Geodesic
Minimization of Degenerate Integral Quadratic Functionals
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal Control and Differential Games, Tome 315 (2021), pp. 108-127

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We present a method for finding the infimum of a degenerate integral quadratic functional by passing from a given functional to another quadratic functional that is nondegenerate with respect to some new control. The minimum point of the latter can be found by a standard procedure. This point corresponds to a minimizing sequence for the original functional. The advantage of this method over the well-known regularization method (addition of a small nondegenerate term) is that the latter requires solving a parametric series of problems with a vanishingly small additional term, while our method deals with a single problem. 
@article{TM_2021_315_a7,
     author = {A. V. Dmitruk and N. A. Manuilovich},
     title = {Minimization of {Degenerate} {Integral} {Quadratic} {Functionals}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {108--127},
     publisher = {mathdoc},
     volume = {315},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2021_315_a7/}
}
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A. V. Dmitruk; N. A. Manuilovich. Minimization of Degenerate Integral Quadratic Functionals. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal Control and Differential Games, Tome 315 (2021), pp. 108-127. http://geodesic.mathdoc.fr/item/TM_2021_315_a7/