Optimal control system of a microbeam model with the boundary term

S. G. Körpeoğlu, K. Yildirim

In this paper, a hyperbolic system governed by boundary control, modeled as an optimal control problem is discussed. The control problem is formulated using boundary control mechanisms for the microbeam model to control undesirable free vibrations in the system. Wellposedness of the optimal solution on the control set is demonstrated and controllability of the problem is investigated. Solution procedure of the boundary control characterization of the microbeam model is examined by Maximum Principle. The necessary conditions for the optimal control problem are obtained thanks to this principle and these conditions are shown to be also sufficient conditions due to convexity. The proposed approach is based on transforming the problem into a system of partial differential equations. The obtained distributed parameter system model includes state and costate variables with terminal time initial conditions. An eigenfunction expansion method is used for the solution of the optimality conditions derived from the Maximum principle. Numerical results are obtained by using the computer codes produced in MATLAB and presented in graphical and table forms. Numerical simulation studies show the applicability and effectiveness of this approach. 

Tbilisi Mathematical Journal, Special Issue (8 - 2021), pp. 147-156