Geodesic
Memoryless solution to the optimal control problem for linear systems with delayed input
Kybernetika, Tome 49 (2013) no. 4, pp. 568-589.

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This note investigates the optimal control problem for a time-invariant linear systems with an arbitrary constant time-delay in in the input channel. A state feedback is provided for the infinite horizon case with a quadratic cost function. The solution is memoryless, except at an initial time interval of measure equal to the time-delay. If the initial input is set equal to zero, then the optimal feedback control law is memoryless from the beginning. Stability results are established for the closed loop system, in the scalar case.
Classification : 62A10, 93E12
Keywords: time-delay systems; optimal control; stability 
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     title = {Memoryless solution to the optimal control problem for linear systems with delayed input},
     journal = {Kybernetika},
     pages = {568--589},
     publisher = {mathdoc},
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     number = {4},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2013__49_4_a4/}
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Carravetta, Francesco; Palumbo, Pasquale; Pepe, Pierdomenico. Memoryless solution to the optimal control problem for linear systems with delayed input. Kybernetika, Tome 49 (2013) no. 4, pp. 568-589. http://geodesic.mathdoc.fr/item/KYB_2013__49_4_a4/