Geodesic
Numerical optimization of time-dependent multidimensional systems under polyhedral constraints
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 4, pp. 617-636

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The construction of open-loop and closed-loop optimal controls of linear time-dependent systems with multiple inputs is considered when the controls satisfy polyhedral constraints. The problem is solved using linear programming methods that are adapted with regard for the specific features of the model and the constraints. The optimal controls are found by a dual method. The feedback optimal controls are synthesized using an optimal regulator, which is based on the dual method. This enables us to compute the current values of the optimal feedback in real time for every particular control process. The efficiency of the proposed methods is illustrated using a fifth-order optimal control as an example. 
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     title = {Numerical optimization of time-dependent multidimensional systems under polyhedral constraints},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {617--636},
     publisher = {mathdoc},
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     number = {4},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_4_a5/}
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R. Gabasov; N. M. Dmitruk; F. M. Kirillova. Numerical optimization of time-dependent multidimensional systems under polyhedral constraints. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 4, pp. 617-636. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_4_a5/