Topological Obstructions to Stability and Stabilization History, Recent Advances and Open Problems

• Հիմնական հեղինակ: Jongeneel, Wouter (auth)
• Այլ հեղինակներ: Moulay, Emmanuel (auth)
• Ձևաչափ: Էլեկտրոնային Գրքի գլուխ
• Լեզու: անգլերեն
• Հրապարակվել է: Cham Springer Nature 2023
• Շարք: SpringerBriefs in Electrical and Computer Engineering; SpringerBriefs in Control, Automation and Robotics
• Խորագրեր: Automatic control engineering; Nonlinear science; Dynamics & vibration; Topology; Artificial intelligence; Algorithms & data structures; Control Systems; Feedback Control; Algebraic Topology; Differential Topology; Index Theory; Retractive Theory; Topological Obstruction
• Առցանց հասանելիություն: OAPEN Library: download the publication; OAPEN Library: description of the publication

Ամփոփում

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.

Ֆիզիկական նկարագրություն

1 electronic resource (132 p.)

ISBN

978-3-031-30133-9
9783031301339
9783031301322

Հասանելի

Open Access