minimum Principle for Endpoint Optimization of Batch Processes