ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Suboptimal Solution of One Singular Integral Equation with Perturbed Operator Based on Probabilistic Methods


Alexander Anatolievich Rogoza

Bauman Moscow State Technical University (BMSTU),
Kaluga, Bazenova st, 2.


In this article we constructed a new projection method for solving a class of singular Fredholm integral equations of the second kind including the disturbed integral operator, which is important for tasks of robust control in mathematical control theory. We also studied the properties of this method and designed the algorithm of its numerical implementation. In particular a modification of the Galerkin projection method for solving singular Fredholm integral equations of the second kind with perturbed operator and piecewise linear functions as the approximating space has been constructed. The resulting estimation errors of this method for equations with a singular smooth kernels and right parts belonging to weight Lebegue spaces, space of continuous functions, and Sobolev space have been obtained. The effective algorithm for numerical realization of the projection method is designed. We performed a series of computational experiments to assess the quality of the proposed projection method. In the context of this point the problem to be solved is the based on probabilistic methods synthesis of robust controller under parametric uncertainty.



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