Inverse parametric problem for one large system of differential equations with nonlocal boundary conditions
Yegana Ramiz Ashrafova1,1
Baku, Azerbaijan
Keywords: inverse parametric problem, large system of ODEs, nonlocal conditions, convexity of functional, gradient projection method
Abstract
The problem of determining the parameters of a large system of non-autonomous differential equations consisting of subsystems connected in an arbitrary order by non-local boundary conditions is solved. Unknown parameters participate both in differential equations and in boundary conditions. The problem under study is reduced to a parametric optimal control problem with a mean-square residual criterion estimating the degree of non-fulfillment of additionally specified boundary conditions. To apply first-order numerical methods, analytical formulas for the components of the gradient of the objective functional in the space of optimized parameters are obtained. The analysis of the obtained results of computer experiments is made using a test problem as an example.
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