Квазіоптимальне керування в задачах із мінімальноюеэнергією для параболічних рівнянь із нелокальними крайовими умовами

• Date: 2013
• Main Author: Lazarenko, I. S.
• Format: Article
• Language: Ukrainian
• Published: The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2013
• Online Access: http://journal.iasa.kpi.ua/article/view/33641
• Journal Title: System research and information technologies

One-parameter family of initial boundary-value problem for an one-dimensional heat equation with nonlocal boundary value conditions containing a real parameter was considered. Boundary conditions of this task are not strongly regular for any value of the parameter. The system of eigenfunctions of the operator of the second derivative, subjected to the boundary conditions, does not form the basis of Riesz in L2(0,1) and is not complete. Classic problem of optimal control theory with distributed parameters is considered for parabolic equation with nonlocal boundary value conditions – the control minimum energy in the special norm. In this article the initial two-dimensional problem with minimum energy is replaced by two one-dimensional problems, i.e. the quasioptimal approximate solution of the minimum energy problem is given for parabolic equation with nonlocal boundary value conditions in the distributed control case and special quality criterion. Applying the separation of variables method the solution, which is presented in the form of series by bi-orthogonal Riesz basis, which converge to continuous functions, is obtained. A comparative analysis of optimal and quasi-optimal control is carried out. Refs: 2 titles.