Topological Obstructions To Stability And Stabilization
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Topological Obstructions to Stability and Stabilization
This open access book provides a unified overview of topological obstructions to the stability and stabilization of dynamical systems defined on manifolds and an overview that is self-contained and accessible to the control-oriented graduate student. The authors review the interplay between the topology of an attractor, its domain of attraction, and the underlying manifold that is supposed to contain these sets. They present some proofs of known results in order to highlight assumptions and to develop extensions, and they provide new results showcasing the most effective methods to cope with these obstructions to stability and stabilization. Moreover, the book shows how Borsuk’s retraction theory and the index-theoretic methodology of Krasnosel’skii and Zabreiko underlie a large fraction of currently known results. This point of view reveals important open problems, and for that reason, this book is of interest to any researcher in control, dynamical systems, topology, or related fields.
Advanced Control Methods for Industrial Processes
Author: Pablo A. López-Pérez
language: en
Publisher: John Wiley & Sons
Release Date: 2025-06-09
A detailed introduction to mathematical models for new and established control engineers Control engineering is a system that helps us understand electrical, physical, chemical, and biochemical systems through the use of mathematical modeling, using inputs, outputs, and simulations. These experimental platforms are implemented in most systems of modern advanced control engineering. Advanced Control Methods for Industrial Processes provides a solid grounding in traditional control techniques. It emphasizes practical application methods alongside the underlying theory and core instrumentation. Each chapter discusses the full profile of the technology covered, from the field layer and control layer to its implementation. It also includes the interfaces for advanced control systems: between controllers and systems theory, between different layers, and between operators-systems. Through an emphasis on the practical issues of components, devices, and hardware circuits, the book offers working principles and operation mechanisms that allow an engineer to put theory into practice for the advanced control techniques. Advanced Control Methods for Industrial Processes readers will also find: A practical overview on advanced control methods applied to real-time and in-silico systems Specific parameters, install procedures, calibration and configuration methodologies necessary to conduct the relevant models Clear insights into the necessary mathematical models Tutorial material to facilitate the understanding of core concepts Advanced Control Methods for Industrial Processes is an ideal companion for process engineers, control engineers, and chemists in industry.
Constructive Approaches to Submanifold Stabilization
Author: Jan Maximilian Montenbruck
language: en
Publisher: Logos Verlag Berlin GmbH
Release Date: 2016-07-15
Submanifold stabilization is the problem of steering a quantity towards a desired submanifold of the space in which it evolves. This is done by controlling the system producing the quantity in an appropriate fashion. In this thesis, methods for explicitly constructing controllers which solve submanifold stabilization problems are proposed. To this end, three distinct approaches are pursued: For control systems modeled by input-affne differential equations, a construction for turning the submanifold into an asymptotically stable invariant set is presented. For controllers which shall stabilize the submanifold with minimal energy consumption, the structure of such optimal controls is investigated. For control systems modeled by input-output relationships, a framework for bounding the integral deviation of the output from the submanifold is proposed.