Differential-algebraic equations (DAEs) are the most natural way to mathematically model many complex systems in science and engineering. This book provides a guide to the theory and practice of modelling with DAEs. In particular, the reader will learn to maximise the performance of their models by optimising the design parameters. Presented within are cutting-edge theory and state-of-the-art numerical methods for the optimal control of differential-algebraic equations, alongside real-world applications of the results. This accessible treatment of the subject, written by leading experts, is suitable for applied mathematicians, engineers and computational scientists from a variety of disciplines. It will be of interest to those developing theory and those working on real-world applications, especially in the optimal control of problems in chemical and mechanical engineering.
Lorenz T. Biegler is the Bayer Professor of Chemical Engineering at Carnegie Mellon University and a Fellow of the American Institute of Chemical Engineers. Stephen L. Campbell is a Distinguished Professor of Mathematics at North Carolina State University. He is a Fellow of the Institute of Electrical and Electronics Engineers (IEEE) and the Society for Industrial and Applied Mathematics (SIAM). Volker Mehrmann is a Professor of Mathematics at TU Berlin. He is a member of acatech (the German Academy of Science and Engineering) and is currently president of GAMM (the German Society for Applied Mathematics and Mechanics).
1. DAEs, control, and optimization; 2. Regularization of linear and nonlinear descriptor systems; 3. Notes on linearization of DAEs and on optimization with differential-algebraic constraints; 4. Spectra and leading directions for linear DAEs; 5. StratiGraph tool: matrix stratifications in control applications; 6. Descriptor system techniques in solving H / -optimal fault detection and isolation problems; 7. Normal forms, high-gain, and funnel control for linear differential-algebraic systems; 8. Linear-quadratic optimal control problems with switch points and a small parameter; 9. Mixed-integer DAE optimal control problems: necessary conditions and bounds; 10. Optimal control of a delay PDE; 11. Direct transcription with moving finite elements; 12. Solving parameter estimation problems with SOCX; 13. Control of integrated chemical process systems using underlying DAE models; 14. DMPC for building temperature regulation; 15. Dynamic regularization, level set shape optimization, and computed myography; 16. The application of Pontryagin's minimum principle for endpoint optimization of batch processes.