Hdr Année : 2025

Modelling and Operating Physical Systems with Geometrical Methods : an Interdisciplinary Inquiry

Résumé

This manuscript provides a synthetic overview of my research work since the award of my PhD degree in 2004. It includes the most important journal and congress papers of this period, which are cited according to their place in the list given in Appendix A. For this volume I have selected the most important results where my personal contribution has been most significant, abandoning the idea of describing the integrity of my publications. The document is divided into two parts: Physical Process Operation and Physical Process Modelling. These parts are almost independent and can be read separately. Each principal section starts with a list of the related publications and ends with a display of the first page of these publications. Part I is structured around applications of Optimal Control to physical systems of different scales. It starts with Chapter 1, which provides a short overview of the main concepts of Optimal Control Theory: Pontryagin’s Maximum Principle, normal and abnormal extremals, criteria of local and global optimality. Chapter 2 describes the results of application of Optimal Control theory to the analysis of the extremals of quantum systems and to the rigid body motion. Chapter 3 describes the Optimal Control Problem of batch distillation. Part II focuses on physical process modelling and simulation results. It is divided into three chapters of unequal length, reflecting the spectre of my scientific interests in this domain. Thus, Chapter 4 provides the essential introduction into the novel geometrical approach for the analysis and computation of different types of diagrams arising in the Distillation Theory and Phase separation. Chapter 5 introduces the concepts Non - equilibrium Thermodynamics in relation to nature inspired chemical engineering processes. The manuscript concludes with Part III that puts into a perspective the presented results in order to outline the further short - and long - term development of my research activity.

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tel-05296466 , version 1 (03-10-2025)

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  • HAL Id : tel-05296466 , version 1

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Nataliya Shcherbakova. Modelling and Operating Physical Systems with Geometrical Methods : an Interdisciplinary Inquiry. Optimization and Control [math.OC]. Institut National Polytechnique De Toulouse, 2025. ⟨tel-05296466⟩
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