Abstract
The optimal open-loop control of a beam subject to initial disturbances is studied by means of a maximum principle developed for hyperbolic partial differential equations in one space dimension. The cost functional representing the dynamic response of the beam is taken as quadratic in the displacement and its space and time derivatives. The objective of the control is to minimize a performance index consisting of the cost functional and a penalty term involving the control function. Application of the maximum principle leads to boundary-value problems for hyperbolic partial differential equations subject to initial and terminal conditions. The explicit solution of this system is obtained yielding the expressions for the state and optimal control functions. The behavior of the controlled and uncontrolled beam is studied numerically, and the effectiveness of the proposed control is illustrated.
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Communicated by L. Meirovitch
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Bruch, J.C., Adali, S., Sloss, J.M. et al. Maximum principle for the optimal control of a hyperbolic equation in one space dimension, part 2: Application. J Optim Theory Appl 87, 287–300 (1995). https://doi.org/10.1007/BF02192565
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DOI: https://doi.org/10.1007/BF02192565