The problem of the optimal control of the transverse vibrations of a uniform beam with a bound on the potential energy is considered. Approximation theory is used. It is shown that the optimal control exists, and a simple method for its computation is suggested.
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Komkov, V.,The Optimal Control of a Transverse Vibration of a Beam, SIAM Journal on Control, Vol. 6, No. 3, 1968.
Yonkin, W. H.,Optimal Control of Two Distributed Parameter Systems, University of California at Los Angeles, Department of Engineering, Report No. 66-64, 1966.
Butkovskii, A. G.,The Maximum Principle for Optimum Systems with Distributed Parameters, Automation and Remote Control, Vol. 22, No. 10, 1961.
Demyanov, V. F.,Solution of Certain Extremal Problems, Automation and Remote Control, Vol. 26, No. 7, 1965.
Akhiezer, N. I., andGlazman, I. M.,Theory of Linear Operators in Hilbert Space, Frederick Ungar Publishing Company, New York, 1961.
Rosenblum, M.,Some Hilbert Space Extremal Problems, Proceedings of the American Mathematical Society, Vol. 16, No. 4, 1965.
Communicated by W. Prager
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Yavin, Y. Optimal control of the transverse vibrations of a beam with a bound on the potential energy. J Optim Theory Appl 5, 376–381 (1970). https://doi.org/10.1007/BF00928673
- Potential Energy
- Approximation Theory
- Transverse Vibration
- Uniform Beam