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IMA Journal of Mathematical Control and Information 1989 6(2):199-216; doi:10.1093/imamci/6.2.199
© 1989 by Institute of Mathematics and its Applications
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A Maximum Principle for Nonconservative Self-Adjoint Systems

J. M. SLOSS1, J. C. BRUCH, JR.2 and I. S. SADEK3

1Department of Mathematics, University of California Santa Barbara, CA 93106.
2Departmental of Mechanical and Environmental Engineering, University of California Santa Barbara, CA 93106.
3Departmental of Mathematical Sciences, University of North Carolina at Wilmington Wilmington, NC 28403.

A class of control problems for a damped distributed-parameter system governed by a system of partial differential equations is considered. An existence and uniqueness theory for the solutions of the system is given along with the existence and uniqueness of the optimal control. Problems in structural mechanics are often of this type. A maximum principle is shown to be a sufficient conditon for the control to be optimal, provided that the cost function is a linear combination of convex functions of displacment, velocity, and the applied force.


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 Journal of Vibration and ControlHome page
J. M. Sloss, I. S. Sadek, J. C. Bruch Jr, and S. Adali
Optimal Control of Structural Dynamic Systems in One Space Dimension Using a Maximum Principle
Journal of Vibration and Control, February 1, 2005; 11(2): 245 - 261.
[Abstract] [PDF]


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