Geodesic
On synthesizing impulse controls and the theory of fast controls
Informatics and Automation, Differential equations and topology. I, Tome 268 (2010), pp. 215-230

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We describe the theory of feedback control in the class of impulse-type inputs which allow higher derivatives of delta functions. We provide solutions based on Hamiltonian techniques in the dynamic programming form. Further we describe physically realizable approximations of the “ideal” impulse-type solutions by bounded functions which may also serve as “fast” feedback controls that solve the target control problem in arbitrarily small time. 
@article{TRSPY_2010_268_a13,
     author = {A. B. Kurzhanski},
     title = {On synthesizing impulse controls and the theory of fast controls},
     journal = {Informatics and Automation},
     pages = {215--230},
     publisher = {mathdoc},
     volume = {268},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2010_268_a13/}
}
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A. B. Kurzhanski. On synthesizing impulse controls and the theory of fast controls. Informatics and Automation, Differential equations and topology. I, Tome 268 (2010), pp. 215-230. http://geodesic.mathdoc.fr/item/TRSPY_2010_268_a13/