An Inverse Parametric Problem for a Large System of Differential Equations with Nonlocal Boundary Conditions

The problem of determining the parameters of a large system of non-autonomous differential equations consisting of subsystems connected in an arbitrary order by nonlocal boundary conditions is solved. The unknown parameters are in both the differential equations and the 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 an objective functional in the space of the parameters being optimized are obtained. An analysis of the results of computer experiments is made using a test problem as an example.