Dynamics Response Control of a Mindlin-Type Beam

Optimal boundary control for damping the vibrations in a Mindlin-type beam is considered. Wellposedness and controllability of the system are investigated. A maximum principle is introduced and optimal control function is obtained by means of maximum principle. Also, by using maximum principle, control problem is reduced to solving a system of partial differential equations including state, adjoint variables, which are subject to initial, boundary and terminal conditions. The solution of the system is obtained by using MATLAB. Numerical results are presented in table and graphical forms.

A nonlinear plate control without linearization

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.

CONTROL AND SYNCHRONIZATION OF JULIA SETS OF THE COMPLEX PERTURBED RATIONAL MAPS

The dynamical and fractal behaviors of the complex perturbed rational maps [Formula: see text] are discussed in this paper. And the optimal control function method is taken on the Julia set of this system. In this control method, infinity is regarded as a fixed point to be controlled. By substituting the driving item for an item in the optimal control function, synchronization of Julia sets of two such different systems is also studied.