Affiliation:
1. Mus Alparslan University, Mus, Istanbul Turkey
2. Yildiz Technical University, Istanbul, Turkey
Abstract
Abstract
In this paper, an optimal vibration control problem for a nonlinear plate is considered. In order to obtain the optimal control function, wellposedness and controllability of the nonlinear system is investigated. The performance index functional of the system, to be minimized by minimum level of control, is chosen as the sum of the quadratic 10 functional of the displacement. The velocity of the plate and quadratic functional of the control function is added to the performance index functional as a penalty term. By using a maximum principle, the nonlinear control problem is transformed to solving a system of partial differential equations including state and adjoint variables linked by initial-boundary-terminal conditions. Hence, it is shown that optimal control of the nonlinear systems can be obtained without linearization of the nonlinear term and optimal control function can be obtained analytically for nonlinear systems without linearization.
Reference58 articles.
1. Nonlinear vibration control of a cantilever beam by a nonlinear energy sink;Mechanism and Machine Theory,2012
2. A sufficient condition in the theory of optimal control;SIAM Journal on Control,1963
3. General decay of solutions for a viscoelastic equation with Balakrishnan-Taylor damping;Taiwanese Journal of Mathematics,2015
4. On linearization in non-linear structural finite element analysis;Computers and Structures,2001
5. The exact controllability problem for the second order linear hyperbolic equation;Differential Equations and Control Processes,2010