Geodesic
On the time-optimal problem for three- and four-dimensional control systems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematical control theory and differential equations, Tome 277 (2012), pp. 192-198

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The paper is devoted to the time-optimal problem for three- and four-dimensional nonlinear control systems with one-dimensional control. We obtain sufficient conditions for a time-optimal control to be equivalent (in the Lebesgue sense) to a piecewise constant control that is also optimal, has a finite number of discontinuity points, and takes only extreme values. Such optimal controls are called bang-bang solutions and are of considerable interest in control theory and its applications. 
@article{TM_2012_277_a12,
     author = {M. S. Nikol'skii},
     title = {On the time-optimal problem for three- and four-dimensional control systems},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {192--198},
     publisher = {mathdoc},
     volume = {277},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2012_277_a12/}
}
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M. S. Nikol'skii. On the time-optimal problem for three- and four-dimensional control systems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematical control theory and differential equations, Tome 277 (2012), pp. 192-198. http://geodesic.mathdoc.fr/item/TM_2012_277_a12/