| Автор | Sadek, I.S. |
| Автор | Sloss, J.M. |
| Автор | Adali, S. |
| Автор | Bruch, J.C. |
| Дата выпуска | 1998 |
| dc.description | The problem of characterizing optimal controls for a class of damped distributed parameter systems is considered. The system is governed by a variable-coefficient, linear-partial differential equation involving up to second-order time derivatives and up to fourth-order space derivatives of the state variable. Pointwise controllers extending over the spatial region occupied by the system are considered. A class of performance indexes is introduced that includes convex functions of the state velocity, spatial state derivatives, and the control force. The state variable and its derivatives are evaluated at a preassigned terminal time. A maximum principle is given that facilitates the determination of the optimal control, which is shown to be unique. The use of the maximum principle is demonstrated by determining the optimal pointwise control of the vibrations for a uniform undamped Euler-Bernoulli beam. |
| Издатель | Sage Publications |
| Тема | Maximum principle |
| Тема | spatially distributed pointwise controller |
| Тема | Euler-Bernoulli beam |
| Тема | convex performance index |
| Название | A Maximum Principle for Optimal Control Using Spatially Distributed Pointwise Controllers |
| Тип | Journal Article |
| DOI | 10.1177/107754639800400406 |
| Print ISSN | 1077-5463 |
| Журнал | Journal of Vibration and Control |
| Том | 4 |
| Первая страница | 445 |
| Последняя страница | 462 |
| Аффилиация | Sadek, I.S., Department of Mathematical Sciences, University of North Carolina, Wilmington, NC 28403, USA |
| Аффилиация | Sloss, J.M., Department of Mathematics, University of California, Santa Barbara, CA 93106, USA |
| Аффилиация | Adali, S., Department of Mechanical Engineering, University of Natal, Durban, South Africa |
| Аффилиация | Bruch, J.C., Department of Mechanical and Environmental Engineering, University of California, Santa Barbara, CA 93106, USA |
| Выпуск | 4 |
| Библиографическая ссылка | Adali, S., Sadek, I.S., Sloss, J.M., and Bruch, J.C. Jr., 1988, " Distributed control of layered orthotropic plates with damping," Optimal Control Applications and Methods9, 1-17. |
| Библиографическая ссылка | Ahmed, N.U. and Teo, K.L., 1981, Optimal Control of Distributed Parameter Systems, North Holland, New York. |
| Библиографическая ссылка | Balakrishnan, A.V., 1965, "Optimal control problems in banach spaces," SIAM Journal of Control, Series A 3(1), 152-180. |
| Библиографическая ссылка | Butkovskii, A.G., 1969, Distributed Control Systems, Elsevier , New York. |
| Библиографическая ссылка | Butkovskii, A.G. and Lerner, A.Y.A., 1960, "On the optimal control of systems with distributed parameters ," Automat. Remote Control 21(6), 472-477. |
| Библиографическая ссылка | Clarke, F., 1976, "The maximum principle under minimum hypotheses," SIAM Journal of Control and Optimization14, 1078-1091. |
| Библиографическая ссылка | Egorov, A.I., 1965a, "Optimal process in systems containing distributed parameter plants—I," Automat. Remote Control26(6), 972-988. |
| Библиографическая ссылка | Egorov, A.I., 1965b, "Optimal process in systems containing distributed parameter plants—II," Automat. Remote Control26(7), 1178-1187. |
| Библиографическая ссылка | Fattorini, H.O., 1985, "The maximum principle for nonlinear nonconvex systems in infinite dimensional spaces," Lecture Notes in Control and Information Sciences 75, Springer-Verlag, New York. |
| Библиографическая ссылка | Fond, S., 1979, "A dynamic programming approach to the maximum principle of distributed-parameter systems," Journal of Optimization Theory and Applications27, 583-601. |
| Библиографическая ссылка | Komkov, V., 1972, "Optimal control theory for the damping of vibrations of simple elastic systems," Lecture Notes in Mathematics , Springer-Verlag, New York. |
| Библиографическая ссылка | Komkov, V., 1973, "Formulation of Pontryagin's maximality principle in a problem of structural mechanics," International Journal of Control17, 455-464. |
| Библиографическая ссылка | Lions, J.L., 1971, Optimal Control of Systems Governed by Partial Differential Equations, Springer-Verlag, New York. |
| Библиографическая ссылка | Lions, J.L., 1992, "Pointwise control for distributed systems," in Control and Estimation in Distributed Parameter Systems, H. T. Banks, ed., Frontiers in Applied Mathematics 11, SIAM, Philadelphia, PA. |
| Библиографическая ссылка | Lukes, D.L. and Russell, D.L., 1969, "The quadratic criterion for distributed systems," SIAM Journal of Control 7, 101-121. |
| Библиографическая ссылка | Magrab, E.B., 1979, Vibrations of Elastic Structural Members, Sijthoff and Noordhoff, The Netherlands. |
| Библиографическая ссылка | Meirovitch, L., 1997, Principles and Techniques of Vibrations, Prentice Hall, Upper Saddle River, NJ. |
| Библиографическая ссылка | Russell, D.L., 1967, "Nonharmonic Fourier series in the control theory of distributed parameter systems," Journal of Mathematical Analysis and Application18, 542-560. |
| Библиографическая ссылка | Sadek, I.S. and Adali, S., 1993, "Control of the dynamic response of a damped membrane by distributed forces," Journal of Sound and Vibration 96, 391-406. |
| Библиографическая ссылка | Sadek, I.S., Sloss, J.M., Bruch, J.C. Jr., and Adali, S., 1986, "Optimal control of a Timoshenko beam by distributed forces ," Journal of Optimization Theory and Applications 50, 451-461. |
| Библиографическая ссылка | Sirazetdinov, T.K., 1964, "On the theory of optimal processes with distributed parameters ," Automat. Remote Control 25(4), 431-440. |
| Библиографическая ссылка | Sloss, J.M., Bruch, J.C. Jr., and Sadek, I.S., 1989, "A maximum principle for nonconservative self-adjoint systems," IMA Journal of Mathematical Control and Information6, 199-216. |
| Библиографическая ссылка | Stavroulakis, P., ed., 1983, Distributed Parameter Systems Theory: Part I. Control, Hutchinson Ross, Pittsburgh, PA. |
| Библиографическая ссылка | Stavroulakis, P. and Tzafestas, S., 1980, "Matrix minimum principle for distributed parameter control systems," International Journal of System Sciences 11, 793-801. |
| Библиографическая ссылка | Tzafestas, S.G., 1970, "Optimal distributed-parameter using classical variational theory," International Journal of Control12, 593-608. |
| Библиографическая ссылка | Tzafestas, S.G. and Stavroulakis, P. , 1983, "Recent advances in the study of distributed parameter systems," Journal of the Franklin Institute 315(516), 285-305. |
