Abstract
This chapter deals with the geometry of chattering arcs near the manifold of singular extremals of order greater than or equal to 3. It appears that in this case there exists a number of two-dimensional piecewise smooth manifolds which represent α- and ω-limit sets of all chattering trajectories in orbit space. The main result of the chapter is a solution of the three-dimensional Fuller problem. Besides that, we state a number of verisimilar conjectures concerning the problems of higher order. The theoretical and numerical foundations of these conjectures are presented.
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© 1994 Birkhäuser Boston
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Zelikin, M.I., Borisov, V. (1994). Higher Order Singular Extremals. In: Theory of Chattering Control. Systems & Control: Foundations & Applications. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2702-1_5
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DOI: https://doi.org/10.1007/978-1-4612-2702-1_5
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-7634-0
Online ISBN: 978-1-4612-2702-1
eBook Packages: Springer Book Archive