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IMA Journal of Mathematical Control and Information 1996 13(4):335-358; doi:10.1093/imamci/13.4.335
© 1996 by Institute of Mathematics and its Applications
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Optimal control of serially connected structures using spatially distributed pointwise controllers

IBRAHIM S. SADEK * and VALERIE H. MELVIN **

Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals Dhahran -31261, Saudi Arabia
Department of Mathematical Sciences, University of North Carolina at Wilmington Wilmington, North Carolina 28403, USA

A mathematical theory for a class of optimal control problems for a damped distributed-parameter system represented by N serially connnected flexible structures coupled through boundary conditions is formulated. The control is to be implemented by applying a finite number of actuators to a discrete number of points within the structure. A maximum principle is proved for a system of N partial differential equations of second order in time and forth order in space, coercive in space variables, with variable coefficients. Under additional convexity assumptions on the state variables and their derivatives, the optimal control is shown to be unique. The proposed theory is demonstrated by applying it to problem of controlling the vibrations of the two strings that are coupled at the connecting point. Numerical results are given for various parameters, and the efficiency of the control is investigated.

*On leave from the Department of Mathematical Sciences, University of North Carolina, Wilmington, NC 28403.

**A portiion of this paper was taken the author's thesis, University of North Carolina at Wilmington, 1993.


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