Geodesic
Linear problem of tracking a~given motion under an integral constraint on control
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and topology. II, Tome 271 (2010), pp. 181-186

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We consider the problem of optimally tracking a given vector function by means of a generalized projection of the trajectory of a linear controlled object with an integral constraint on the control. The deviation from a given motion is measured in the metric of the space $C^m[0,T]$ of continuous vector functions of appropriate dimension $m$. We describe a constructive method for solving this optimization problem with a given accuracy. 
@article{TM_2010_271_a12,
     author = {M. S. Nikol'skii},
     title = {Linear problem of tracking a~given motion under an integral constraint on control},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {181--186},
     publisher = {mathdoc},
     volume = {271},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2010_271_a12/}
}
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M. S. Nikol'skii. Linear problem of tracking a~given motion under an integral constraint on control. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and topology. II, Tome 271 (2010), pp. 181-186. http://geodesic.mathdoc.fr/item/TM_2010_271_a12/