Geodesic
The Topological Structure of the Phase Portrait of a~Typical Fiber of Optimal Synthesis for Chattering Problems
Informatics and Automation, Differential equations. Certain mathematical problems of optimal control, Tome 233 (2001), pp. 125-152.

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This paper continues the program of optimal chattering synthesis design for problems with a multidimensional control. In contrast to the paper where the case of independent constraints on different components of the control was explored, here the control takes its values in a two-dimensional simplex. In this case, one again deals with integral varieties like the Reeb foliation; however, the inclusion of these varieties in the phase space is much more exotic. This paper is devoted to the description of the corresponding phase portrait. 
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M. I. Zelikin; N. B. Melnikov; R. Hildebrand. The Topological Structure of the Phase Portrait of a~Typical Fiber of Optimal Synthesis for Chattering Problems. Informatics and Automation, Differential equations. Certain mathematical problems of optimal control, Tome 233 (2001), pp. 125-152. http://geodesic.mathdoc.fr/item/TRSPY_2001_233_a4/

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