TY - JOUR
T1 - Optimal control of vibrations of a dynamic Gao beam in contact with a reactive foundation
AU - Sun, Bing
N1 - Publisher Copyright:
© 2016 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2017/4/4
Y1 - 2017/4/4
N2 - In this paper, we investigate the optimal control of vibrations of a nonlinear viscoelastic beam, which is acted upon by a horizontal traction, that may come in contact with a reactive foundation underneath it. By the Dubovitskii and Milyutin functional analytical approach, we derive the Pontryagin maximum principle of the system governed by the Gao beam equation. And the first-order necessary optimality condition is presented for the optimal control problem in fixed final horizon case. Finally, we also sketch the numerical solution based on the obtained theoretical results.
AB - In this paper, we investigate the optimal control of vibrations of a nonlinear viscoelastic beam, which is acted upon by a horizontal traction, that may come in contact with a reactive foundation underneath it. By the Dubovitskii and Milyutin functional analytical approach, we derive the Pontryagin maximum principle of the system governed by the Gao beam equation. And the first-order necessary optimality condition is presented for the optimal control problem in fixed final horizon case. Finally, we also sketch the numerical solution based on the obtained theoretical results.
KW - Gao beam
KW - Nonlinear viscoelastic beam
KW - maximum principle
KW - necessary optimality condition
KW - optimal control
UR - http://www.scopus.com/inward/record.url?scp=84988703671&partnerID=8YFLogxK
U2 - 10.1080/00207721.2016.1236994
DO - 10.1080/00207721.2016.1236994
M3 - Article
AN - SCOPUS:84988703671
SN - 0020-7721
VL - 48
SP - 1084
EP - 1091
JO - International Journal of Systems Science
JF - International Journal of Systems Science
IS - 5
ER -