Geodesic
Singular Sets of Extremal Controls in Optimal Control Problems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal control and differential equations, Tome 304 (2019), pp. 252-256.

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Some optimal control problems are considered with an integral functional (to be minimized), fixed motion time of the controlled object, and free right endpoint. In these problems, the set of degeneracy points of the Pontryagin maximum principle (singular set) for the extremal control is studied. For a wide class of linear control systems, sufficient conditions are obtained under which the singular set is either empty or consists of a finite set of points. In addition, an example of a control system is constructed in which the singular set has a very general form. 
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     author = {M. S. Nikol'skii},
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M. S. Nikol'skii. Singular Sets of Extremal Controls in Optimal Control Problems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal control and differential equations, Tome 304 (2019), pp. 252-256. http://geodesic.mathdoc.fr/item/TM_2019_304_a15/

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