Optimal active pointwise control of vibrating thin plates
The optimal control of thin vibrating plates is studied in the paper. The objective of the control problem is to minimize a given performance index in a prescribed time interval, where the performance index constitutes the total energy of the structure, together with the total force used in open-loop and closed-loop control processes. The orthogonality of the self-adjoint system is used to convert the problem into the optimal control problem for lumped parameter systems. In the first part of the paper, the authors formulate the mathematical control problem, reducing it to a system of integral equations. In the following parts they establish necessary and sufficient conditions for optimality by a variational approach and an algorithm for the determination of control parameters. Finally, they illustrate the effectiveness of the proposed control considering a simply supported plate.
necessary and sufficient conditions for optimality
scientific article; zbMATH DE number 536924
scientific article