Optimal open/closed-loop control for systems with distributed parameter
An optimal control problem for multi-dimensional structures described by a system of partial differential equations is considered. A combined open- and closed-loop mechanism is incorporated into the formulation of the problem and a general method of solution is presented. Two performance indices are...
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| Published in: | Journal of the Franklin Institute Vol. 332; no. 1; pp. 5 - 19 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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1995
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| ISSN: | 0016-0032, 1879-2693 |
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| Abstract | An optimal control problem for multi-dimensional structures described by a system of partial differential equations is considered. A combined open- and closed-loop mechanism is incorporated into the formulation of the problem and a general method of solution is presented. Two performance indices are introduced and minimized with respect to the open-loop control functions and the closed-loop control parameters. The optimality condition for the open-loop control is derived in form of the integral equations by using the methods of eigenfunction expansion and variational calculus. The closed-loop control parameters are numerically determined from the minimization of the energy of the system subject to a constraint on the maximum amount of closed-loop control force that can be applied. The proposed approach is applied to a shear deformable beam excited by an initial disturbance. An explicit solution of the problem is obtained and numerical results are given to investigate the effectiveness of the proposed control mechanism. |
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| AbstractList | An optimal control problem for multi-dimensional structures described by a system of partial differential equations is considered. A combined open- and closed-loop mechanism is incorporated into the formulation of the problem and a general method of solution is presented. Two performance indices are introduced and minimized with respect to the open-loop control functions and the closed-loop control parameters. The optimality condition for the open-loop control is derived in form of the integral equations by using the methods of eigenfunction expansion and variational calculus. The closed-loop control parameters are numerically determined from the minimization of the energy of the system subject to a constraint on the maximum amount of closed-loop control force that can be applied. The proposed approach is applied to a shear deformable beam excited by an initial disturbance. An explicit solution of the problem is obtained and numerical results are given to investigate the effectiveness of the proposed control mechanism. |
| Author | Yürekli, Osman Sadek, Ibrahim S. |
| Author_xml | – sequence: 1 givenname: Ibrahim S. surname: Sadek fullname: Sadek, Ibrahim S. organization: Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia – sequence: 2 givenname: Osman surname: Yürekli fullname: Yürekli, Osman organization: Mathematics and Computer Science Department, Ithaca College, Ithaca, NY 14850, U.S.A |
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| Cites_doi | 10.1137/0325078 10.1061/(ASCE)0733-9399(1983)109:3(691) 10.1002/oca.4660140303 10.1093/imamci/6.2.199 10.1177/058310248501701005 10.1093/imamci/7.1.59 10.1093/imamci/6.2.217 10.1007/BF00938631 10.1016/0141-0296(88)90033-8 10.1007/BF00932903 10.1061/JSDEAG.0003280 10.1109/TAC.1982.1102953 10.1002/oca.4660040409 10.1016/0016-0032(92)90029-G 10.1016/0022-460X(84)90274-8 10.1016/0016-0032(87)90376-0 10.1016/0022-460X(92)90693-R |
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| References | Vol. 17, pp. 7–16. Sadek, Adali, Sloss, Bruch (BIB10) 1992; Vol. 329 Sadek, Sloss, Bruch, Adali (BIB4) 1987; Vol. 324 Bruch, Sadek, Adali, Sloss (BIB9) 1993; Vol. 14 Zuk (BIB12) 1980 Meirovitch, Silverberg (BIB16) 1983; Vol. 4 Adali, Bruch, Sadek, Sloss (BIB7) 1990; Vol. 156 A. M. Reinhorn and G. D. Manalis, “Current state of knowledge on structural control” H. O. Fattorini, “The maximum principle for nonlinear nonconvex systems in infinite dimensional spaces”, Private communication. Hrovat, Barak, Rabins (BIB11) 1983; Vol. 109 Sadek, Esfandiari (BIB21) 1990; Vol. 7 Balas (BIB1) 1982; Vol. AC-27 Soong (BIB14) 1988; Vol. 10 Sloss, Bruch, Sadek (BIB18) 1989; Vol. 6 Yao (BIB13) 1972; Vol. 98 Sadek, Sloss, Bruch, Adalí (BIB3) 1986; Vol. 50 Balas (BIB2) 1978; Vol. 25 Bruch, Sloss, Adali, Sadek (BIB8) 1990; Vol. 38 Meirovitch, Silverberg (BIB19) 1989; Vol. 97 Kim, Renardy (BIB20) 1987; Vol. 25 Sloss, Sadek, Bruch, Adali (BIB5) 1989; Vol. 6 Lions (BIB15) 1971 Sloss (10.1016/0016-0032(94)00018-F_BIB18) 1989; Vol. 6 Bruch (10.1016/0016-0032(94)00018-F_BIB8) 1990; Vol. 38 Sloss (10.1016/0016-0032(94)00018-F_BIB5) 1989; Vol. 6 10.1016/0016-0032(94)00018-F_BIB6 Adali (10.1016/0016-0032(94)00018-F_BIB7) 1990; Vol. 156 Bruch (10.1016/0016-0032(94)00018-F_BIB9) 1993; Vol. 14 Yao (10.1016/0016-0032(94)00018-F_BIB13) 1972; Vol. 98 Soong (10.1016/0016-0032(94)00018-F_BIB14) 1988; Vol. 10 Kim (10.1016/0016-0032(94)00018-F_BIB20) 1987; Vol. 25 Sadek (10.1016/0016-0032(94)00018-F_BIB21) 1990; Vol. 7 Lions (10.1016/0016-0032(94)00018-F_BIB15) 1971 Balas (10.1016/0016-0032(94)00018-F_BIB2) 1978; Vol. 25 Hrovat (10.1016/0016-0032(94)00018-F_BIB11) 1983; Vol. 109 Sadek (10.1016/0016-0032(94)00018-F_BIB4) 1987; Vol. 324 Meirovitch (10.1016/0016-0032(94)00018-F_BIB19) 1989; Vol. 97 Sadek (10.1016/0016-0032(94)00018-F_BIB10) 1992; Vol. 329 Meirovitch (10.1016/0016-0032(94)00018-F_BIB16) 1983; Vol. 4 10.1016/0016-0032(94)00018-F_BIB17 Balas (10.1016/0016-0032(94)00018-F_BIB1) 1982; Vol. AC-27 Sadek (10.1016/0016-0032(94)00018-F_BIB3) 1986; Vol. 50 Zuk (10.1016/0016-0032(94)00018-F_BIB12) 1980 |
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