Geodesic
The Topological Structure of the Phase Portrait of a~Typical Fiber of Optimal Synthesis for Chattering Problems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, 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. 
@article{TM_2001_233_a4,
     author = {M. I. Zelikin and N. B. Melnikov and R. Hildebrand},
     title = {The {Topological} {Structure} of the {Phase} {Portrait} of {a~Typical} {Fiber} of {Optimal} {Synthesis} for {Chattering} {Problems}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {125--152},
     publisher = {mathdoc},
     volume = {233},
     year = {2001},
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     url = {http://geodesic.mathdoc.fr/item/TM_2001_233_a4/}
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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. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations. Certain mathematical problems of optimal control, Tome 233 (2001), pp. 125-152. http://geodesic.mathdoc.fr/item/TM_2001_233_a4/