Geodesic
An analytic-numerical method for the construction of the reference law of operation for a class of mechanical controlled systems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 4, pp. 625-632

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An analytic-numerical method for the construction of a reference law of operation for a class of dynamic systems describing vibrations in controlled mechanical systems is proposed. By the reference law of operation of a system, we mean a law of the system motion that satisfies all the requirements for the quality and design features of the system under permanent external disturbances. As disturbances, we consider polyharmonic functions with known amplitudes and frequencies of the harmonics but unknown initial phases. For constructing the reference law of motion, an auxiliary optimal control problem is solved in which the cost function depends on a weighting coefficient. The choice of the weighting coefficient ensures the design of the reference law. Theoretical foundations of the proposed method are given. 
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     author = {A. D. Mizhidon and K. A. Mizhidon},
     title = {An analytic-numerical method for the construction of the reference law of operation for a class of mechanical controlled systems},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {625--632},
     publisher = {mathdoc},
     volume = {57},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_4_a3/}
}
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A. D. Mizhidon; K. A. Mizhidon. An analytic-numerical method for the construction of the reference law of operation for a class of mechanical controlled systems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 4, pp. 625-632. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_4_a3/